Emergent universe in Hor̆ava gravity
Recently Hor̆ava has proposed a non-relativistic renormalisable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein’s gravity at large distances with a non-vanishing cosmological constant but with improved UV behaviour. In this paper, we have considered the Friedman-Lemaître-Robertson-Walker cosmological model in Hor̆ava gravity and the emergent scenario for all values of the spatial curvature k (=0,±1) has been studied. As a result, there are constraints on the parameters involved.

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: 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: 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: 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: Calculating the jet quenching parameter in the plasma of NCYM theory from gauge/gravity duality
abstract: A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in ($3+1$) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as ${T}^{7}$ for fixed noncommutativity and fixed 't Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.

title: Collective flavor oscillations of supernova neutrinos and r-process nucleosynthesis
abstract: Neutrino-neutrino interactions inside core-collapse supernovae may give rise to collective flavor oscillations resulting in swap between flavors. These oscillations depend on the initial energy spectra, and relative fluxes or relative luminosities of the neutrinos. It has been observed that departure from energy equipartition among different flavors can give rise to one or more sharp spectral swap over energy, termed as splits. We study the occurrence of splits in the neutrino and antineutrino spectra, varying the initial relative fluxes for different models of initial energy spectrum, in both normal and inverted hierarchy. These initial relative flux variations give rise to several possible split patterns whereas variation over different models of energy spectra give similar results. We explore the effect of these spectral splits on the electron fraction, Ye, that governs r-process nucleosynthesis inside supernovae. Since spectral splits modify the electron neutrino and antineutrino spectra in the region where r-process is postulated to happen, and since the pattern of spectral splits depends on the initial conditions of the spectra and the neutrino mass hierarchy, we show that the condition Ye < 0.5 required for successful r-process nucleosynthesis will lead to constraints on the initial spectral conditions, for a given neutrino mass hierarchy.

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: 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.

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.