Motion of test particles around monopoles
We present a detailed analysis of the motion of test particles around gauge and global monopoles using the Hamilton-Jacobi (HJ) formalism. We find that particles cannot be trapped by gauge monopoles while there may exist bound orbits for global monopoles under certain conditions.

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: 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: 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: No collective neutrino flavor conversions during the supernova accretion phase.
abstract: We perform a dedicated study of the supernova (SN) neutrino flavor evolution during the accretion phase, using results from recent neutrino radiation hydrodynamics simulations. In contrast to what was expected in the presence of only neutrino-neutrino interactions, we find that the multiangle effects associated with the dense ordinary matter suppress collective oscillations. The matter suppression implies that neutrino oscillations will start outside the neutrino decoupling region and therefore will have a negligible impact on the neutrino heating and the explosion dynamics. Furthermore, the possible detection of the next galactic SN neutrino signal from the accretion phase, based on the usual Mikheyev-Smirnov-Wolfenstein effect in the SN mantle and Earth matter effects, can reveal the neutrino mass hierarchy in the case that the mixing angle θ(13) is not very small.

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.

title: Multi-azimuthal-angle instability for different supernova neutrino fluxes
abstract: It has been recently discovered 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 trigger flavor conversions in addition to the ones caused by the bimodal and multi-zenith-angle (MZA) instabilities. We investigate the dependence of the MAA instability on the original SN neutrino fluxes, performing a stability analysis of the linearized neutrino equations of motion. We compare these results with the numerical evolution of the SN neutrino non-linear equations, looking at a local solution along a specific line of sight, under the assumption that the transverse variations of the global solution are small. We also assume that self-induced conversions are not suppressed by large matter effects. We show that the pattern of the spectral crossings (energies where F_{\nu_e} = F_{\nu_x}, and F_{\bar\nu_e} = F_{\bar\nu_x}) is crucial in determining the impact of MAA effects on the flavor evolution. For neutrino spectra with a strong excess of \nu_e over \bar\nu_e, presenting only a single-crossing, MAA instabilities would trigger new flavor conversions in normal mass hierarchy. In our simplified flavor evolution scheme, these would lead to spectral swaps and splits analogous to what produced in inverted hierarchy by the bimodal instability. Conversely, in the presence of spectra with a moderate flavor hierarchy, having multiple crossing energies, MZA effects would produce a sizable delay in the onset of the flavor conversions, inhibiting the growth of the MAA instability. In this case the splitting features for the oscillated spectra in both the mass hierarchies are the ones induced by the only bimodal and MZA effects.

title: Stringent constraint on neutrino Lorentz-invariance violation from the two IceCube PeV neutrinos
abstract: LAPTh,  As a consequence, particles may not travel at the universal speed of light. Inparticular, superluminal extragalactic neutrinos would rapidly lose energy via the bremssthralung ofelectron-positron pairs (ν → ν e

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.