A DYNAMICAL SYMMETRY OF THE QUASI-SPHERICAL (OR SPHERICAL) COLLAPSE
By linearly scaling the initial data set (mass and kinetic energy functions), it is found that the dynamics of quasi-spherical (or spherical) collapse remains invariant for dust or a general (Type I) matter field, provided the comoving radius is also appropriately scaled. This defines a symmetry of the quasi spherical (or spherical) collapse. That is, the linear transformation identifies an equivalence class of data sets which lead to the same end result as well as its evolution all through. In particular, it is shown that the physical parameters, density and shear remain invariant. What the transformation is exhibiting is an interesting scaling relationship between mass, kinetic energy and the size of the collapsing sphere which is respected not only by the initial data set but remarkably also by the dynamics of collapse.

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: 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: 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: 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: 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: Interpreting the bounds on Dark Matter induced muons at Super-Kamiokande in the light of CDMS data

title: On the Observability of Collective Flavor Oscillations in Diffuse Supernova Neutrino Background
abstract: Collective flavor oscillations are known to bring multiple splits in the supernova (SN) neutrino and antineutrino spectra. These spectral splits depend not only on the mass hierarchy of the neutrinos but also on the initial relative flux composition. Observation of spectral splits in a future galactic supernova signal is expected to throw light on the mass hierarchy pattern of the neutrinos. However, since the Diffuse Supernova Neutrino Background (DSNB) comprises of a superposition of neutrino fluxes from all past supernovae, and since different supernovae are expected to have slightly different initial fluxes, it is pertinent to check if the hierarchy dependent signature of collective oscillations can survive this averaging of the flux spectra. Since the actual distribution of SN with initial relative flux spectra of the neutrinos and antineutrinos is unknown, we assume a log-normal distribution for them. We study the dependence of the hierarchy sensitivity to the mean and variance of the log-normal distribution function. We find that the hierarchy sensitivity depends crucially on the mean value of the relative initial luminosity. The effect of the width is to reduce the hierarchy sensitivity for all values of the mean initial relative luminosity. We find that in the very small mixing angle ( θ 13 ) limit considering only statistical errors even for very moderate values of variance, there is almost no detectable hierarchy sensitivity if the mean relative luminosities of ν e and ν ¯ e are greater than 1.

title: Probing the neutrino mass hierarchy with the rise time of a supernova burst
abstract: The rise time of a Galactic supernova (SN) bar-nue lightcurve, observable at a high-statistics experiment such as the IceCube Cherenkov detector, can provide a diagnostic tool for the neutrino mass hierarchy at "large" 1-3 leptonic mixing angle theta_13. Thanks to the combination of matter suppression of collective effects at early postbounce times on one hand and the presence of the ordinary Mikheyev-Smirnov-Wolfenstein effect in the outer layers of the SN on the other hand, a sufficiently fast rise time on O(100) ms scale is indicative of an inverted mass hierarchy. We investigate results from an extensive set of stellar core-collapse simulations, providing a first exploration of the astrophysical robustness of these features. We find that for all the models analyzed (sharing the same weak interaction microphysics) the rise times for the same hierarchy are similar not only qualitatively, but also quantitatively, with the signals for the two classes of hierarchies significantly separated. We show via Monte Carlo simulations that the two cases should be distinguishable at IceCube for SNe at a typical Galactic distance 99% of the times. Finally, a preliminary survey seems to show that the faster rise time for inverted hierarchy as compared to normal hierarchy is a qualitatively robust feature predicted by several simulation groups. Since the viability of this signature ultimately depends on the quantitative assessment of theoretical/numerical uncertainties, our results motivate an extensive campaign of comparison of different code predictions at early accretion times with implementation of microphysics of comparable sophistication, including effects such like nucleon recoils in weak interactions.

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.

title: Analysis of matter suppression in collective neutrino oscillations during the supernova accretion phase
abstract: The usual description of self-induced neutrino flavor conversions in core collapse supernovae (SNe) is based on the dominance of the neutrino density n_nu over the net electron density n_e. However, this condition is not met during the post-bounce accretion phase, when the dense matter in a SN is piled up above the neutrinosphere. As recently pointed-out, a dominant matter term in the anisotropic SN environment would dephase the flavor evolution for neutrinos traveling on different trajectories, challenging the occurrence of the collective behavior in the dense neutrino gas. Using the results from recent long term simulations of core-collapse SN explosions, based on three flavor Boltzmann neutrino transport in spherical symmetry, we find that both the situations of complete matter suppression (when n_e >> n_nu) and matter-induced decoherence (when n_e \gtrsim n_nu) of flavor conversions are realized during the accretion phase. The matter suppression at high densities prevents any possible impact of the neutrino oscillations on the neutrino heating and hence on the dynamics of the explosion. Furthermore, it changes the interpretation of the Earth matter effect on the SN neutrino signal during the accretion phase, allowing the possibility of the neutrino mass hierarchy discrimination at not too small values of the leptonic mixing angle \theta_{13} (i.e. \sin^2{\theta}_{13} \gtrsim 10^{-3}).