VACUUM BRANS–DICKE THEORY AND WORMHOLES
This paper deals with vacuum Brans–Dicke theory in an anisotropic Kantowski–Sachs model and Euclidean wormhole solutions have been obtained. The Wheeler–Dewitt (WD) equation has been solved using separable form of the wave function and these solutions have been examined whether wormhole boundary condition due to Hawking is satisfied or not.

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: 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: 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: 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: An eigenvalue problem in two dimensions for an irregular boundary
abstract: An analytical perturbative method is suggested for solving the Helmholtz equation (∇2 + k2)ψ = 0 in two dimensions where ψ vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed.

title: Higgs boson mass, neutrino masses and mixing and keV dark matter in an U(1)R − lepton number model
abstract: A bstractWe discuss neutrino masses and mixing in the framework of a supersymmetric model with an U(1)R symmetry, consisting of a single right handed neutrino superfield with an appropriate R charge. The lepton number (L) of the standard model fermions are identified with the negative of their R-charges. As a result, a subset of leptonic R-parity violating operators can be present and are consistent with the U(1)R symmetry. This model can produce one light Dirac neutrino mass at the tree level without the need of introducing a very small neutrino Yukawa coupling. We analyze the scalar sector of this model in detail paying special attention to the mass of the lightest Higgs boson. One of the sneutrinos might acquire a substantial vacuum expectation value leading to interesting phenomenological consequences. Different sum rules involving the physical scalar masses are obtained and we show that the lightest Higgs boson mass receives a contribution proportional to the square of the neutrino Yukawa coupling f. This allows for a 125 GeV Higgs boson at the tree level for f ~ $ \mathcal{O}(1) $ and still having a small tree level mass for the active neutrino. In order to fit the experimental results involving neutrino masses and mixing angles we introduce a small breaking of U(1)R symmetry, in the context of anomaly mediated supersymmetry breaking. In the presence of this small R-symmetry breaking, light neutrino masses receive contributions at the one-loop level involving the R-parity violating interactions. We also identify the right handed neutrino as a warm dark matter candidate in our model. In the case of R-symmetry breaking, the large f case is characterized by a few hundred MeV lightest neutralino as an unstable lightest supersymmetric particle (LSP) and we brieflydiscuss the cosmological implications of such a scenario.

title: Wilson loops in (p+1)-dimensional Yang–Mills theories using gravity/gauge theory correspondence
abstract: We compute the expectation values of both the time-like and the light-like Wilson loops in a strongly coupled plasma of ( p + 1 ) -dimensional Yang–Mills theories using gravity/gauge theory correspondence. From the time-like Wilson loop we obtain the velocity dependent quark–antiquark potential where the dipole is moving through the plasma with an arbitrary velocity 0 v 1 and also obtain expressions for the screening lengths. When the velocity v → 1 , the Wilson loop becomes light-like and we obtain the form of the jet quenching parameter in those strongly coupled plasma.

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.

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.