Is emergent universe a consequence of particle creation process
A model of an emergent universe is formulated using the mechanism of particle creation. Here the universe is considered as a non-equilibrium thermodynamical system with dissipation due to particle creation mechanism. The universe is chosen as spatially flat FRW space–time and the cosmic substratum is chosen as perfect fluid with barotropic equation of state. Both first and second order deviations from equilibrium prescription are considered and it is found that the scenario of emergent universe is possible in both the cases.

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: 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: 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: 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: 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.

title: Interpreting the bounds on Dark Matter induced muons at Super-Kamiokande in the light of CDMS data

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.