NO-BOUNDARY WAVE FUNCTION IN A HIGHER-DIMENSIONAL SPHERICALLY SYMMETRIC MICROSUPERSPACE MODEL
The wave function following the Hartle-Hawking (HH) no-boundary proposal is evaluated in five-dimensional space-time with topology of the four space S1×S3, generalizing the concept of microsuperspace. The functional integral in the expression for the wave function is simplified to an ordinary integration of one variable and is evaluated by the method of steepest-descent.

title: NAKED SINGULARITIES IN HIGHER DIMENSIONAL GRAVITATIONAL COLLAPSE
abstract: Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space–time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space–time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space–time is discussed in details. The five-dimensional space–time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.

title: Emergent universe in brane world scenario with Schwarzschild–de Sitter bulk
abstract: A model of an emergent universe is obtained in brane world. Here the bulk energy is in the form of cosmological constant, while the brane consists of a fluid satisfying an equation of state of the form $${p_{b}=\frac{1}{3}\rho_{b}}$$ , which is effectively a radiation equation of state at high energies. It is shown that with the positive bulk cosmological constant, one of our models represents an emergent universe.

title: Interacting Holographic Dark Energy at the Ricci scale and Dynamical system
abstract: In this work, we consider homogeneous and isotropic FRW model of the universe, filled with interacting dark matter and dark energy. The dark matter is chosen as usual in the form of dust while dark energy is holographic in nature with IR cut off at the Ricci's length and it is in the form of a perfect fluid with variable equation of state. We have chosen the interaction term of the following two types: (i) a linear combination of the matter density of the two fluids, (ii) a product of the two matter densities. For both the choices the evolution equations are transformed to an autonomous system and the corresponding critical points are analyzed. Finally, for the first choice of the interaction term the evolution of the ratio of the energy densities has been studied from the point of view of the present coincidence problem.

title: Energy Conditions, Cosmological Solutions and Cosmic No-Hair Conjecture in Gauss-Bonnet Theory
abstract: A detailed investigation of Gauss-Bonnet theory has been done from a different perspective. At first, the standard energy conditions are discussed and modified forms have been presented. Then some cosmological solutions have been obtained in 5D for perfect fluid assuming that the extra dimensional metric coefficient decreases with time. For some particular choice of the parameters, exponential solutions are obtained and finally, Cosmic No-Hair Conjecture has been proved for Gauss-Bonnet dilatonic scalar coupled to Einstein gravity with coupling parameter growing linearly in time.

title: Exact solutions of the field equations for Charap’s chiral invariant model of the pion dynamics
abstract: The field equations for the chiral invariant model of pion dynamics developed by Charap have been revisited. Two new types of solutions of these equations have been obtained. Each type allows infinite number of solutions. It has also been shown that the chiral invariant field equations admit invariance for a transformation of the dependent variables.

title: Brownian motion in strongly coupled, anisotropic Yang-Mills plasma: A holographic approach
abstract: We employ methods of gauge/string duality to analyze the Brownian motion and the concomitant Langevin equation of a heavy quark in a strongly coupled, thermal, anisotropic Yang-Mills plasma. We consider fluctuations both along and perpendicular to the direction of anisotropy and study the effects of anisotropy on the drag coefficient, the diffusion constant and the Langevin coefficient for both the directions. We also verify the fluctuation-dissipation theorem for Brownian motion in an anisotropic medium.

title: Upper limit on the cosmic gamma-ray burst rate from high energy diffuse neutrino background
abstract: We derive upper limits on the ratio f{sub GRB/CCSN}(z){identical_to}R{sub GRB}(z)/R{sub CCSN}(z){identical_to}f{sub GRB/CCSN}(0)(1+z){sup {alpha}}, the ratio of the rate, R{sub GRB}, of long-duration gamma-ray bursts (GRBs) to the rate, R{sub CCSN}, of core-collapse supernovae (CCSNe) in the Universe (z being the cosmological redshift and {), by using the upper limit on the diffuse TeV-PeV neutrino background given by the AMANDA-II experiment in the South Pole, under the assumption that GRBs are sources of TeV-PeV neutrinos produced from decay of charged pions produced in p{gamma} interaction of protons accelerated to ultrahigh energies at internal shocks within GRB jets. For the assumed ''concordance model'' of cosmic star formation rate, R{sub SF}, with R{sub CCSN}(z){proportional_to}R{sub SF}(z), our conservative upper limits are f{sub GRB/CCSN}(0){ =}1, already more restrictive than) the current upper limit on this ratio inferred from other astronomical considerations, thus providing a useful independent probe of and constraint on the CCSN-GRB connection. Nondetection of a diffuse TeV-PeV neutrino background by the upcoming IceCube detector in the South Pole after three years of operation, for example, will bring down the upper limit on f{sub GRB/CCSN}(0)more » to below a few x10{sup -5} level, while a detection will confirm the hypothesis of proton acceleration to ultrahigh energies in GRBs and will potentially also yield the true rate of occurrence of these events in the Universe.« less

title: Supernova deleptonization asymmetry: Impact on self-induced flavor conversion
abstract: During the accretion phase of a core-collapse supernova (SN), the deleptonization flux has recently been found to develop a global dipole pattern (LESA---Lepton Emission Self-sustained Asymmetry). The $\nu_e$ minus $\bar\nu_e$ flux essentially vanishes in one direction, potentially facilitating self-induced flavor conversion. On the other hand, below the stalled shock wave, self-induced flavor conversion is typically suppressed by multi-angle matter effects, preventing any impact of flavor conversion on SN explosion dynamics. In a schematic model of SN neutrino fluxes, we study the impact of modified $\bar\nu_e$-$\nu_e$ flux asymmetries on collective flavor conversion. In the parameter space consisting of matter density and effective neutrino density, the region of instability with regard to self-induced flavor conversion is much larger for a vanishing lepton number flux, yet this modification does not intersect a realistic SN profile. Therefore, it appears that, even in the presence of LESA, self-induced flavor conversion remains suppressed below the shock front.

title: Turbulence patterns and neutrino flavor transitions in high-resolution supernova models
abstract: During the shock-wave propagation in a core-collapse supernova (SN), matter turbulence may affect neutrino flavor conversion probabilities. Such effects have been usually studied by adding parametrized small-scale random fluctuations (with arbitrary amplitude) on top of coarse, spherically symmetric matter density profiles. Recently, however, two-dimensional (2D) SN models have reached a space resolution high enough to directly trace anisotropic density profiles, down to scales smaller than the typical neutrino oscillation length. In this context, we analyze the statistical properties of a large set of SN matter density profiles obtained in a high-resolution 2D simulation, focusing on a post-bounce time (2 s) suited to study shock-wave effects on neutrino propagation on scales as small as O(100) km and possibly below. We clearly find the imprint of a broken (Kolmogorov-Kraichnan) power-law structure, as generically expected in 2D turbulence spectra. We then compute the flavor evolution of SN neutrinos along representative realizations of the turbulent matter density profiles, and observe no or modest damping of the neutrino crossing probabilities on their way through the shock wave. In order to check the effect of possibly unresolved fluctuations at scales below O(100) km, we also apply a randomization procedure anchored to the power spectrum calculated frommore » the simulation, and find consistent results within ± 1σ fluctuations. These results show the importance of anchoring turbulence effects on SN neutrinos to realistic, fine-grained SN models.« less

title: Suppression of the multi-azimuthal-angle instability in dense neutrino gas during supernova accretion phase
abstract: It has been recently pointed out that removing the axial symmetry in the "multi-angle effects" associated with the neutrino-neutrino interactions for supernova (SN) neutrinos, a new multi- azimuthal-angle (MAA) instability would arise. In particular, for a flux ordering Fe > Fe > Fx, as expected during the SN accretion phase, this instability occurs in the normal neutrino mass hier- archy. However, during this phase the ordinary matter density can be larger than the neutrino one, suppressing the self-induced conversions. At this regard, we investigate the matter suppression of the MAA effects, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. We compare these results with the numerical solution of the SN neutrino non-linear evolution equations. We find that the large matter term strongly inhibits the MAA effects. In particular, the hindrance becomes stronger including realistic forward- peaked neutrino angular distributions. As a result, in our model for a 10.8 M⊙ iron-core SNe, MAA instability does not trigger any flavor conversion during the accretion phase. Instead, for a 8.8 M⊙ O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, flavor conversions are possible also at early times.