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This has a remarkable consequence. A proper distance $L_P$ at $t=0$ will inflate to a size $10^{10^8}$cm after a time $\Delta t \sim 5\times 10^{-36}$ seconds. It is important at this point to know that the size of the observable universe today is $H_0^{-1} \sim and has not had enough 10^{28}$cm! Therefore, only a small fraction of the original Planck length comprises today's entire visible universe. Thus, homogeneity over a patch less than or of order the Planck length at the onset of inflation is all that is required to solve the horizon problem. Of course, if we wait sufficiently long we will start to see those inhomogeneities (originally sub-Planckian) that were inflated away. However, if inflation lasts long enough (typically about sixty e-folds or so) then this would not be apparent today. Similarly, any unwanted relics are diluted by the tremendous expansion; so long as the GUT phase transition happens before inflation, monopoles will have an extremely low density.

astro-ph/0401547

UNITS, UNITS

A schematic picture of the Planck satellite is shown in the left panel of Fig. REF. The satellite is composed by two main modules: the payload module (PLM) with the telescope and the instruments in the focal plane and a Service Module (SVM) that houses the compressor systems of the on-board coolers and all the instrument and satellite warm electronics and subsystems. Three thermal shields of conical shape (called V-Grooves) at $\sim$ 150 K, $\sim$ 100 K and $\sim$ 50 K thermally decouple the passively cooled payload (at $\lesssim$ 60 K) from the warm SVM (at $\sim$ 300 K). The necessary power is provided by the solar panels located on the back of the SVM which are always oriented toward the Sun during the survey.

astro-ph/0402528

MISSION

To derive the Kähler potential and superpotential of the effective $D=4$ supergravity, however, we should integrate over $y$ eqs. (REF) and (REF), and compare the result with the bosonic Lagrangian of $N=1$, $D=4$ Poincaré supergravity coupled to a chiral supermultiplet $U$ in an arbitrary frame: FORMULA where $\widehat{V}_4$ is now the scalar potential in units of the $D=4$ field-dependent Planck mass $M_4^2[r(x)]=\Phi_4[r(x)]$. If desired, the dilaton prefactor $\Phi_4$ can be eliminated by a field-dependent rescaling of the $D=4$ metric $\widehat{g}_{\mu\nu} (x)$. However, we do not need to integrate eq. (REF) exactly. Both the original $D=5$ supergravity and the effective $D=4$ supergravity are being considered for small values of their respective cosmological constants, $\lambda$ and $\lambda_4$, with respect to their respective Planck masses, $M_5$ and $M_4$. We will then consider in the following two possible expansions, either in $\lambda_4$ or in $\lambda \pi r$, and derive the effective $D=4$ supergravity in these two limits.

hep-th/0403043

UNITS, UNITS

As to theory, the critical task concerns any proposal in which Lorentz symmetry is substantially broken at the Planck scale. It is to find and implement a mechanism to give automatic local Lorentz invariance at low energies, despite a violation at the Planck scale. We assume here that the treatment involves real time, not an analytic continuation to imaginary time, as is common in treatments of quantum field theories in *flat* space-time. One mechanism is to have a custodial symmetry that is sufficient to prohibit Lorentz-violating dimension 4 terms, without itself being the full Lorentz group. But such a symmetry does not appear to be known. Corresponding issues arise in any proposal that involves modified dispersion relations, e.g., [CIT]; its proponents must show that the proposal survives experimental scrutiny after inclusion of known interactions.

gr-qc/0403053

UNITS, UNITS

The would-be logarithmic divergence ensures that there is an order unity contribution from Planck-scale momenta, with their Lorentz violation. Note that a cutoff provided by preferred frame granularity is Lorentz-violating. As a simple illustration we modify the usual free-fermion propagator $i(\gamma\cdot k + m)/(k^2-m^2+i\epsilon)$ by a factor of a smooth function $f(|\bm{\mathbf{k}}|/\Lambda)$ that obeys $f(0)=1$ and $f(\infty)=0$, with a cutoff parameter $\Lambda$. Then FORMULA Thus the corresponding Lorentz violation is of order the square of the coupling independently of $\Lambda$. The exact value depends on the details of the Planck-scale free propagator, of course. The main point, however, is that the power counting that gives the would-be logarithmic divergence follows from standard arguments in the theory of renormalization, and that it applies to self-energy graphs for all fields. So the above integral gives a reasonable estimate of the size of the Lorentz violation, in the absence of some special cancellation. Typical measured standard-model couplings then give our percent estimate.

gr-qc/0403053

UNITS, UNITS

Let us list some of the issues we shall have to face to construct a fully acceptable supersymmetric theory. $\Box$ Weak-scale supersymmetry (i.e., superpartners on the electroweak scale) protects the Higgs-boson mass and keeps it naturally below $1\hbox{ TeV}$, but does not explain the why the weak scale itself is so much smaller than the Planck scale. This is called the $\mu$ problem.[^22] $\Box$ Global supersymmetry must deal with the threat of flavor-changing neutral currents. $\Box$ In parallel with the standard model, supersymmetric models make reasonably clear predictions for the masses of gauge bosons and gauge fermions (gauginos), but are more equivocal about the masses of squarks and sleptons. $\Box$ Not only is supersymmetry a hidden symmetry in the technical sense, it seems to be a very well hidden symmetry, in that we have no direct experimental evidence in its favor. A certain number of contortions are required to accommodate a (lightest) Higgs-boson mass above $115\hbox{ GeV}$. $\Box$ We might have hoped that supersymmetry would relate particles to forces---quarks and leptons to gauge bosons---but instead it doubled the spectrum. $\Box$ Dangerous baryon- and lepton-number--violating interactions arise naturally from a supersymmetric Lagrangian, but we have only learned to banish them by decree. $\Box$ Supersymmetry introduces new sources of $\mathcal{CP}$ violation that are potentially too large. $\Box$ We haven't yet found a convincing and viable picture of the TeV superworld.

hep-ph/0404228

UNITS

We advocate the idea that proton decay may probe physics at the Planck scale instead of the GUT scale. This is possible because supersymmetric theories have dimension-5 operators that can induce proton decay at dangerous rates, even with R-parity conservation. These operators are expected to be suppressed by the same physics that explains the fermion masses and mixings. We present a thorough analysis of nucleon partial lifetimes in models with a string-inspired anomalous U(1)_X family symmetry which is responsible for the fermionic mass spectrum as well as forbidding R-parity violating interactions. Protons and neutrons can decay via R-parity conserving non-renormalizable superpotential terms that are suppressed by the Planck scale and powers of the Cabibbo angle. Many of the models naturally lead to nucleon decay near present limits without any reference to grand unification.

hep-ph/0404260

UNITS, UNITS

We thank members of the SDSS collaboration who made the SDSS project a success and who made the EDR spectra available. We acknowledge support from NASA-STScI, NASA-LTSA, and NSF. HST-UV spectroscopy made the $N_{HI}$ determinations possible, while follow-up metal abundance measurements (MMT) and imaging (IRTF) were among the aims of our LTSA and NSF programs. Funding for creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, Participating Institutions, NASA, NSF, DOE, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is www.sdss.org. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions: University of Chicago, Fermilab, Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and University of Washington.

astro-ph/0404609

MPS, MPS, MPS

This work was supported by NASA through grants AISR NAG5-11996, ATP NAG5-12101, and by NSF through grants AST02-06243 and ITR 1120201-128440. We thank Pablo Fosalba for stimulating discussions. The simulations in this paper were carried out by the Virgo Supercomputing Consortium using computers based at Computing Centre of the Max-Planck Society in Garching and at the Edinburgh Parallel Computing Centre[^3].

astro-ph/0405590

MPS

In this work we investigate the yield, completeness and purity of such a Planck SZ survey for a range of cosmological models and estimate the cosmological significance of such the resulting cluster catalogue. Furthermore, based on our simulations and cluster selection we estimate a Planck cluster survey flux limit and provide tabulated cluster number counts for each model. In contrast to previous work (Kay, Liddle, & Thomas 2001; Diego et al.,2002; White 2003), which studied the cluster sample either on sky patches or neglected contaminants, we perform full-sky simulations including all known significant extragalactic and Galactic contaminating components. Our modelling of the SZ effect as well as contaminants aims to be as realistic as current observational constraints allow. To recover the SZ signal of single clusters we make use of the harmonic-space maximum entropy method introduced by Stolyarov et al.,(2002) in combination with a cluster finding algorithm based on peak detection, thresholding and flux integration. As Stolyarov et al.,(2002) show the HSMEM is a novel method to separate various CMB components. The cluster finding algorithm is shown in this paper to be able to obtain reliable flux as well as radius estimates for a cluster sample above the estimated survey flux limit. Note that besides the assumed cosmological model the cluster recovery algorithm has major implications on the number of clusters obtained by the Planck survey and thus its impact on constraining cosmological parameters. It is therefore important to explore, improve and combine techniques in order to find the optimal method and maximise the survey yield. Since our modelling exhibits a high degree of realism, the given estimate of the cluster number which can be obtained by the Planck survey using our algorithm is reliable. Even though further improvement is possible, the presented combined cluster detection method -- as we show below -- provides already the quality to draw interesting cosmological conclusions from the obtained cluster sample.

astro-ph/0406190

MISSION, MISSION, MISSION, MISSION

As a test of the previous ideas, we now apply both the standard and the unbiased matched multifilters to simulated Planck observations in order to estimate the thermal and kinematic SZ of test clusters placed on the simulations. Our goal is just to show by an example how the biases described in section [3] appear and how the unbiased matched multifilters are able to cancel it. Therefore, to keep the example simple and clear we will restrict ourselves to ideal conditions in which the spatial profile of the clusters is perfectly known from the beginning. A full study of the performance of the filters in the Planck case, including uncertainties in the cluster profile, asymmetric profiles and realistic cluster distributions is out of the scope of this work and will be addressed in the future.

astro-ph/0406226

MISSION, MISSION

[CIT] have estimated the number counts of unresolved infra-red galaxies at Planckfrequencies, which was used by [CIT] in order to estimate the level of fluctuation in the Planck-beam. In the easiest case, the sources are uncorrelated and the fluctuations obey Poissonian statistics, but the inclusion of correlations is expected to boost the fluctuations by a factor of $\sim1.7$ [CIT]. According to [CIT], the resulting fluctuations vary between a few $10^2 \mathrm{Jy}/\mathrm{sr}$ and $10^5 \mathrm{Jy}/\mathrm{sr}$, depending on observing channel. A proper modeling would involve a biasing scheme for populating halos, the knowledge of the star formation history and template spectra in order to determine the K-corrections.

astro-ph/0407090

MISSION, MISSION

The net left-handed neutrino to entropy ratio $N_L$ in a homogeneous and isotropic universe evolves according to the kinetic equation [CIT] FORMULA where $M_p$ is the Planck mass, $z$ is proportional to the cosmological redshift via the relation $T = m_\phi/z$, where $T$ is the temperature of radiation, $Y_X$ denotes the ratio between the number density of $X$ particles and the entropy density (and the superscript *eq* indicates the value of the corresponding quantity in thermal equilibrium), and $\gamma$ is proportional to the cross section (see below). Note that the effects of the Hubble expansion cancel out if we track the ratio of particle number densities. Note also that we are neglecting the production of neutrinos by back-reaction effects.

hep-ph/0407090

UNITS

Here we emphasize that, for the central values of the experimental parameters: FORMULA and identifying the position of the second minimum with the fundamental scale, $\mu_{fundamental} = \phi_{min2}$, we predict the fundamental scale to be close to the Planck scale FORMULA which coincides with the result of Refs. [1,28,31,32]. We note that for the value $h(M_t)=0.98$, and for the values $h(M_t)=0.95$ and $\alpha_3(M_Z)= 0.119$, the second minimum of the effective potential turns out to be beyond the Planck scale ($M_{Planck}\sim 10^{19}$ GeV). On the other hand, for the extreme values $\alpha_s\approx 0.115$ and $h(M_t)\approx 0.92$, the fundamental scale becomes $\mu_{fundamental}\approx 10^{16}$ GeV, corresponding to the string scale.

hep-ph/0407102

UNITS, UNITS, UNITS

If one assumes $y_s \sim O(1)$, then the acceptable range for $\epsilon_s$ represents large energies: so large that at a redshift of $10^{11}$ the typical particle's energy would be above the Planck mass. One way to arrange this is to suppose that the screening particles arise from decays of very heavy particles which have long but finite lifetime: for masses on the order of $M_{\rm Pl}$, the lifetime should be on the order of a month. An alternative --- making $\epsilon \sim 1,{\rm eV}$ --- requires $n_s\sim 0.1$ cm$^{-3}$ and $y_s\sim 10^{-20}$, an exceedingly small value.

hep-th/0407097

UNITS

On one hand, broad quantum theoretical considerations suggest that space-time may be discrete at the Planck scale, and some specific quantum gravity models indeed have been shown to incorporate this feature when examined in detail. If this is so, not only does it remove the real number line as a *physics* construct, but it *inter alia* has the potential to remove the ultraviolet divergences that otherwise plague field theory -- a major bonus.

astro-ph/0407329

UNITS

Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/.

astro-ph/0407372

MPS

We perform a Fisher matrix analysis to quantify cosmological constraints obtainable from a 2-dimensional Sunyaev-Zel'dovich (SZ) cluster catalog using the counts and the angular correlation function. Three kinds of SZ survey are considered: the almost all-sky Planck survey and two deeper ground-based surveys, one with 10% sky coverage, the other one with a coverage of 250 square degrees. With the counts and angular function, and adding the constraint from the local X-ray cluster temperature function, joint 10% to 30% errors (1 sigma) are achievable on the cosmological parameter pair (sigma_8, Omega_m) in the flat concordance model. Constraints from a 2D distribution remain relatively robust to uncertainties in possible cluster gas evolution for the case of Planck. Alternatively, we examine constraints on cluster gas physics when assuming priors on the cosmological parameters (e.g., from cosmic microwave background anisotropies and SNIa data), finding a poor ability to constrain gas evolution with the 2-dimensional catalog. From just the SZ counts and angular correlation function we obtain, however, a constraint on the product between the present-day cluster gas mass fraction and the normalization of the mass-temperature relation, T_*, with a precision of 15%. This is particularly interesting because it would be based on a very large catalog and is independent of any X-ray data.

astro-ph/0407436

MISSION, MISSION

A large number of non-supersymmetric three family Standard-like models have been constructed, based on the original work [CIT] (for a partial list, see [CIT] - [CIT]). These models satisfy the Ramond-Ramond (RR) tadpole cancellation conditions; however, since the models are non-supersymmetric, there are uncancelled Neveu-Schwarz-Neveu-Schwarz (NS-NS) tadpoles. In addition, in these toroidal/orbifold constructions the string scale is close to the Planck scale, thus these models typically suffer from the large Planck scale corrections at the loop level.

hep-th/0407178

UNITS, UNITS

We establish Einstein-Hilbert gravity couplings in the effective action for Intersecting Brane Worlds. The four-dimensional induced Planck mass is determined by calculating graviton scattering amplitudes at one-loop in the string perturbation expansion. We derive a general formula linking the induced Planck mass for N=1 supersymmetric backgrounds directly to the string partition function. We carry out the computation explicitly for simple examples, obtaining analytic expressions.

hep-th/0408105

UNITS, UNITS

We have assumed that self-gravity of the scalar field is negligible, and the background geometry is given by other matter fields. In this case, the background is $AdS_4/AdS_5$ and it is generated by $\Lambda_5$ and $\Lambda_4$.[^3] Meanwhile, as we observed above, these quantities are related with the parameters of the scalar field by $\Lambda_5 = -2\lambda\eta^2$ and $\Lambda_4= -{3\over 2}\overline{\lambda}\overline{\eta}^2$. Then one may wonder how consistently we can keep the parameters $\Lambda_5$ and $\Lambda_4$ as the source of curvature, while we are ignoring the corresponding scalar-field parameters. The clue is that the scalar-field contribution to the curvature (to the energy-momentum tensor, in other words) is suppressed by the Planck-mass scale, so the condition, $\eta \ll \mbox{Planck-sacle}$, is sufficient to ignore its effect, and the same reasoning is true for $\Lambda_4$ and the 4D parameters.

hep-th/0408219

UNITS, UNITS

In the following, we would like to focus on an alternative solution to the $S$ problem which has additional beneficial side-effects. It has been known for a long time in Randall-Sundrum (RS) models with a Higgs that the effective $S$ parameter is large and negative [CIT] if the fermions are localized on the TeV brane as originally proposed [CIT]. When the fermions are localized on the Planck brane the contribution to $S$ is positive, and so for some intermediate localization the $S$ parameter vanishes, as first pointed out for RS models by Agashe et al. [CIT]. The reason for this is fairly simple. Since the $W$ and $Z$ wavefunctions are approximately flat, and the gauge KK mode wavefunctions are orthogonal to them, when the fermion wavefunctions are also approximately flat the overlap of a gauge KK mode with two fermions will approximately vanish. Since it is the coupling of the gauge KK modes to the fermions that induces a shift in the $S$ parameter, for approximately flat fermion wavefunctions the $S$ parameter must be small. Note that not only does reducing the coupling to gauge KK modes reduce the $S$ parameter, it also weakens the experimental constraints on the existence of light KK modes. This case of delocalized bulk fermions is not covered by the no--go theorem of [CIT], since there it was assumed that the fermions are localized on the Planck brane.

hep-ph/0409126

BRANE, BRANE

**The flatness problem.**\ The present contribution of the spatial curvature to the expansion is given by $\Omega_k = \rho_0(t_0)/\rho_c(t_0) - 1$. But this contribution has evolved with time. From the Friedmann law, it is straightforward to see that FORMULA During the domination of radiation (resp. matter), the factor $\dot{a}^{-2}$ grows like $t$ (resp. $t^{2/3}$). Therefore, a spatially flat Universe is unstable: if initially, $k$ is *exactly* zero, $\Omega_k$ will remain zero; but if it is only *close* to zero, $\Omega_k$ will increase with time! In order to have no significant curvature--domination today ($| \Omega_k(t_0)| \leq 0.1$), we find that near the Planck time, the curvature was incredibly small, roughly $| \Omega_k(t) | \leq 10^{-60}$\... The standard cosmological model provides no explanation for obtaining such a small number in the early Universe: the fact that the Universe is spatially flat -- even approximately -- appears like the most unnatural possibility! This is called the "flatness problem".

astro-ph/0409426

UNITS

To summarize, in this paper we have proposed a new method for resolving the Brustein-Steinhardt moduli overshoot problem [CIT] in string cosmology. We find that a gas of primordial black holes in the early universe, where the mass of black holes depends on the modulus, can provide a transient attractor for the modulus. When such black holes are produced they will trap the modulus temporarily, and keep it within the basin of attraction of the minima of the nonperturbative modulus potential $V$. As time goes on, the black hole density will redshift away, placing the modulus gently on the potential slope. Following this the modulus will slowly settle into the minimum, where it can drive inflation. A key ingredient of our mechanism is that the universe should be created near the Planck scale, so that the heavy states are produced initially with non-negligible number density. Such an approach has been proposed recently in [CIT], and our mechanism may be a natural ingredient for helping the modulus stop in the inflationary valleys in the landscape. After inflation has begun, the density of black holes redshifts away to exponentially small numbers, just like the density of heavy monopoles in the early models of inflation. These black holes are pushed outside of the current horizon. We stress that our mechanism relies mainly on the presence of heavy states in the theory whose mass depends on the modulus. It may be possible to realize a similar mechanism in other regimes, using different massive states. It would be interesting to consider such mechanisms in other cosmological models, where for example the initial density of massive states could be small, but the minima of the potential lie at very large *vevs*, such as in the theories with low scale unification.

hep-th/0409226

UNITS

Concerning the energy density, one has now to integrate on the plane orthogonal to the string. This gives an extra factor $\sqrt{\mu}$ so that the energy density per unit length reads FORMULA where $\kappa(\alpha)$ is a dimensionless function. We have put a cut-off at a radius where the field attains $95$ percent of its asymptotic value. If gauge symmetry is broken at the GUT scale while Lorentz symmetry breaking takes place at the Planck scale, this number is of order of a few hundreds. Basically, the difference with the usual case is not as important as for domain walls. This means such defects will behave as the ones of the orthodox theory.

hep-ph/0409285

UNITS

Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington.

astro-ph/0410011

MPS, MPS, MPS

The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington.

astro-ph/0410054

MPS, MPS

't Hooft [CIT] has argued that one can describe the scattering of two massless particles at energies close to (but under) the Planck scale, ($m_{1,2}\ll M_P, Gs\sim 1$, yet $Gs<1$) as follows. Particle two creates a massless shockwave of momentum $p_{\mu}^{(2)}$ and particle one follows a massless geodesic in that metric. He has shown that the S matrix corresponds to a gravitational Rutherford scattering (single graviton being exchanged).

hep-th/0410173

UNITS

If the physics responsible for Dark Matter in the Universe is accessible at the next generation of colliders, a major goal of these colliders will be to predict the Dark Matter density at the same level of accuracy as it can be measured experimentally. The WMAP results [CIT] have led to a measurement of the Dark Matter content at the 10% level. This precision will further improve with the Planck satellite mission, scheduled for 2007, which aims at a 2% measurement [CIT].

hep-ph/0410364

MISSION

If the model has supersymmetry in the bulk, the Higgs can be localized near the Planck brane since SUSY protects its mass. Thus, SM fermions can also be localized very close to the Planck brane ($c \gg 1/2$) so that higher-dimensional baryon-number violating operators are suppressed by Planckian scales. There is no longer a need to impose baryon-number symmetry. There will be no stable KK state. However, there is still a possibility to account for dark matter if the lightest supersymmetric particle is stable via R-parity conservation. Of course, one loses the explanation of the hierarchy of fermion masses which is one of the appealing features of non-SUSY RS. One has to introduce small Yukawa couplings by hand. If one was to address the issue of Yukawa hierarchy by delocalizing the fermions ($c \stackrel{<}{\sim} 1/2$), then a baryon number symmetry would be required. In addition, the Higgs would also have to be in the bulk and should be given almost a flat profile. Otherwise, MSSM unification will be spoiled by the modification of the contribution of the Higgs to the running. For recent works on warped supersymmetric $SO(10)$, see references [CIT].

hep-ph/0411254

BRANE, BRANE

The remaining issue is how to eliminate the linear term in the expansion (REF) when one expands around a Minkowski background. We will show that this can be done by the bi--gravity theory that corresponds to chiral gravity, containing two vielbeins $e_{\pm,\gm}{}^a,$ and metrics $g_{\pm,\gm\gn}$. This theory consists of a copy of the standard action (REF) for each sector with their own Planck mass and cosmological constant. In addition, there is an interaction that couples the two vielbeins in a covariant way via a term which, though similar to, cannot be represented as a determinant. The Minkowski background is not introduced by hand as in [CIT], but it arises dynamically by a subtle balance between the two gravitational sectors, given by a single fine--tuning of cosmological constant--like parameters. This constitutes the same amount of fine--tuning as for the cosmological constant in the standard theory of gravity.

hep-th/0411184

UNITS

The Dirac-Born-Infeld type effective 4-dimensional action for our system is described by [CIT] FORMULA where $M_p$ is the reduced Planck mass, $R$ is the scalar curvature and $V(\phi)$ is the potential of the tachyon field $\phi$. The above tachyon DBI action is believed to describe the physics of tachyon condensation for all values of $\phi$ as long as string coupling and the second derivative of $\phi$ are small.

hep-th/0411192

UNITS

We consider a phenomenologically viable SO(10) grand unification model of the unification scale $M_G$ around $10^{16} $ GeV which reproduces the MSSM at low energy and allows perturbative calculations up to the Planck scale $M_P$ or the string scale $M_{st}$. Both requirements strongly restrict a choice of Higgs representations in a model. We propose a simple SO(10) model with a set of Higgs representations $\{2 \times {\bf 10} + {\bf \bar{16}} + {\bf 16} + {\bf 45} \}$ and show its phenomenological viability. This model can indeed reproduce the low-energy experimental data relating the charged fermion masses and mixings. Neutrino oscillation data can be consistently incorporated in the model, leading to the right-handed neutrino mass scale $M_R \simeq M_G^2/M_P$. Furthermore, there exists a parameter region which results the proton life time consistent with the experimental results.

hep-ph/0412011

UNITS

Above the scale of the pseudo-Goldstone fields, but below the GUT breaking scale, the one-loop beta function coefficients of the SM couplings are shifted by an amount FORMULA In a weakly-coupled product gauge theory, taking the pseudo-Goldstone fields to have roughly the same mass scale $v^2/M \sim 10^{-2} v$, these shifts in the beta functions induce a very significant threshold correction to gauge coupling unification.[^3] This would-be disaster is averted due to the large anomalous dimensions of the strongly-coupled Sp(4) that provide a large enhancement to the mass parameters of the model, as we found in Eq. (REF). Let us consider the maximum enhancement, when the Sp(4) gauge interaction is conformal up to the Planck scale. Starting with dimension-5 operators that are $1/M_{\rm Pl}$ suppressed, the conformal enhancement causes $1/M_{\rm Pl}(M_{\rm GUT}/M_{\rm Pl})^{-1} \rightarrow 1/M_{\rm GUT}$, and therefore the masses of the pseudo-Goldstone fields are increased up to roughly the GUT scale. Obviously no large threshold correction from these fields is expected. This required assuming the Sp(4) group was conformal up to the Planck scale, which is consistent with maximizing the enhancement of the top Yukawa. We sketch the spectrum of this theory in a purely weakly-coupled case and in the strongly-coupled, conformal up to the Planck scale case in Fig. REF.

hep-ph/0501047

UNITS, UNITS, UNITS

Having determined the velocity cross-correlation for $\kappa_{XY}$ in the previous section, one can now proceed and evaluate the corresponding Fokker-Planck coefficient $D_{XY}$. Upon substituting equation (REF) into (REF), one obtains FORMULA with the auxiliary functions FORMULA The integration with respect to $\xi$ leads to the complex resonance function, FORMULA which describes interactions of the particles with the plasma wave turbulence. The calculations for the Fokker-Planck coefficient $D_{YX}$ are analogous to the calculations for $D_{XY}$ and result in FORMULA with the corresponding auxiliary functions FORMULA Equations (REF) and (REF), one of the main results of this paper and presented here in this general form for the first time, allow one to calculate QLT drift coefficients for arbitrary turbulence geometry, where the turbulence consists of transverse wave modes with dispersion relations depending arbitrarily on wavevector.

astro-ph/0501243

FOKKER, FOKKER

But we are almost there. As I said before, the entanglement entropy is proportional to the surface area, with a proportionality constant $\eta$ that seems quite plausibly universal, since all local Rindler horizons are equivalent. Thus it only remains to explain why $\eta=1/4\ell_{\rm Planck}^2$. One might just refer to the classical geometric derivation of the first law in general relativity, and "read off\" this relation by comparison with the statistical first law, as did Zurek and Thorne. But I think this would not be fulfilling your call for a truly statistical derivation of the first law for black holes. To establish this link between $\eta$ and the Planck length, I will invoke my derivation of the Einstein equation as a thermodynamic equation of state[^10]. In that paper, I showed that the validity of the first law for an entropy of the form $S=\eta A$ at all local Rindler horizons implies that the Einstein equation *must* hold, with Newton's constant, or rather $\hbar G = \ell_{\rm Planck}^2$, equal to $1/4\eta$.

hep-th/0501103

UNITS, UNITS, UNITS

The mediators $\Phi$ and ${\bar \Phi}$, which are massive, may be integrated out. [^3] Owing to their SM and SUSY-breaking gauge interactions, they induce SUSY-breaking soft masses of the SM superpartners. When the $Sp(2)$ gauge interaction becomes strong around the mass scale $m$ with the mediators decoupling [CIT], we obtain FORMULA and FORMULA where the overall factor $4$ takes into account the mediator number of SM flavors and naive dimensional counting [CIT] is applied. Here, $\alpha$ corresponds to the relevant SM gauge couplings to the sfermions and the gauginos. On the other hand, the gravitino mass is obtained as FORMULA where $M_{Pl}$ denotes the reduced Planck scale: $M_{Pl} \simeq 2.4 \times 10^{18},{\rm GeV}$.

hep-ph/0501254

UNITS

The localization of gauge fields on D-branes provides a concrete stringy realization of the brane world scenario in which the Standard Model fields are confined on the branes whereas gravity propagates in the bulk. As a result, the four-dimensional gauge couplings are determined by the volume of the cycles that the D-branes wrap around, while the gravitational coupling depends on the total internal volume. This opens up the possibility of lowering the string scale. More specifically, by dimensional reduction to four dimensions[^1]: FORMULA where $V_{p-3}$ is the volume of the $p-3$ cycle wrapped by a Dp-brane (which is in general different for different branes) and $V_6$ is the total internal volume. In this article, we will focus on models with intersecting D6-branes so that FORMULA The experimental bounds on the masses of Kaluza-Klein replicas of the Standard Model gauge bosons imply that the volume of three-cycles cannot be larger than the inverse TeV scale generically. For a general internal space (such as a Calabi-Yau manifold), the volumes of the three-cycles are not directly constrained by the scale of the total internal volume, and can be much smaller than $\sqrt{V_6}$. In this case, a large Planck mass can be generated from a large total internal volume. This is precisely the idea of the large extra dimension scenario.

hep-th/0502005

UNITS

Equation (REF) has another surprising property. Indeed, an important simplification takes place if we suppose that FORMULA *ie* that the codimension of the brane is larger than its intrinsic dimension. In that case, using Gauss's equation, we have FORMULA and the matching conditions (REF) are simply the induced Lovelock equations on the brane with no extrinsic curvature terms! Therefore, the action for a distributional 3-brane embedded in $D=8,10,... 2d$ dimensions is exactly the Einstein-Hilbert plus cosmological constant action FORMULA with Planck scale set by FORMULA For a 4 or 5-brane, we will have in addition the Gauss-Bonnet term etc. In other words, if the codimension verifies (REF), all the extrinsic curvature corrections drop out and there is a complete Lovelock reduction from the bulk to the brane. All the degrees of freedom originating from the bulk at zero thickness level are exactly integrated out giving the most general classical equations of motion for the brane. As a consequence we have in particular energy-conservation on the brane (see also [CIT]).

hep-th/0502171

UNITS

*Introduction*: Pointers from diverse areas in high energy physics indicate that one has to look beyond a *local* quantum field theoretic description in the formulation of quantum gravity. Very general considerations in black hole physics lead to the notion of a fuzzy or Non-Commutative (NC) spacetime which can avoid the paradoxes one faces in trying to localize a spacetime point within the Planck length [CIT]. This is also corroborated in the modified Heisenberg uncertainty principle that is obtained in string scattering results. The recent excitement in NC spacetime physics is generated from the seminal work of Seiberg and Witten [CIT] who explicitely demonstrated the emergence of NC manifold in certain low energy limit of open strings moving in the background of a two form gauge field. In this instance, the NC spacetime is expressed by the Poisson bracket algebra (to be interpreted as commutators in the quantum analogue), FORMULA where $\theta ^{\mu\nu}$ is a $c$-number constant. Up till now this form of NC extension has been the popular one. However, notice that Lorentz invarianc is manifestly violated in quantum field theories built on this spacetime. Somehow, it appears that the very idea of formulating field theories in this sort of spacetime, consistent with quantum gravity, gets defeated by this pathology!

hep-th/0502192

UNITS

Provided that the dynamical friction time is significantly longer than the orbital timescale ($\sim \tau_D$), the Fokker-Planck equation can be averaged over particle trajectories, and expressed in terms of the integrals of motion in the smoothed out potential. The orbit averaged Fokker-Planck equation and its properties have been elucidated in detail by Henon (1961), and discussed in Binney & Tremaine (1987) and Spitzer (1987). Other works include that of Kohn (1979, 1980) and Merritt (1983), the latter being particularly relevant to the situation at hand here.

astro-ph/0502472

FOKKER, FOKKER

Cosmological perturbation theory expands the exact equations in powers of the perturbations and keeps terms only up to the $n$th order. Since the observed curvature perturbation is of order $10^{-5}$, one might think that first-order perturbation theory will be adequate for all comparisons with observation. That may not be the case however, because the PLANCK satellite [CIT] and its successors may be sensitive to non-gaussianity of the curvature perturbation at the level of second-order perturbation theory [CIT].

astro-ph/0502578

MISSION

As Galactic foregrounds we have included simulations of synchrotron, thermal dust and free-free emissions, which have been simulated at the frequency of 353 GHz. The different emissions have been simulated assuming that the frequency dependence is spatially constant. The synchrotron template at this frequency has been obtained using the model of [CIT]. To simulate this component at the different Planck frequencies we have rescaled this template using a power law $I_\nu \propto \nu^{-\alpha_{\rm syn}}$ with $\alpha_{\rm syn}=-0.9$. The thermal dust template has been generated using the model of [- [CIT]]. For simplicity, we have then assumed a simple grey body law with parameters $T_d=18 K$ and $\beta_{\rm emis}=2.0$ to simulate the contribution of this component at the Planck frequency maps. Finally, the free-free has been simulated using the correlation with dust emission in the way proposed by [CIT]. The template has then been extrapolated to the considered frequencies using a power law with $\alpha_{\rm ff}=-0.16$. In order to test the robustness of the results we have tested the methods using four different Galactic regions of the sky with $|b| > 20^\circ$. The dispersion of the three Galactic components at the frequency of 300 GHz for the four considered regions is given in Table REF. Two of the regions (1 and 3) are within the brightest 2 per cent of the sky in dust emission, whereas the other two regions (2 and 4) correspond to more typical regions with lower Galactic dust emission. Fig. REF shows the synchrotron, free-free and dust components for one of the considered regions of the sky.

astro-ph/0503039

MISSION, MISSION

When the center-of-mass (CM) energy of a collision exceeds the Planck scale, which is of the order of TeV here, the cross section is dominated by a black hole production [CIT], which is predicted to be of the order of the geometrical one [CIT], increasing with the CM energy. In this trans-Planckian energy domain, the larger the CM energy is, the larger the mass of the resulting black hole is, and hence the better its decay is treated semi-classically via Hawking radiation [CIT]. Main purpose of this series of work is to discuss such decay signals in the hope that these will serve as the basis to pursue stringy or quantum gravitational corrections to them.

hep-th/0503052

UNITS

We calculate the bolometric temperature by the prescription given in [CIT], FORMULA where $\zeta(m)$ is the Riemann zeta function of argument $m$, $h$ is Planck's constant, $k$ is Boltzmann's constant, and the mean frequency, $\bar{\nu}$, is the ratio of the first and zeroth frequency moments: FORMULA

astro-ph/0503456

CONSTANT

The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington.

astro-ph/0503601

MPS, MPS

We suppose that the disk is heated only by the stellar radiation and we call $\alpha$ the incident angle beetwen the radiation and the disk surface. The incident beam is absorbed exponentially as it penetrates the dusts and if $\tau_d$ is the optical depth for the emitted radiation, the dust temperature $T(\tau_d)$ is given by the relation (C92) FORMULA where $\mu = \sin\alpha$ and $\epsilon$ is an efficiency factor that characterizes the grain opacity, defined as the ratio of the Planck mean opacity of the grains at the local temperature $T(\tau_d)$ and at the stellar temperature $T_\star$, respectively. In writing the previous equation we have assumed that the scattering of the dust grain is negligible and that the Planck mean opacity is defined as: FORMULA Following Muzerolle et al. ([CIT]), the continuum emission of the disk is assumed to originate from the surface characterized by the optical depth $\tau_d=2/3$.

astro-ph/0503635

OPACITY, OPACITY

v\) *'Recovery' of the 'apparently lost' information:* Since the black hole evaporates only in a finite amount of time, the point at which the black hole shrinks to zero (or Planck) size is *not* $i^+$ and the space-time diagram looks like figure REF rather than figure REF. Now, $i^+$ lies to the 'future' of the 'deep Planck' region and there are observers lying entirely in the asymptotic region going from $i^-$ to $i^+$ (represented by the dotted continuation of the solid line in figure REF). This family of observers will recover the apparently lost correlations. Note that these observers always remain in the asymptotic region where there is a classical metric to an excellent approximation; they never go near the deep Planck region. The total quantum state on ${\mathscr{I}}^+$ will be pure and will have the complete information about the initial state on ${\mathscr{I}^-}$. It looked approximately thermal at early times, i.e., to observers represented by the solid line, only because they ignore a part of space-time. The situation has some similarity with the EPR experiment in which the two subsystems are first widely separated and then brought together (see also [CIT]).

gr-qc/0504029

UNITS, UNITS, UNITS

A possible extension of the model is considering a bulk Higgs instead of brane localized Higgses, in order to give an explicit mass to the top-pion in analogy with the QCD case studied in [CIT]. We imagine that we have a single Higgs stretching over the two bulks. The generic profile for the Higgs VEV along the AdS space will be [CIT] : FORMULA where the exponents $\Delta_{\pm} = 2 \pm \sqrt{4+M^2_{bulk} R^2}$ are determined by the bulk mass of the scalar. The bulk mass controls the localization of the VEV near the two IR branes, and in the large mass limit we recover the two Higgses case: all the resonances become very heavy and decouple, except for one triplet that becomes light and corresponds to the top-pion. Indeed, its mass will be proportional to the value of the VEV on the Planck brane, that is breaking the two global symmetries explicitly. In the CFT picture, the bulk VEV is an operator that connects the two CFTs and gives a tree level mass to the top-pion. However, the bulk tail will also contribute to the $W$mass: we numerically checked in a simple case that in any interesting limit, when the bulk Higgs does not contribute to unitarity, the tree level mass is negligibly small. Nevertheless, this picture solves the photon mass issue: indeed we have only one Higgs. In other words, the connection on the Planck brane is forcing the two VEVs on the boundaries to be aligned.

hep-ph/0505001

BRANE, BRANE

The stellar photosphere and circumstellar dust shell are usually treated as completely separate regimes, as justified by the following simple argument. As a first approximation, one might consider that dust grains in an optically thin envelope are grey or nearly so, and exist in thermal equilibrium with the radiation field. Furthermore, we can approximate the star as having a small angular extent, so that the mean intensity, $J(\lambda)$ at the dust condensation radius $R_c$ is equal to the luminosity of the central star $L(\lambda)$ divided by $16\pi^2R_c^2$. In this case Equation REF gives an estimate of the dust formation radius (here $R_s$ the radius of the central star, $T_s$ the effective temperature of the star and $T_c$ the dust condensation temperature). Given an effective temperature of 3000,K and a dust condensation temperature of 1100,K, the dust formation radius is 3.7 stellar radii, which means that the physics of the photosphere and the circumstellar environment could be considered well-separated. Where dust is considered to be non-grey, but the dust formation radius still lies well-outside the photosphere, conservation of energy and radiative equilibrium gives Equation REF, where $Q$ is the absorption coefficient of the dust and $B$ is the Planck function in the form which gives power per unit area per steradian per unit wavelength. Further discussion of these kinds of approximations can be found in [CIT].

astro-ph/0505112

LAW

Here we propose that the log-area leading correction might admit a simple description, just like the argument presented by Bekenstein in Ref. [CIT] gives a simple description of the dominant linear-in-$A$ contribution. Our simple description will also explain why the coefficient $\rho$ of the log-area term takes different values in different quantum-gravity theories. And we stress that the availability of results on the log-area correction might provide motivation for reversing the Bekenstein argument: the knowledge of the black-hole entropy-area law up to the leading log correction can be used to establish the Planck-scale modifications of the ingredients of the Bekenstein analysis.

hep-th/0506182

UNITS

The plot in figure REF has been made for all first-order slow-roll parameters equal to $0.05$, except ${\tilde\eta}^\perp=0.2$ and $\chi= 0.01$, and all second-order slow-roll parameters equal to $0.003$. We see that there is a dependence on the relative magnitude of the momenta. Though not visible in the figure, this dependence is strongest very near the vertices of the triangle, which is the limit of (REF), where for this specific example the value $9.4$ is reached. Of course logarithmically the region near the vertices covers an infinite range of magnitudes in momentum ratios. (The fact that the result is largest in the squeezed momentum limit agrees with the findings of [CIT].) The value at the centre is $3.7$. Assuming that a naive extrapolation of this result at the end of inflation to the time of recombination is allowed, so that the quantity plotted is indeed comparable to the observable $f_\mathrm{NL}$, we see that this model does produce sufficient non-Gaussianity to be detectable with the Planck satellite. To compare this plot with the one for the single-field case in [CIT] one should keep in mind that there an additional factor of $(2{\tilde\epsilon}+{\tilde\eta}^\parallel)$ was left out (and there are some differences in the momentum normalisation factor, but that does not change the magnitude much), so that the multiple-field result is indeed about two orders of magnitude larger.

astro-ph/0506704

MISSION

Here we show that within the braneworld picture, it is possible that the 4-dimensional Planck scale is not fundamental but only an effective scale which can become much larger than the fundamental Planck scale $M_P$ if the extra-dimensions are much large than $M_P^{-1}$. Our argument goes back to Arkani-Hamed, Dimopoulos and Dvali (1998) [CIT].

hep-th/0507006

UNITS, UNITS

The noise is assumed to be Gaussian and uncorrelated, but non-uniform according to the scanning strategy of each detector. For *WMAP*, we assume a six-year mission, and rescale the published first-year sensitivity levels by $1/\sqrt{6}$. For Planck, we adopt the requirement levels, which are a factor of two worse than the goals, for the baseline one-year mission.

astro-ph/0508268

MISSION

Considering the TeV threshold scale for this decay and the Planck suppression of the correction $\delta f$, the ultrarelativistic approximation is indeed excellent if one is interested in the particle energy only. However, threshold analyses are based on exact energy--momentum conservation and can thus be sensitive to the slightest deviations. Even in a conventional photon decay, the ultrarelativistic approximation renders the lepton momenta lightlike, which seemingly permits the decay in forward direction. In the present case, $E\simeq|\vec{p}|$ introduces an additional degeneracy into the problem. As a result, the approximate solution is spacelike, whereas the exact expression (REF) determines both a timelike and a spacelike branch. It is the presence of the timelike momenta that permits the decay.

astro-ph/0508625

UNITS

- As was demonstrated by the recent results from the WMAP satellite (Bennett et al. 2003), the strongest constraints are derived when combining CMB measurements (constraining the power spectrum on large spatial scales) with measurements on substantially smaller scales, to break parameter degeneracies remaining from the CMB results alone (see Spergel et al. 2003). Hu & Tegmark (1999) have explicitly demonstrated how much the accuracy of estimates of cosmological parameters is improved when the CMB results from missions like WMAP and later Planck is complemented by cosmic shear measurements (see Fig. REF). In fact, as we shall see later, combinations of CMB anisotropy measurements have already been combined with cosmic shear measurements (see Fig. REF) and lead to substantially improved constraints on the cosmological parameters.

astro-ph/0509252

MISSION

We used the values of density, flow radial speed and sound speed $\rho_{\infty}$, $v_{\infty}$ and $a_{\infty}$ at the BH accretion radius to calculate the Bernoulli constant $B$, necessary to solve the algebraic system. The unknowns are $\rho$, $v$ and $a$. By solving for these quantities, we obtained their radial profiles $\rho(r)$, $v(r)$ and $a(r)$. Finally, from $a(r)$ we found the temperature profile $T(r)=(m_H a^2)/(2 \gamma K_B)$, where $m_H$ is the proton mass and $K_B$ is the Boltzmann constant. From the density $\rho$ and the temperature $T$ at a certain radius $r$ we calculated the emitted power density at the same $r$ for the bremsstrahlung emission process. Defining $e_{ff}$ as the emitted power density, $n_{e}$ and $n_{i}$ as the electron and ion densities in the gas, $Z$ as the atomic number of the ions, $g_{B}$ as the Gaunt factor, $e$ and $m_{e}$ as the electron charge and mass, $h$ as the Planck constant, the formula we used for bremsstrahlung is the following:

astro-ph/0509670

CONSTANT

Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/.

astro-ph/0509802

MPS

Assume a human observer has finite size and just requires a 1 kg brain to last 0.1 second. The dimensionless action for this is FORMULA Therefore, in any spacetime volume $V_4(\mathrm{brain}) \sim (10\:\mathrm{cm})^3 (0.1\:\mathrm{s}) \sim 10^{144}\: l^4_{\mathrm{Pl}} \sim e^{331}\: l^4_{\mathrm{Pl}}$, one would expect a human observation to have probability $P \geq P(\mathrm{brain}) \sim e^{-I} \sim e^{-10^{50}}$. Thus observations should occur at a rate per Planck 4-volume of FORMULA

hep-th/0510003

UNITS

We shall first consider the case where each of the masses, as well as the total mass of the system, is much, much smaller than Planck mass; say typically in the atomic mass range, or smaller. If we observe this box from an external classical spacetime, the dynamics of the particles will obey the rules of quantum mechanics. We also assume that the total mean energy associated with the system is much smaller than the Planck energy scale $E_p \sim 10^{19} GeV$. Since both Planck-mass and Planck-energy scale inversely with the gravitational constant, the approximation we are considering is equivalent to considering the limit $m_{Pl} \rightarrow\infty$, or letting $G\rightarrow 0$. It is thus reasonable, in this approximation, to neglect the gravitational field produced by the particles inside the box. The reason for doing so is the same, for example, as to why we ignore the gravitational field of the hydrogen atom while studying its spectrum. What we thus have in the box is a collection of particles obeying quantum dynamics in an external spacetime, and the gravitation of these particles can be neglected.

gr-qc/0510042

UNITS, UNITS, UNITS, UNITS

Continuing on this issue, it is said that quantum gravity effects can be probed by accelerating an elementary particle (whose rest mass is much smaller than Planck mass) to Planck energies, so that it can probe length scales as small as Planck length. While this is of course true, it would certainly also be possible to probe quantum gravity effects with an elementary particle (if such a particle existed) whose rest mass becomes comparable to Planck mass, so that its Compton wavelength becomes comparable to Planck length. Known objects with mass in the Planck mass range are much, much larger than Planck length, in physical size, because of non-gravitational effects (the nuclear and the electromagnetic force). This rules them out as probes of physics on the Planck length scale. (It is also interesting to note that Planck mass is perhaps the mass scale where classicality sets in, because for objects with a mass larger than Planck mass the Schwarzschild radius becomes larger than the Compton wavelength, so that the quantum nature of the object is hidden behind the Schwarzschild radius.)

gr-qc/0510042

UNITS, UNITS, UNITS, UNITS, UNITS, UNITS, UNITS, UNITS, UNITS, UNITS

For our forecasts, we assume the following probes: LSST for WL and GC, Planck for CMB, and a Joint Dark Energy Mission (JDEM) for SN. For the galaxy distribution we assume the most optimistic LSST-like survey with several billion galaxies distributed out to $z=3$. We then divide the total galaxies into ten and six photometric bins for the calculation of GC and WL respectively. The survey parameters were adopted from the recent review of the LSST collaboration [CIT]. Namely, we use $f_{\rm sky}= 0.5$, $N_G = 50$ gal/arcmin$^2$ for both WL and counts; the shear uncertainty is assumed to be $\gamma_{\rm rms} = 0.18 + 0.042 z$, and the photometric redshift uncertainty is given by $\sigma(z) = 0.03 (1 + z)$. We only use the information from scales that are safely in the linear regime (corresponding to $k\le 0.1$h/Mpc). For CMB we include the Planck temperature and polarization spectra and their cross-correlation; for the SN we assume the detection of 2000 SN distributed out to a redshift of 1.7. Details of the assumptions for the experiments and the calculation of the Fisher matrices can be found in [CIT] and in [CIT].

astro-ph/0510293

MISSION, MISSION

The one loop renormalization group equations are: $\alpha_i^{-1}(\mu)=\alpha_i^{-1}(M_Z)-\frac{b_i}{2,\pi} \ln\frac{\mu}{M_Z}$ where $i=2,3,Y$ for $M_Z\le\mu\le M_R$ and $\alpha_i^{-1}(\mu)=\alpha_i^{-1}(M_R)-\frac{b_j'}{2,\pi} \ln\frac{\mu}{M_Z}$ where $j=C,L,R,Z'$ for $M_R\le\mu\le M_S$. The two Higgs SM beta functions are: $b_3=-7, b_2=-3, b_Y=7$ and the ${SU(3)}^3$ beta functions are: $b_{C}'=-5$, $b_{L}'=b_{R}'=-\frac{59}{12}+\frac{n_{\hat H}}{4},$, where $n_{\hat H}$ the number of the Higgs fields ${\cal H}_{{\cal L},{\cal R}}$ which in our case is taken to be $n_{\hat H}=2$. Solving the RGEs for the three cases mentioned above we obtain $M_R$ and $M_S$ as a function of the common coupling $a$. The results are presented in Figure REF. The curves extend from the point $M_S=M_R$ to the Planck scale.

hep-ph/0510230

UNITS

In the last model proposed, the basic assumption is that the correction to the metric can be extracted from the linearized Einstein equations. The main point in this approach is that, in spite of the fact that Einstein equations cannot be assumed as fundamental at the Planck scale, they provide a starting point to construct the perturbations on the metric. The additional information --- what makes this approach different from [CIT] --- comes from the average which, at this point, is constructed making a few (reasonable) physical assumptions. In any case, this can not be considered as a problem since our goal is not to obtain a precise definition of the average from first principles but to show how the proposal of [CIT] could work.

gr-qc/0511031

UNITS

We propose a fast and efficient bispectrum statistic for Cosmic Microwave Background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter f_NL. We show how the method can achieve a remarkable computational advantage by focussing on subsets of the multipole configurations, where the non-Gaussian signal is more concentrated. The detection power of the test, increases roughly linearly with the maximum multipole, as shown in the ideal case of an experiment without noise and gaps. The CPU-time scales as l_{max}^3 instead of l_{max}^5 for the full bispectrum which for Planck resolution l_{max} \sim 3000 means an improvement in speed of a factor 10^7 compared to the full bispectrum analysis with minor loss in precision. We find that the introduction of a galactic cut partially destroys the optimality of the configuration, which will then need to be dealt with in the future. We find for an ideal experiment with l_{max}=2000 that upper limits of f_{NL}<8 can be obtained at 1 sigma. For the case of the WMAP experiment, we would be able to put limits of |f_{NL}|<40 if no galactic cut were present. Using the real data with galactic cut, we obtain an estimate of -80<f_{NL}<80 and -160<f_{NL}<160 at 1 and 2 sigma respectively.

astro-ph/0512112

MISSION

Axion fluctuations generated during inflation lead to isocurvature and non-Gaussian temperature fluctuations in the cosmic microwave background radiation. Following a previous analysis for the model independent string axion we consider the consequences of a measurement of these fluctuations for two additional string axions. We do so independent of any cosmological assumptions except for the axions being massless during inflation. The first axion has been shown to solve the strong CP problem for most compactifications of the heterotic string while the second axion, which does not solve the strong CP problem, obeys a mass formula which is independent of the axion scale. We find that if gravitational waves interpreted as arising from inflation are observed by the PLANCK polarimetry experiment with a Hubble constant during inflation of H_inf \apprge 10^13 GeV the existence of the first axion is ruled out and the second axion cannot obey the scale independent mass formula. In an appendix we quantitatively justify the often held assumption that temperature corrections to the zero temperature QCD axion mass may be ignored for temperatures T \apprle \Lambda_QCD.

hep-th/0512199

MISSION

This article is organized as follows. In Sec. 2, using the maximum radiated power of gravitational waves, we prove that the Planck time is a minimal time. In Sec. 3, we discuss the cosmological constant duality, and in Sec. 4 we analyze the magnetic monopole mass from a duality perspective. Finally, in Sec. 5, we make some latter remarks.

hep-th/0512256

UNITS

A complete treatment of the loss-cone problem involves the solution of the Fokker-Planck equation in $(\mathcal{E},J)$-space (Cohn & Kulsrud [CIT]). However, an approximate solution can be obtained by solving the Fokker-Planck equation in $\mathcal{E}$-space only, while accounting for the loss-cone by adding sink terms to the equation (BW77). This is the approach we adopt here. The tidal disruption rate due to NR relaxation has been discussed extensively in the literature (see e.g. Lightman and Shapiro [CIT]; Frank & Rees [CIT]; Cohn & Kulsrud [CIT]; Syer & Ulmer [CIT]; Magorrian & Tremaine [CIT]; Alexander & Hopman [CIT]; Merritt & Poon [CIT]; Wang & Merritt [CIT]; Hopman & Alexander [CIT]; Baumgardt et al. [CIT]). The differential NR loss-cone diffusion rate (stars per $\mathrm{d}\mathcal{E}\mathrm{d}t$) is estimated to be of the order

astro-ph/0601161

FOKKER, FOKKER

In each of the above mentioned theories there are important reasons for investigating a quantum mechanics based on Snyder commutators. The free massless particle is only one of the many dual physical systems that have a unified description given by the two-time physics model. The list includes the harmonic oscillator, the Hydrogen atom, the particle moving in a de Sitter space, the particle moving in arbitrary attractive and repulsive potentials and possibly others still unknown. As for the free massless particle, Snyder brackets may also be hidden in the dynamics of all these dual physical systems, possibly in different space-time dimensions. As we saw in section three, the Snyder brackets for the two-time physics model enlarge the duality gauge algebra of the model and consequently may also enlarge the number of dual systems it can describe, while still preserving its $D+2$ dimensional Lorentz invariance. As we saw in this work, the gravitodynamic theory brings with it a clear comprehension of the gravitational Aharonov-Bohm effect (also called the Aharonov-Carmi effect [28]). However, Snyder brackets for the gravitodynamic theory open the possibility of the existence of entirely new and unexpected gravitational effects, with no parallel in electrodynamics. Above all advances, relativistic quantum gravitodynamics in a noncommutative space-time can bring with it a clue of which is the fundamental physical object occupying the Planck area.

hep-th/0601117

UNITS

In this section, the simulation is outlined: First, the foreground emission components considered are summarised (Sect. [3.1]), and instrumental issues connected to sub-millimetric observations with Planckare discussed (Sect. [3.2]). The data products resulting from the simulation at this point will be spherical harmonics expansion coefficients $\langle S_{\ell m}\rangle_\nu$ of the flux maps $S_{\nu}(\bmath{\theta})$ for all nine observing frequencies $\nu$, where the spectra have been convolved with Planck's frequency response windows and the spatial resolution of each channel is properly accounted for. Next, the signal extraction methodology based on matched and scale-adaptive filtering is described (Sect. [3.3]), followed by the application to simulated Planck-data (Sect. [3.4]). The morphology of peaks in the filtered maps as a function of signal profile model parameters is discussed (Sect. [3.5]) and finally the algorithm for the extration of peaks in the filtered maps and the identification with objects in the cluster catalogue is described (Sect. [3.6]). A description of the software tools and the foreground modelling used for our simulation can be found in [CIT].

astro-ph/0602406

MISSION, MISSION, MISSION

Fig. REF shows the number density of clusters as a function of ecliptic latitude $y\equiv\cos\beta$. The figure states that the Planckcluster sample extracted with the specific filters is highly non-uniform for low significance thresholds, where most of the clusters are detected on a belt around the celestial sphere, but gets increasingly more uniform with higher threshold values for the significance. This is due to the incomplete removal of low-$\ell$ modes in the filtered maps, which bears interesting analogies to the *peak-background split* [CIT] in biasing schemes for linking galaxy number densities to dark matter densities: Essentially, the likelihood maps are composed of a large number of small-scale fluctuations superimposed on a background exhibiting a large-scale modulation. In regions of increased amplitudes due to the long-wavelength mode one observes an enhanced abundance of peaks above a certain threshold and hence an enhanced abundance of detected objects.

astro-ph/0602406

MISSION

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

astro-ph/0602569

MPS, MPS, MPS

The redistribution function from which the RD Fokker-Planck equation (REF) was derived satisfies the symmetry $R(\nu,\nu')=R(\nu',\nu)$. However, because approximations have been made, it is not obvious that the Fokker-Planck redistribution function $R$ defined implicitly through equation (REF) must necessarily satisfy this same symmetry. To investigate this it is useful to consider the following double integral, FORMULA This quantity is bilinear in the two functions $F(\nu)$ and $G(\nu)$, which are completely arbitrary, except that they and their derivatives are assumed to vanish sufficiently rapidly at the limits of integration $(0,\infty)$.

astro-ph/0603047

FOKKER, FOKKER

MJJ acknowledges funding from a PPARC PDRA and RJM acknowledges funding from the Royal Society. We thank the referee Katherine Inskip for a detailed reading of the manuscript. This publication makes use of the material provided in the FIRST, NVSS and SDSS surveys. FIRST is funded by the National Radio Astronomy Observatory (NRAO), and is a research facility of the US National Science foundation and uses the NRAO Very Large Array. Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

astro-ph/0603231

MPS, MPS, MPS

First, one deduces that the present ground-state energy density of SU(2)$_{\tiny\mbox{CMB}}$ is less than 0.4% of the measured value of today's density in dark energy [CIT]. Thus there must be an additional mechanism providing for the latter. A serious possibility is that a Planck-scale axion field, coupling to the topological defects of SU(2)$_{\tiny\mbox{CMB}}$ and thereby acquiring a tiny mass ($m_{\tiny\mbox{axion}}\sim 10^{-36},$eV), is caught at the slope of its potential by cosmological friction. This axion field owes its existence to the chiral anomaly [CIT] taking place due to integrated-out chiral fermions as the temperature of the Universe fell below the Planck mass $M_P\sim 1.2\times 10^{19},$GeV. These fermions may have emerged because an SU(2) or an SU(3) gauge theory of Yang-Mills scale $\Lambda\sim M_P$ went confining. A (to-be-investigated) possibility is that all SU(2) or SU(3) gauge symmetries together with their Yang-Mills scales, describing the matter content of our (four-dimensional) Universe, were set by a dynamical symmetry breakdown: SU($\infty)\to$ gravity + matter. The Planck mass would then be associated with the Yang-Mills scale of SU($\infty$). The Planck-scale axion would trigger CP-violation in particle creation whenever an SU(2) or an SU(3) factor becomes nervous, that is, close to a Hagedorn transition (matter asymmetry [CIT]).

hep-th/0603241

UNITS, UNITS, UNITS, UNITS

The third polarimeter scheme consists in a differential receiver subtracting the two linear polarizations and providing directly $Q$. Discussed by [CIT], it is realized by a dual polarization antenna directly feeding an OMT, whose outputs are $E_x$ and $E_y$. They are then differentiated by a PLANCK-like receiver, with the second polarization which substitutes the 4 K reference load: $E_x$ and $E_y$ enter a magic-T providing their sum and difference ($(E_x + E_y)/\sqrt{2}$ and $(E_x - E_y)/\sqrt{2}$). After the amplification, these enter a second magic-T which provide two quantities proportional to $E_x$ and $E_y$. After a square detection performed by diodes, they are differentiated thus providing $Q$.

astro-ph/0604169

MISSION

Thus, we can conclude that, from a phenomenological point of view, the Evolutionary Quantum Cosmology overlaps, in the generic inhomogeneous case, the Wheeler-Dewitt description and no evidence appears of the non-zero eigenvalue in the Universe critical parameter. As a final point, we want to emphasize how the Planckian dimension of the quantum Universe, predicted by our model, provides good indications on the solution of the horizon paradox within a Quantum Mechanics endowed with a cut-off. In fact, if (like here) the mean size of the primordial Universe is comparable to the classical horizon at the Planck time, no real puzzle arises about its later strong uniformity.

gr-qc/0604049

UNITS

The parameter $\nu$ appears in the Schrödinger equation in a manner analogous to the Planck constant in real quantum mechanics. However, the system we are considering here is entirely classical and thus $\nu$ is treated as an adjustable parameter that controls the quantum pressure term $\mathcal{P}\propto\nu^2$ appearing in the Bernoulli equation (REF). The quantum pressure term acts as a regularizing term in the fluid equations, preventing the generation of multi-stream regions and singularities in the density field when particle trajectories cross. This was demonstrated by Coles and Spencer [CIT] who used the wave-mechanical approach to follow the gravitational collapse of a one-dimensional sinusoidal density perturbation through shell-crossing. The effect of the quantum pressure is thus qualitatively similar to that of the term $\mu\nabla_{\mathbf{x}}^2\phi$ in the adhesion model and $\nu$ plays a similar role to the viscosity parameter $\mu$, in the sense that they are both approximations to a general gravitational multi-stream coefficient arising in collisionless systems. The link between the wave-mechanical approach and the adhesion approximation will be further discussed below. In the *semi-classical* limit $\nu\rightarrow 0$ we expect the effect of the quantum pressure term to be minimized and thus our wave-mechanical representation of self-gravitating CDM will approach the standard hydrodynamical description.

astro-ph/0605012

CONSTANT

Let us estimate the scales without any contribution of Higgs scalars using eq. (REF). These values are summarized in Table REF. It is found that $M_G$ rests between $10^{16}- 10^{17}$ GeV and $M_R$ between $10^{10}-10^{11}$ GeV for various values of $\ln(M_G/M_C)$ and acceptable input values of the electroweak parameters at $M_F=(\sqrt{2}, G_F)^{-1/2} \cong 246.22$ GeV where especially $\alpha_s^{-1}(M_F)=10$. For smaller values of $\alpha_s^{-1}$, the $SO(10)$ model is no more physically viable, because $M_G$ moves inescapably towards the Planck scale. The various values of $\alpha(M_G)$ are also given in Table. REF for the respective values of the intermediate mass scales where the fine structure constant $\alpha$ at $M_G$ is obtained as FORMULA This expression can be solved for $\alpha(M_G)$ at $Q=M_F$. If we compare the values of $\alpha^{-1}$ at $M_G$ and $M_F$, given in the last six rows in Table. REF, it is observed that they are very close. This does not happen in the effective $SU(3)_C \times SU(2)_L \times U(1)_Y$ running of $\alpha^{-1}$. The difference is caused by the existence of the $U(1)_{B-L} \times SU(2)_{R}$ symmetries above the $M_R$ scale. The beta functions $b^{em}_1$ in the interval $Q > M_R$ becomes negative. The running of $\alpha,\alpha_W,\alpha_s,\alpha_Y$ are sketched in Fig. REF. As seen in the figure $\alpha^{-1}$ reaches a minimum value of approximately $117$ at the mass scale $M_R$, beyond this scale the electromagnetic interactions become gradually weaker again.

hep-ph/0605004

UNITS

Black hole mechanics is one of the most tantalizing features of general relativity. Its formal analogy with thermodynamics was noticed early on [CIT]. The quantum nature of the underlying physics was clarified by the discovery of the Hawking radiation [CIT]. While the quantum theory of black holes struggles with unsolved problems such as the information paradox [CIT], it successfully motivated the holographic conjecture [CIT] : the entropy in a spherical volume cannot exceed the quarter of its surface area in Planck units (see [CIT] for alternative and generalized definitions). Despite the general belief that the explanation of the holographic conjecture must be of quantum nature, it is non-trivial to find simple quantum systems representing black hole mechanics. In this paper, we set out to construct a quantum statistical model displaying the holographic behavior of a Schwarzschild black hole.

hep-th/0605190

UNITS

We have thus shown that in most cases the future singularities are avoided because of the presence of loop quantum corrections. Our analysis of the resolution of singularities clearly reflects the important role played by non-perturbative quantum gravity modifications in order to fully understand the dynamics of universe around the Planck energy.

gr-qc/0605113

UNITS

We have worked with idealised beams that are circularly symmetric and Gaussian-shaped. In a real experiment this will not be the case. The real response of the beam shows more complexity, with side lobes, ellipticity and even changing the orientation in the sky of the projected shape. As long as the beam profile is well known, it is straightforward to construct the corresponding MF. Even in the case of non-symmetric beams this can be done, by increasing the computational complexity of the problem. Therefore, when using the MF, real beams can be in principle handled. Regarding the standard Mexican Hat Wavelet, [CIT] have tested the influence of realistic asymmetric beams. Those authors have shown that, although the MHW is an isotropic wavelet, it can also be adequate to perform the detection of point sources that show a slight Gaussian asymmetry. This is precisely the situation for the Planck beams (see the Planck BlueBook, ESA-SCI(2005)1). For a more detailed discussion, the reader is referred to [CIT].

astro-ph/0606199

MISSION, MISSION

Then by the simplified derivation of Yurtsever's result [CIT], the dimension of the gravitational truncated symmetric Fock space approximately reads FORMULA Here $I_0$ is the zeroth-order Bessel function of the second kind, and $z$ is obtained by FORMULA where the density of states $\rho(\omega)=\frac{V}{2\pi^2}\omega^2$ has been employed with the volume $V=\frac{4\pi}{3}R^3$ and the area $A=4\pi R^2$. Later, according to the asymptotic behavior of $I_0$ as $x\rightarrow\infty$, i.e., FORMULA the maximum entropy takes the form FORMULA Some remarks on this result are presented in order. Firstly the leading term is obviously dependent on the the Planck scale physics where the ordinary quantum field theory is broken. Specifically, if $\Lambda=\frac{\pi\cdot\sqrt{6\pi}}{2}$, the leading term is the just the famous linear entropy-area relation formula. While the sub-leading correction is independent of the Planck scale physics. In particular, it is worth noting that the logarithmic term has also arisen in both Loop Quantum Gravity and String Theory. However, one should emphasize that there is no general agreement on the coefficient of the logarithmic correction [CIT]. Therefore the resultant coefficient $-\frac{1}{2}$ obtained here acquires much importance: since our foregoing assumptions only rely on classical general relativity and quantum field theory below the Planck scale, it provides another semi-classical constraint onto all candidates for quantum gravity such as Loop Quantum Gravity and String Theory.

gr-qc/0606070

UNITS, UNITS, UNITS

As noted above, the spectral index of the amorphous silicate emissivity might be less steep than the $\beta \sim 2$ inherent in our calculations. A modest change was introduced by Li & Draine ([CIT], their eq. 1 and Fig. 9) to fit the frequency dependence of the diffuse emission. Boudet *et al.*([CIT]) suggest even stronger variations with frequency over the range 150 -- 3000 GHz. In this case, the factor $d$ would be tend to increase with decreasing frequency as the relative importance of large silicates to the submillimetre emission rose. In models where it is the silicates that produce the polarization (subscribed to here), this frequency dependence of $d$ would result in an increase in the net $p_{em}$ at the lower frequencies and our estimate at 353 GHz could be low by a factor $\sim 1.6$ (not included in the systematic errors below). It will be interesting to learn the results from B2K (and Planck) which measure within this interesting range of frequencies.

astro-ph/0606430

MISSION

A particularly exciting prospect is to look for qualitatively new effects due to physics at or beyond the string or Planck scale. As have been argued in many works -- the references [2-24] just represent a selected few -- there are reasons to expect a characteristic signal consisting of a modulation in the primordial spectrum with a periodicity determined by the slow roll parameters. The magnitude of the effect is believed to be quite small but could nevertheless be within reach of present or upcoming observatories.

astro-ph/0606474

UNITS

In models with large extra dimensions, where the fundamental gravity scale can be in the electroweak range, gravitational effects in particle physics may be noticeable even at relatively low energies. In this paper, we perform simple estimates of the decays of elementary particles with a black hole intermediate state. Since black holes are believed to violate global symmetries, particle decays can violate lepton and baryon numbers. Whereas previous literature has claimed incompatibility between these rates (e.g. $p$-decay) and existing experimental bounds, we find suppressed baryon and lepton-violating rates due to a new conjecture about the nature of the virtual black holes. We assume here that black holes lighter than the (effective) Planck mass must have zero electric and color charge and zero angular momentum -- this statement is true in classical general relativity and we make the conjecture that it holds in quantum gravity as well. If true, the rates for proton-decay, neutron-antineutron oscillations, and lepton-violating rare decays are suppressed to below experimental bounds even for large extra dimensions with TeV-scale gravity. Neutron-antineutron oscillations and anomalous decays of muons, $\tau$-leptons, and $K$ and $B$-mesons open a promising possibility to observe TeV gravity effects with a minor increase of existing experimental accuracy.

hep-ph/0606321

UNITS

This paper is organized as follows. In Sec. II, we discuss the effect of the primordial magnetic fields on the hydrogen temperature and the density fluctuations. In Sec. III, we summarize CMB bright temperature fluctuations produced by the hydrogen 21cm line. In Sec. IV, we compute the angular power spectrum of bright temperature fluctuations with the primordial magnetic fields and discuss the effect of the primordial magnetic fields. Sec. V is devoted to summary. Throughout the paper, we take WMAP values for the cosmological parameters, i.e., $h=0.71 (H_0=h \times 100 {\rm Km/s \cdot Mpc})$, $T_0 = 2.725$K, $h^2 \Omega _{\rm b} =0.0224$ and $h^2 \Omega_{\rm m} =0.135$ [CIT]. And $\hbar$ and $c$ are Planck's constant over $2 \pi$ and speed of light, respectively.

astro-ph/0607169

CONSTANT

A comment is worth mentioning at this point. Whereas the accretion mechanism used above is classical in nature the very structure of the wormholes should be quantum mechanically considered on some regimes [16]. In particular, sub-microscopic wormholes have been shown to be stabilized by quantum mechanical effects that induce a possible discretization of time [17]. We note however that our approximation can safely be applied to wormhole sizes which widely separate from those where quantum effects are expected to be important. Moreover, being true that both the energy density and curvature of the universe increase with time, it is easy to check that these quantities only acquires the sufficiently high values approaching the Planck scale that requires a proper quantization of space-time [18] as one comes close to the big rip singularity, a regime still far enough from that characterizing the big trip phenomenon as to allow one to take the classical approach to be reliable. In fact, at the time when the wormhole throat starts exceeding the radius of the universe, the value of the scale factor, and hence of the energy density and curvature of the universe are expected to be many orders of magnitude smaller than their counterparts at the close neighborhood of the big rip.

hep-th/0607137

UNITS

The results for $(B-V)$ are shown in Fig. REF which confirms that the cooler hydrogen-deficient models may be *redder* at a given temperature than their hydrogen-rich counterparts. This is a direct consequence of the much lower continuum opacities in the hydrogen-poor models. Strong metal line blanketing due to singly-ionized iron-group elements in the near-UV coincides with the peak of the Planck function and has a much stronger effect than in the hydrogen-rich model atmospheres -- the *ratio* of line to continuous opacity is the crucial quantity. The increase in metal-line blanketing is partially compounded in the hotter models by a reduction in the contribution from the high-order Balmer series and Balmer continuum. One implication is that, for observations of, the assumption of a normal hydrogen abundance could lead to an underestimate of,*T$_{\rm eff}$*by as much as $1,000,\mbox{K}$ for $\mbox{,\em T$_{\rm eff}$}\mathrel{\raise 1.16pt\hbox{$<$}\kern-7.0pt \lower 3.06pt\hbox{{$\scriptstyle \sim$}}}9,000,\mbox{K}$.

astro-ph/0608542

LAW

For the CMB simulation we consider a simple full-sky ($f_{sky}=1$) simulation at Planck-like sensitivity and ignore the lensing effect and the tensor information. We neglect foregrounds and assume the isotropic noise with variance $N_{l}^{TT}=N_{l}^{EE}/2=3\times10^{-4}\mu K^2$ (Pessimistic Planck-like sensitivity) and a symmetric Gaussian beam of 7 arcminutes full-width half-maximum (FWHM) [CIT]. We use the simulated $\tilde C_{l}$ up to $l=2500$ for temperature and $l=1500$ for polarization. The effective $\chi^2$ is: FORMULA where $C_{l}^{XY}$ denote theoretical power spectra and $\tilde C_{l}^{XY}$ denote the power spectra from the simulated data. The likelihood has been normalized with respect to the maximum likelihood, where $C_{l}^{XY}=\tilde C_{l}^{XY}$ [CIT].

astro-ph/0609463

MISSION, MISSION

where $D$ -- the diffusion coefficient. Both decisions of the equation (9) -- $L_0$ = 0 and $L_0$ = 2$R_\mu$ mean that at the first stage during time $\tau _\mu$ diffusion (wandering "on a place" owing to "self-promotion" [28] with characteristic time 1/$\Omega \sim$ 10$% ^{-44}$s) should have character of casual rotation in the volume of the "atom". Plus/minus Planck mass FORMULA

astro-ph/0610063

UNITS

The next step is to determine the particle distribution function $f=f(z,v_{z},t)$, from which quantities such as the vertical semi-thickness can be determined. Its evolution in phase space can be described by the one-dimensional Fokker-Planck equation. For the system we study, the particles are subject to frictional drag and gravity due to the central star as written in equation (REF) while their velocities diffuse in velocity space with diffusion coefficient $D_{\rm{v}}$ given by equation (REF). Then, the Fokker--Planck equation takes the form [CIT] : FORMULA where $b=-\Omega^2 z-v_{z}/\tau_{\rm{st}}$ is the non-stochastic acceleration. The derivation of equation (REF) is given in Appendix [5].

astro-ph/0610075

FOKKER, FOKKER

The energy assignment to the decay particles in the Hawking evaporation phase has been implemented in each generator differently. In CHARYBDIS the particle spices selected by the method described above is given an energy randomly according to its extra-dimension decay spectrum. A different decay spectrum is used for fermions and vector bosons, i.e. the spin statistics factor is taken into account. A Grey-body or a pure black-body spectrum can be used. Grey-body effects are included without approximations [CIT]. The grey-body factors are spin-dependent and depend on the number of dimensions. The choice of energy is made in the rest frame of the black hole before emission. The Hawking temperature of the spectrum is either fixed at the beginning of the decay or updated after each decay. If the Hawking temperature is allowed to vary, it is assumed the decay is quasi-stationary in the sense that the black hole has time to come into equilibrium at each new temperature before the next particle is emitted. If the Hawking temperature is fixed, it is assumed the decay is sudden in the sense that the back hole spends most of its time near its original mass and temperature because that is when it evolves the slowest. The energy of the particle given by the spectrum must be constraint to conserve energy and momentum. If the decay is not kinematically possible, two options exist: 1) try again or 2) go directly to the final stage (Planck phase). Heavy particle production spectra may be unreliable for choices of parameters for which the initial Hawking temperature is below the rest mass of the particle being considered.

hep-ph/0610219

EPOCH

We obtained the solution for $q = 0.99999$ and $\alpha=1$. The resultant radius of the solution is FORMULA where $l_{\rm pl}:= 1/m_{\rm pl}$ is the Planck length. The frequency of the mode is $\omega_{10} = 0.0253909 \times \alpha \: (1-q^2) \: m_{\rm pl}$. The redshift factor $\alpha$ of the singularity and the factor $(1-q^2)$, which is the shift of the Hawking temperature (REF), are directly reflected in the frequency $\omega_{10}$. The form of the radial mode function for the scalar field is displayed in Fig. REF, where the initial value of the radial mode function is FORMULA The distributions of the resultant metric elements $F(r)$ and $G(r)$ are displayed in Fig. REF-a. To contrast our result with that for an ordinary charged black hole, we also plot the exterior part $(r>r_{\rm BH})$ of the Reissner-Nordström metric (REF) with the same radius $r_{\rm BH}$ and the same charge $q$ (the thick dotted curves in Fig. REF-a).

hep-th/0611292

UNITS

By assuming that corrections from both new physics and the curvature effect are very small, we can use the linear approximation, in which, the modified primordial power spectrum is given by FORMULA where the possibly new physics gives a $\xi=H/\Lambda$ factor correction to the primordial power spectrum, and the spatial curvature contributes a $K/k^2$ term, before which the coefficient can be absorbed in $K$. For the open Universe with negative $K$, we can also obtain the same form as Eq. (REF). The physical meaning is clear: If no new physics, the asymptotic behavior of the spherical Hankel function is the free spherical wave. The cutoff due to new physics serves as a boundary condition in momentum space, and therefore, the choice of the vacuum leads to a mixture of the positive and negative mode states, *i.e.*, outward- and inward-going waves classically. The amplitude of the spherical wave in a non-flat space will be modified and contribute a separate term by linear approximation. The modulations of the primordial power spectrum will be magnified in the CMBR fluctuations, which can be probed by WMAP mission and the future PLANCK satellite observations.

astro-ph/0612011

MISSION

This work is based on observations obtained with XMM--Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and the US (NASA). In Germany, the XMM--Newton project is supported by the Bundesministerium für Bildung und Forschung/Deutsches Zentrum für Luft und Raumfahrt, the Max--Planck Society, and the Heidenhain--Stiftung. Part of this work was supported by the Deutsches Zentrum für Luft-- und Raumfahrt, DLR project numbers 50 OR 0207 and 50 OR 0405. We gratefully acknowledge the contributions of the entire COSMOS collaboration consisting of more than 100 scientists. More information on the COSMOS survey is available at [http://www.astro.caltech.edu/ cosmos](http://www.astro.caltech.edu/ cosmos){.uri}. This research has made use of the NASA/IPAC Extragalactic Database (NED) and the SDSS spectral archive. We thank Guinevere Kauffmann and Jarle Brinchmann for help with the object #2608. We acknowledge helpful comments from an anonymous referee.

astro-ph/0612311

MPS

The support of the Namibian authorities and of the University of Namibia in facilitating the construction and operation of H.E.S.S. is gratefully acknowledged, as is the support by the German Ministry for Education and Research (BMBF), the Max Planck Society, the French Ministry for Research, the CNRS-IN2P3 and the Astroparticle Interdisciplinary Programme of the CNRS, the U.K. Particle Physics and Astronomy Research Council (PPARC), the IPNP of the Charles University, the South African Department of Science and Technology and National Research Foundation, and by the University of Namibia. We appreciate the excellent work of the technical support staff in Berlin, Durham, Hamburg, Heidelberg, Palaiseau, Paris, Saclay, and in Namibia in the construction and operation of the equipment. M. Filipovic would like to thank Milorad Stupar for his work on the ATCA data.

astro-ph/0612495

MPS

Consider a particle of energy $E \leq m_{\rm p}c^2$ somewhere in the coordinate system, say at position $x_E$. We might not know what the particle's gravitational field looks like at a Planck scale distance, but we know it obeys the laws of General Relativity for distances far above the Planck scale. In particular, the potential of the particle vanishes for $|x-x_E|\gg l_{\rm p}$ like $(E l_{\rm p})/(m_{\rm p} c^2 |x-x_E|)$. Let us place the particle in the middle of the distance $\Delta x$, and cut out the quantum gravitational region of a size $\sim l_{\rm p}$. Inside this region, the coordinate distance gets distorted to an unknown distance that we will denote $d_{\rm QG}$, and which should not be of macroscopic size.

gr-qc/0612167

UNITS, UNITS

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

astro-ph/0701154

MPS, MPS, MPS

Having obtained the Hubble parameter, the fourth step consists in solving the evolution equation for the scalar field obtained from eqs. (REF,REF): FORMULA where $\tilde{\phi} = \phi/M_{Pl}$ is the scalar field in units of the Planck mass ($M_{Pl} = 1/\sqrt{G}$) and FORMULA In the fifth step one numerically inverts the solution $\tilde{\phi}(u)$ in order to determine $u(\tilde{\phi})$ to finally obtain FORMULA and FORMULA This completes the reconstruction procedure. I will now work out some examples of this procedure. I adopt $\Omega_\phi = 0.7$, $\Omega_{DM} = 0.25$ and $\Omega_b = 0.05$ in the following. In all examples I integrate the field equation starting from $u_{i}=-1.8$, corresponding to $z_i=5.05$ and I arbitrarily set $\tilde{\phi}(u_i) = -1$.

astro-ph/0701213

UNITS