Schwarzschild Solution on the Brane
In this paper it is shown that Schwarzschild solution is possible in brane world for some specific choices of brane matter and the non-local effects from the bulk. A conformally flat bulk space time with fine-tuned vacuum energy (brane tension) shows that Schwarzschild solution may also be the vacuum solution for brane world scenario.

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: 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: Constraining scalar singlet dark matter with CDMS, XENON and DAMA and prediction for direct detection rates
abstract: We consider a simplest extension of the Standard Model (SM) through the incorporation of a real scalar singlet and an additional discrete Z2 symmetry. The model admits the neutral scalar singlet to be stable and thus, a viable component of dark matter. We explore the parameter space of the model keeping in view the constraints arise from different dark matter direct detection experiments through WIMP -nucleon scattering. First of all, we have utilised the data obtained from CDMS, XENON-10 and XENON-100 collaborations. We further constraint the parameter space from the DAMA collaboration results (both with and without channelling) and CoGeNT collaboration results. Throughout our analysis, the constraint arises due to the observed relic density of dark matter reported by WMAP experiment, is also incorporated. Utilising all those constraints, on the model parameter space, we calculate the event rates and the annual variation of event rates in the context of a Liquid Argon Detector experiment.

title: Optimised sensitivity to leptonic CP violation from spectral information: the LBNO case at 2300 km baseline
abstract: One of the main goals of the Long Baseline Neutrino Observatory (LBNO) is to study the $L/E$ behaviour (spectral information) of the electron neutrino and antineutrino appearance probabilities, in order to determine the unknown CP-violation phase $\delta_{CP}$ and discover CP-violation in the leptonic sector. The result is based on the measurement of the appearance probabilities in a broad range of energies, covering t he 1st and 2nd oscillation maxima, at a very long baseline of 2300 km. The sensitivity of the experiment can be maximised by optimising the energy spectra of the neutrino and anti-neutrino fluxes. Such an optimisation requires exploring an extended range of parameters describing in details the geometries and properties of the primary protons, hadron target and focusing elements in the neutrino beam line. In this paper we present a numerical solution that leads to an optimised energy spectra and study its impact on the sensitivity of LBNO to discover leptonic CP violation. In the optimised flux both 1st and 2nd oscillation maxima play an important role in the CP sensitivity. The studies also show that this configuration is less sensitive to systematic errors (e.g. on the total event rates) than an experiment which mainly relies on the neutrino-antineutrino asymmetry at the 1st maximum to determine the existence of CP-violation.

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: 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: 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