Interacting Holographic Dark Energy Model as a Dynamical system and the Coincidence Problem
We examine the evolution of a holographic cosmological model with future event horizon as the infrared cut-off and dark matter and dark energy do not evolve independently $-$ there is interaction between them. The basic evolution equations are reduced to an autonomous system and corresponding phase space is analyzed.

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: 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: 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: 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: 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: 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: Optimised sensitivity to leptonic CP violation from spectral information: the LBNO case at 2300 km baseline
abstract: One of the main goals of the Long Baseline Neutrino Observatory (LBNO) is to study the $L/E$ behaviour (spectral information) of the electron neutrino and antineutrino appearance probabilities, in order to determine the unknown CP-violation phase $\delta_{CP}$ and discover CP-violation in the leptonic sector. The result is based on the measurement of the appearance probabilities in a broad range of energies, covering t he 1st and 2nd oscillation maxima, at a very long baseline of 2300 km. The sensitivity of the experiment can be maximised by optimising the energy spectra of the neutrino and anti-neutrino fluxes. Such an optimisation requires exploring an extended range of parameters describing in details the geometries and properties of the primary protons, hadron target and focusing elements in the neutrino beam line. In this paper we present a numerical solution that leads to an optimised energy spectra and study its impact on the sensitivity of LBNO to discover leptonic CP violation. In the optimised flux both 1st and 2nd oscillation maxima play an important role in the CP sensitivity. The studies also show that this configuration is less sensitive to systematic errors (e.g. on the total event rates) than an experiment which mainly relies on the neutrino-antineutrino asymmetry at the 1st maximum to determine the existence of CP-violation.

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: Suppression of the multi-azimuthal-angle instability in dense neutrino gas during supernova accretion phase
abstract: It has been recently pointed out that removing the axial symmetry in the "multi-angle effects" associated with the neutrino-neutrino interactions for supernova (SN) neutrinos, a new multi- azimuthal-angle (MAA) instability would arise. In particular, for a flux ordering Fe > Fe > Fx, as expected during the SN accretion phase, this instability occurs in the normal neutrino mass hier- archy. However, during this phase the ordinary matter density can be larger than the neutrino one, suppressing the self-induced conversions. At this regard, we investigate the matter suppression of the MAA effects, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. We compare these results with the numerical solution of the SN neutrino non-linear evolution equations. We find that the large matter term strongly inhibits the MAA effects. In particular, the hindrance becomes stronger including realistic forward- peaked neutrino angular distributions. As a result, in our model for a 10.8 M⊙ iron-core SNe, MAA instability does not trigger any flavor conversion during the accretion phase. Instead, for a 8.8 M⊙ O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, flavor conversions are possible also at early times.