Bianchi I cosmological model and the no-boundary condition
A study of the Bianchi I cosmological model is done from both the classical and quantum mechanical points of view. The field equations and their solutions are discussed in the classically forbidden region and classical region. Also the noboundary wave function is evaluated using the concept of microsuperspace and the Hawking-Hartle proposal.

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: 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: Upper limit on the cosmic gamma-ray burst rate from high energy diffuse neutrino background
abstract: We derive upper limits on the ratio f{sub GRB/CCSN}(z){identical_to}R{sub GRB}(z)/R{sub CCSN}(z){identical_to}f{sub GRB/CCSN}(0)(1+z){sup {alpha}}, the ratio of the rate, R{sub GRB}, of long-duration gamma-ray bursts (GRBs) to the rate, R{sub CCSN}, of core-collapse supernovae (CCSNe) in the Universe (z being the cosmological redshift and {), by using the upper limit on the diffuse TeV-PeV neutrino background given by the AMANDA-II experiment in the South Pole, under the assumption that GRBs are sources of TeV-PeV neutrinos produced from decay of charged pions produced in p{gamma} interaction of protons accelerated to ultrahigh energies at internal shocks within GRB jets. For the assumed ''concordance model'' of cosmic star formation rate, R{sub SF}, with R{sub CCSN}(z){proportional_to}R{sub SF}(z), our conservative upper limits are f{sub GRB/CCSN}(0){ =}1, already more restrictive than) the current upper limit on this ratio inferred from other astronomical considerations, thus providing a useful independent probe of and constraint on the CCSN-GRB connection. Nondetection of a diffuse TeV-PeV neutrino background by the upcoming IceCube detector in the South Pole after three years of operation, for example, will bring down the upper limit on f{sub GRB/CCSN}(0)more » to below a few x10{sup -5} level, while a detection will confirm the hypothesis of proton acceleration to ultrahigh energies in GRBs and will potentially also yield the true rate of occurrence of these events in the Universe.« less

title: 7 keV sterile neutrino dark matter in U(1)R-lepton number model
abstract: A bstractWe study the phenomenology of a keV sterile neutrino in a supersymmetric model with U(1)R-lepton number in the light of a very recent observation of an X-ray line signal at around 3.5 keV, detected in the X-ray spectra of Andromeda galaxy and various galaxy clusters including the Perseus galaxy cluster. This model not only provides a small tree level mass to one of the active neutrinos but also renders a suitable warm dark matter candidate in the form of a sterile neutrino with negligible active-sterile mixing. Light neutrino masses and mixing can be explained once one-loop radiative corrections are taken into account. The scalar sector of this model can accommodate a Higgs boson with a mass of ∼125 GeV. In this model gravitino is the lightest supersymmetric particle (LSP) and we also study the cosmological implications of this light gravitino with mass ∼OGeV$$ \sim \mathcal{O}\left(\mathrm{GeV}\right) $$.

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: 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: Non-standard interaction in neutrino oscillations and recent Daya Bay, T2K experiments
abstract: We study the possible constraints on non-standard interaction(NSIs) in a model independent way by considering the recent results from T2K and Daya Bay neutrino oscillations experiments. Using perturbation method we present generic formulas (suitable for T2K baseline and for large $\theta_{13}$ as evident from Daya Bay) for the probability of oscillation for $\nu_\mu \rightarrow \nu_e$, taking into account NSIs at source ($\epsilon^s$), detector ($\epsilon^d$) and during propagation ($\epsilon^m$) of neutrinos through matter. Two separate cases of perturbation with small (slightly large) NSI ($\epsilon_{\alpha\beta}^m \sim 0.03(0.18)$) are discussed in detail. Using various possible presently allowed NSI values we reanalyze numerically the $\theta_{13} - \delta$ allowed region given by recent T2K experimental data. We obtain model independent constraints on NSIs in the $\delta-\epsilon_{\alpha\beta}^m$ plane using the $\theta_{13}$ value as measured by Daya Bay, where $\delta$ is the CP violating phase. Depending on $\delta$ values significant constraints on $\epsilon_{e\tau}$ and $\epsilon_{\tau\tau}$, in particular, are possible for both hierarchies of neutrino masses. Corresponding to T2K's 66% confidence level result, the constraints on $\epsilon_{\tau\tau}$ is shown to be independent of any $\delta$ value.