A study of thin domain wall with spherical symmetry
It is known that for a thin domain wall the pressure in the perpendicular direction to the wall is negligible. In this paper, we have evaluated solutions for thin domain walls with spherical symmetry following two different approaches. The exact solutions are obtained using functional separability of the metric coefficients.

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: 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: 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: 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: 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: Wilson loops in noncommutative Yang–Mills theory using gauge/gravity duality
abstract: By using the gauge/gravity duality and the Maldacena prescription we compute the expectation values of the Wilson loops in hot, noncommutative Yang–Mills (NCYM) theory in ( 3 + 1 ) dimensions. We consider both the time-like and the light-like Wilson loops. The gravity dual background is given by a particular decoupling limit of non-extremal (D1, D3) bound state of type IIB string theory. We obtain the velocity dependent quark–antiquark potential and numerically study how the dipole length and the potential change with velocity (for 0 v 1 , i.e., the Wilson loop is time-like) of the dipole as well as noncommutativity. We discuss and compare the results with the known commutative results. We also obtain an analytic expression for the screening length when the rapidity is large and the noncommutativity parameter is small with the product remaining small. When v → 1 , the time-like Wilson loop becomes light-like and in that case we obtain the form of the jet quenching parameter for the strongly coupled noncommutative Yang–Mills plasma which matches with our earlier results obtained using different approach.

title: Brownian motion in strongly coupled, anisotropic Yang-Mills plasma: A holographic approach
abstract: We employ methods of gauge/string duality to analyze the Brownian motion and the concomitant Langevin equation of a heavy quark in a strongly coupled, thermal, anisotropic Yang-Mills plasma. We consider fluctuations both along and perpendicular to the direction of anisotropy and study the effects of anisotropy on the drag coefficient, the diffusion constant and the Langevin coefficient for both the directions. We also verify the fluctuation-dissipation theorem for Brownian motion in an anisotropic medium.

title: Eigenvalue problem in two dimensions for an irregular boundary: Neumann condition
abstract: We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (∇2 + k2)$ \psi$ = 0 in two dimensions when the normal derivative of $ \psi$ vanishes on an irregular closed curve. The unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as opposed to earlier schemes where the perturbation parameter is an artificial one. The efficacy of the proposed scheme is gauged by calculating the eigenvalues for elliptical and supercircular boundaries and comparing with the results obtained numerically. We also present a simple and interesting semi-empirical formula, determining the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the Neumann condition for a supercircular boundary. A comparison of the eigenspectrum for several low-lying modes obtained by employing the formula with the corresponding numerical estimates shows good agreement for a wide range of the supercircular exponent.