Gravitational collapse in higher dimensional Husain space–time
We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure p and density ρ are related by the following relations (i) p  =  kρ, (ii) $$p = k\rho - \frac{B(v)}{\rho^{\alpha}}$$ (variable modified Chaplygin) and (iii) p  =  kρα (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters k and B namely, (i) k  =  0, B  =  constant (generalized Chaplygin), (ii) B  =  constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space–time is done.

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: 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: 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: 7 keV sterile neutrino dark matter in U(1)R-lepton number model
abstract: A bstractWe study the phenomenology of a keV sterile neutrino in a supersymmetric model with U(1)R-lepton number in the light of a very recent observation of an X-ray line signal at around 3.5 keV, detected in the X-ray spectra of Andromeda galaxy and various galaxy clusters including the Perseus galaxy cluster. This model not only provides a small tree level mass to one of the active neutrinos but also renders a suitable warm dark matter candidate in the form of a sterile neutrino with negligible active-sterile mixing. Light neutrino masses and mixing can be explained once one-loop radiative corrections are taken into account. The scalar sector of this model can accommodate a Higgs boson with a mass of ∼125 GeV. In this model gravitino is the lightest supersymmetric particle (LSP) and we also study the cosmological implications of this light gravitino with mass ∼OGeV$$ \sim \mathcal{O}\left(\mathrm{GeV}\right) $$.

title: Non-standard interaction in neutrino oscillations and recent Daya Bay, T2K experiments
abstract: We study the possible constraints on non-standard interaction(NSIs) in a model independent way by considering the recent results from T2K and Daya Bay neutrino oscillations experiments. Using perturbation method we present generic formulas (suitable for T2K baseline and for large $\theta_{13}$ as evident from Daya Bay) for the probability of oscillation for $\nu_\mu \rightarrow \nu_e$, taking into account NSIs at source ($\epsilon^s$), detector ($\epsilon^d$) and during propagation ($\epsilon^m$) of neutrinos through matter. Two separate cases of perturbation with small (slightly large) NSI ($\epsilon_{\alpha\beta}^m \sim 0.03(0.18)$) are discussed in detail. Using various possible presently allowed NSI values we reanalyze numerically the $\theta_{13} - \delta$ allowed region given by recent T2K experimental data. We obtain model independent constraints on NSIs in the $\delta-\epsilon_{\alpha\beta}^m$ plane using the $\theta_{13}$ value as measured by Daya Bay, where $\delta$ is the CP violating phase. Depending on $\delta$ values significant constraints on $\epsilon_{e\tau}$ and $\epsilon_{\tau\tau}$, in particular, are possible for both hierarchies of neutrino masses. Corresponding to T2K's 66% confidence level result, the constraints on $\epsilon_{\tau\tau}$ is shown to be independent of any $\delta$ value.

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: Wess-Zumino-Witten Model for Galilean Conformal Algebra
abstract: In this note, we construct a Wess–Zumino–Witten model based on the Galilean conformal algebra in two-spacetime dimensions, which is a nonrelativistic analogue of the relativistic conformal algebra. We obtain exact background corresponding to σ-models in six dimensions (the dimension of the group manifold) and a central charge c = 6. We carry out a Sugawara type construction to verify the conformal invariance of the model. Further, we discuss the feasibility of the background obtained as a physical spacetime metric.

title: Testing Lorentz invariance with neutrino bursts from supernova neutronization
abstract: Quantum-gravity (QG) effects might generate Lorentz invariance violation by the interaction of energetic particles with the foamy structure of the space-time. As a consequence, particles may not travel at the universal speed of light. We propose to constrain Lorentz invariance violation for energetic neutrinos exploiting the $\nu_e$ neutronization burst from the next galactic supernova (SN). This prompt signal is expected to produce a sharp peak in the SN $\nu_e$ light curve with a duration of $\sim 25$ ms. However presence of energy-dependent Lorentz invariance violation would significantly spread out the time structure of this signal. We find that the detection the SN $\nu_e$ burst from a typical galactic explosion at $d=10$ kpc in a Mton-class water Cerenkov detector, would be sensitive to a quantum-gravity mass scale $M_{\rm QG} \sim 10^{12}$ GeV ($2 \times10^{5}$ GeV) for the linear (quadratic) energy dependence of Lorentz invariance violation. These limits are rather independent of the neutrino mass hierarchy and whether the neutrino velocity is super or subluminal.