Classical and quantum aspects of Bianchi type IX cosmological model
A detailed study of the Bianchi type IX cosmological model is done. Classical field equations are discussed with a massive scalar field. The Wheeler-DeWitt quantum equation is formed and is solved using a Born-Oppenheimer type of approximation.

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: 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: 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: 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: 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}).

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: 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: Stability analysis of collective neutrino oscillations in the supernova accretion phase with realistic energy and angle distributions
abstract: We revisit our previous results on the matter suppression of self-induced neutrino flavor conversions during a supernova (SN) accretion phase, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. In our previous numerical study, we used a simplified model based on an isotropic neutrino emission with a single typical energy. Here, we take into account realistic neutrino energy and angle distributions. We find that multi-energy effects have a sub-leading impact in the flavor stability of the SN neutrino fluxes with respect to our previous single-energy results. Conversely, realistic forward-peaked neutrino angular distributions would enhance the matter suppression of the self-induced oscillations with respect to an isotropic neutrino emission. As a result, in our models for iron-core SNe, collective flavor conversions have a negligible impact on the characterization of the observable neutrino signal during the accretion phase. Instead, for a low-mass O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, collective conversions are possible also at early times.

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.