Probing dark energy using its density instead of its equation of state
The variation of dark energy density with redshift, ρ X ( z ) , provides a critical clue to the nature of dark energy. Since ρ X ( z ) depends on the dark energy equation of state w X ( z ) through an integral, ρ X ( z ) can be constrained more tightly than w X ( z ) given the same observational data. We demonstrate this explicitly using current type Ia supernova (SN Ia) data [the Tonry/Barris sample], together with the Cosmic Microwave Background (CMB) shift parameter from CMB data (WMAP, CBI, and ACBAR), and the large scale structure (LSS) growth factor from 2dF galaxy survey data. We assume a flat universe, and use Markov Chain Monte Carlo (MCMC) technique in our analysis. We find that, while w X ( z ) extracted from current data is consistent with a cosmological constant at 68% C.L., ρ X ( z ) (which has far smaller uncertainties) is not. Our results clearly show the advantage of using ρ X ( z ) , instead of w X ( z ) , to probe the variation of dark energy.

title: Wavelets and WMAP non-Gaussianity
abstract: We study the statistical properties of the first-year Wilkinson Microwave Anisotropy Probe (WMAP) data on different scales using the spherical Mexican hat wavelet transform. Consistent with the 2004 results of Vielva et al., we find a deviation from Gaussianity in the form of kurtosis of wavelet coefficients on 3-4 scales in the southern Galactic hemisphere. This paper extends the work of Vielva et al. as follows: We find that the non-Gaussian signal shows up more strongly in the form of a larger than expected number of cold pixels and also in the form of scale-scale correlations among wavelet coefficients. We establish the robustness of the non-Gaussian signal under more wide-ranging assumptions regarding the Galactic mask applied to the data and the noise statistics. This signal is unlikely to be due to the usual quadratic term parameterized by the nonlinearity parameter fNL. We use the skewness of the spherical Mexican hat wavelet coefficients to constrain fNL with the first-year WMAP data. Our results constrain fNL to be 50+/-80 at 68% confidence and less than 280 at 99% confidence.

title: Dark Energy Constraints from Baryon Acoustic Oscillations
abstract: Baryon acoustic oscillations (BAOs) in the galaxy power spectrum allow us to extract the scale of the comoving sound horizon at recombination, a cosmological standard ruler accurately determined by the cosmic microwave background anisotropy data. We examine various issues important in the use of BAOs to probe dark energy. We find that if we assume a flat universe and priors on ?m, ?mh2, and ?bh2 as expected from the Planck mission, the constraints on dark energy parameters (w0, w') scale much less steeply with survey area than (area)-1/2 for a given redshift range. The constraints on the dark energy density ?X(z), however, do scale roughly with (area)-1/2 due to the strong correlation between H(z) and ?m (which reduces the effect of priors on ?m). Dark energy constraints from BAOs are very sensitive to the assumed linear scale of matter clustering and the redshift accuracy of the survey. For a BAO survey with 0.5 ? z ? 2, ? (R) = 0.4 [corresponding to kmax (z = 0) = 0.086 h Mpc-1], and ?z/ (1 + z) = 0.001, we find = (0.115,0.183) and (0.069, 0.104) for survey areas of 1000 and 10,000 deg2, respectively. We find that it is critical to minimize the bias in the scale estimates in order to derive reliable dark energy constraints. For a 1000 (10,000) deg2 BAO survey, a 1 ? bias in ln H (z) leads to a 2 ? (3 ?) bias in w'. The bias in w' due to the same scale bias from ln DA (z) is slightly smaller and opposite in sign. The results from this paper will be useful in assessing different proposed BAO surveys and guiding the design of optimal dark energy detection strategies.

title: A robust distance measurement and dark energy constraints from the spherically averaged correlation function of Sloan Digital Sky Survey luminous red Galaxies
abstract: We measure the effective distance to z = 0.26, DV (0.26), and mh 2 from the overall shape of the spherically-averaged two-point correlati on function of the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) volume-limited luminous red galaxy (LRG) sample, without assuming a dark energy model or a flat Universe. We giv e the mean and covariance matrix of DV (0.26), mh 2 , bh 2 , and ns. We show that these provide an efficient and accurate summary of the volume-limited LRG data. With flat priors on bh 2 and ns (7σWMAP7), we find mh 2 = 0.131 ± 0.020, and rs/DV (0.26) = 0.1466 +0.0068 0.0073 (the ratio of the sound horizon at the drag epoch to the effective distance to z = 0.26). We find that measurements of mh 2 or m are biased low if flux-limited (instead of volume-limited) L RG sample is used. By scaling the spherically-averaged correlation fun ction, we find the Hubble parameter H(0.26) = 79 +12 13 km s 1 Mpc 1 and the angular diameter distance DA(0.26) = 848 +86 88 Mpc. Combining our results with the cosmic microwave background and supernova data, we obtain k = 0.0059 +0.0092 0.0093 andw = 1.023 +0.054 0.053 (assuming a constant dark energy equation of state). We use LasDamas SDSS mock catalogs to compute the covariance matrix of the correlation function, and investigate the use of lognormal catal ogs as an alternative. We find that the input correlation function can be accurately recovered from lognormal catalogs, although they give larger errors on all scales (especially on small sc ales) compared to the mock catalogs derived from cosmological N-body simulations.

title: Constraints on generalized extended inflationary models.
abstract: We study the physical constraints on generalized extended inflationary theories, in which the Brans-Dicke field {Phi} couples to the inflaton sector in the form of two arbitrary power-law functions of {Phi}. We find that the most stringent constraints arise from the need to suppress large bubbles and from considerations of the density perturbations generated during extended inflation. We find that there are sizable portions of the parameter spaces in which all the constraints are satisfied.

title: Dark Energy Search with Supernovae
abstract: To determine the nature of dark energy from observational data, it is important that we use model-independent and optimal methods. We should probe dark energy using its density (allowed to be a free function of cosmic time) instead of its equation of state. We should minimize gravitational lensing effect on supernovae by flux-averaging. We need to include complementary data (for example, from the cosmic microwave background (CMB) and large scale structure (LSS)) in a consistent manner to help break the degeneracy between the dark energy density and the matter density fraction. We should push for ambitious future supernova surveys that can observe a large number of supernovae at the highest possible redshifts. I discuss these and other issues that will be important in our quest to unravel the mystery of the nature of dark energy. Current supernova, CMB, and LSS data already rule out dark energy models with dark energy densities that vary greatly with time; with the cosmological constant model providing an excellent fit to the data. A precise measurement of dark energy density as a free function of cosmic time will have a fundamental impact on particle physics and cosmology.

title: Current observational constraints to the holographic dark energy model with a new infrared cutoff via the Markov chain Monte Carlo method
abstract: In this paper, the holographic dark energy models with the new infrared cutoff for both the flat case and the nonflat case are confronted with the combined constraints of current cosmological observations: type Ia supernovae, baryon acoustic oscillations, current cosmic microwave background, and the observational Hubble data. By utilizing the Markov chain Monte Carlo method, we obtain the best fit values of the parameters with $1\ensuremath{\sigma}$, $2\ensuremath{\sigma}$ errors in the flat model: ${\ensuremath{\Omega}}_{b}{h}^{2}={0.0233}_{\ensuremath{-}0.0009\ensuremath{-}0.0014}^{+0.0009+0.0013}$, $\ensuremath{\alpha}={0.8502}_{\ensuremath{-}0.0875\ensuremath{-}0.1064}^{+0.0984+0.1299}$, $\ensuremath{\beta}={0.4817}_{\ensuremath{-}0.0773\ensuremath{-}0.0955}^{+0.0842+0.1176}$, ${\ensuremath{\Omega}}_{\mathrm{de}0}={0.7287}_{\ensuremath{-}0.0294\ensuremath{-}0.0429}^{+0.0296+0.0432}$, ${\ensuremath{\Omega}}_{m0}={0.2713}_{\ensuremath{-}0.0296\ensuremath{-}0.0432}^{+0.0294+0.0429}$, ${H}_{0}={66.35}_{\ensuremath{-}2.14\ensuremath{-}3.07}^{+2.38+3.35}$. In the nonflat model, the constraint results are found in $1\ensuremath{\sigma}$, $2\ensuremath{\sigma}$ regions: ${\ensuremath{\Omega}}_{b}{h}^{2}={0.0228}_{\ensuremath{-}0.0010\ensuremath{-}0.0014}^{+0.0010+0.0014}$, ${\ensuremath{\Omega}}_{k}={0.0305}_{\ensuremath{-}0.0134\ensuremath{-}0.0176}^{+0.0092+0.0140}$, $\ensuremath{\alpha}={0.8824}_{\ensuremath{-}0.1163\ensuremath{-}0.1378}^{+0.2180+0.2213}$, $\ensuremath{\beta}={0.5016}_{\ensuremath{-}0.0871\ensuremath{-}0.1102}^{+0.0973+0.1247}$, ${\ensuremath{\Omega}}_{\mathrm{de}0}={0.6934}_{\ensuremath{-}0.0304\ensuremath{-}0.0413}^{+0.0364+0.0495}$, ${\ensuremath{\Omega}}_{m0}={0.2762}_{\ensuremath{-}0.0302\ensuremath{-}0.0412}^{+0.0278+0.0402}$, ${H}_{0}={70.20}_{\ensuremath{-}3.17\ensuremath{-}4.00}^{+3.03+3.58}$. In the best fit holographic dark energy models, the equation of state of dark energy and the deceleration parameter at present are characterized by ${w}_{\mathrm{de}0}=\ensuremath{-}1.1414\ifmmode\pm\else\textpm\fi{}0.0608$, ${q}_{0}=\ensuremath{-}0.7476\ifmmode\pm\else\textpm\fi{}0.0466$ (flat case) and ${w}_{\mathrm{de}0}=\ensuremath{-}1.0653\ifmmode\pm\else\textpm\fi{}0.0661$, ${q}_{0}=\ensuremath{-}0.6231\ifmmode\pm\else\textpm\fi{}0.0569$ (nonflat case). Compared to the $\ensuremath{\Lambda}\mathrm{CDM}$ model, it is found the current combined data sets do not favor the holographic dark energy model over the $\ensuremath{\Lambda}\mathrm{CDM}$ model.

title: Constraints on neutrino degeneracy from the cosmic microwave background and primordial nucleosynthesis
abstract: We reanalyze the cosmological constraints on the existence of a net universal lepton asymmetry and neutrino degeneracy based upon the latest high resolution CMB sky maps from BOOMERANG, DASI, and MAXIMA-1. We generate likelihood functions by marginalizing over $(\omegab h^2,\xinumt, \xinue, \Omega_\Lambda,h,n)$ plus the calibaration uncertainties. We consider flat $\Omega_M + \Omega_\Lambda = 1$ cosmological models with two identical degenerate neutrino species, $\xinumt \equiv \vert \xinum \vert = \vert \xinut \vert$ and a small $\xinue$. We assign weak top-hat priors on the electron-neutrino degeneracy parameter $\xinue$ and $\Omega_b h^2$ based upon allowed values consistent with the nucleosynthesis constraints as a function of $\xinumt$. The change in the background neutrino temperature with degeneracy is also explicitly included, and Gaussian priors for $h = 0.72 \pm 0.08$ and the experimental calibration uncertainties are adopted. The marginalized likelihood functions show a slight (0.5$\sigma$) preference for neutrino degeneracy. Optimum values with two equally degenerate $\mu$ and $\tau$ neutrinos imply $\xinumt = 1.0^{+0.8 (1\sigma)}_{-1.0 (0.5\sigma)}$, from which we deduce $\xi_{\nu_e} = 0.09^{+0.15}_{-0.09}$, and $\Omega_b h^2 = 0.021^{+0.06}_{- 0.002}$. The $2\sigma$ upper limit becomes $ \xinumt \le 2.1$, which implies $\xi_{\nu_e} \le 0.30$, and $\Omega_b h^2 \le 0.030$. For only a single large-degeneracy species the optimal value is $\vert \xinum \vert$ or $\vert \xinut \vert = 1.4$ with a $2\sigma$ upper limit of $\vert \xinum \vert$ or $\vert \xinut \vert \le 2.5$

title: Angular 21 cm power spectrum of a scaling distribution of cosmic string wakes
abstract: Cosmic string wakes lead to a large signal in 21 cm redshift maps at redshifts larger than that corresponding to reionization. Here, we compute the angular power spectrum of 21 cm radiation as predicted by a scaling distribution of cosmic strings whose wakes have undergone shock heating.

title: A New form of Self-duality Equations with Topological Term
abstract: Based on the U(1) gauge potential decomposition theory and $\phi$-mapping theory, the topological inner structure of the self-duality (Bogomol'nyi-type) equations are studied. The special form of the gauge potential decomposition is obtained directly from the first of the self-duality equations. Using this decomposition, the topological inner structure of the Chern-Simons-Higgs (CSH) vortex is discussed. Furthermore, we obtain a rigorous self-dual equation with topological term for the first time, in which the topological term has been ignored by other physicists.

title: Probing interaction and spatial curvature in the holographic dark energy model
abstract: In this paper we place observational constraints on the interaction and spatial curvature in the holographic dark energy model. We consider three kinds of phenomenological interactions between holographic dark energy and matter, i.e., the interaction term Q is proportional to the energy densities of dark energy (rho(A)), matter (p(m)), and matter plus dark energy (p(m) + p(A)). For probing the interaction and spatial curvature in the holographic dark energy model, we use the latest observational data including the type la supernovae (SNIa) Constitution data, the shift parameter of the cosmic microwave background (CMB) given by the five-year Wilkinson Microwave Anisotropy Probe (WMAP5) observations, and the baryon acoustic oscillation (BAO) measurement, from the Sloan Digital Sky Survey (SDSS). Our results show that, the interaction and spatial curvature in the holographic dark energy model are both rather small. Besides, it is interesting to find that there exists significant degeneracy between the phenomenological interaction and the spatial curvature in the holographic dark energy model.