BIANCHI TYPE I COSMOLOGIES WITH THE DARK MATTER IN THE BACKGROUND OF DARK ENERGY
This paper deals with the cosmological study of the Bianchi type I model made of dust fluid in the background of dark energy. Cosmological solutions are obtained for the following four cases: (i) only with dark matter; (ii) only with dark energy; (iii) both dark matter and dark energy are present but without interaction; (iv) interactive dark matter and dark energy.

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: 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: 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: The LBNO long-baseline oscillation sensitivities with two conventional neutrino beams at different baselines
abstract: The proposed Long Baseline Neutrino Observatory (LBNO) initially consists of $\sim 20$ kton liquid double phase TPC complemented by a magnetised iron calorimeter, to be installed at the Pyh\"asalmi mine, at a distance of 2300 km from CERN. The conventional neutrino beam is produced by 400 GeV protons accelerated at the SPS accelerator delivering 700 kW of power. The long baseline provides a unique opportunity to study neutrino flavour oscillations over their 1st and 2nd oscillation maxima exploring the $L/E$ behaviour, and distinguishing effects arising from $\delta_{CP}$ and matter. In this paper we show how this comprehensive physics case can be further enhanced and complemented if a neutrino beam produced at the Protvino IHEP accelerator complex, at a distance of 1160 km, and with modest power of 450 kW is aimed towards the same far detectors. We show that the coupling of two independent sub-MW conventional neutrino and antineutrino beams at different baselines from CERN and Protvino will allow to measure CP violation in the leptonic sector at a confidence level of at least $3\sigma$ for 50\% of the true values of $\delta_{CP}$ with a 20 kton detector. With a far detector of 70 kton, the combination allows a $3\sigma$ sensitivity for 75\% of the true values of $\delta_{CP}$ after 10 years of running. Running two independent neutrino beams, each at a power below 1 MW, is more within today's state of the art than the long-term operation of a new single high-energy multi-MW facility, which has several technical challenges and will likely require a learning curve.

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: Stringent constraint on neutrino Lorentz-invariance violation from the two IceCube PeV neutrinos
abstract: LAPTh,  As a consequence, particles may not travel at the universal speed of light. Inparticular, superluminal extragalactic neutrinos would rapidly lose energy via the bremssthralung ofelectron-positron pairs (ν → ν e

title: Wess-Zumino-Witten Model for Galilean Conformal Algebra
abstract: In this note, we construct a Wess–Zumino–Witten model based on the Galilean conformal algebra in two-spacetime dimensions, which is a nonrelativistic analogue of the relativistic conformal algebra. We obtain exact background corresponding to σ-models in six dimensions (the dimension of the group manifold) and a central charge c = 6. We carry out a Sugawara type construction to verify the conformal invariance of the model. Further, we discuss the feasibility of the background obtained as a physical spacetime metric.

title: Stability analysis of collective neutrino oscillations in the supernova accretion phase with realistic energy and angle distributions
abstract: We revisit our previous results on the matter suppression of self-induced neutrino flavor conversions during a supernova (SN) accretion phase, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. In our previous numerical study, we used a simplified model based on an isotropic neutrino emission with a single typical energy. Here, we take into account realistic neutrino energy and angle distributions. We find that multi-energy effects have a sub-leading impact in the flavor stability of the SN neutrino fluxes with respect to our previous single-energy results. Conversely, realistic forward-peaked neutrino angular distributions would enhance the matter suppression of the self-induced oscillations with respect to an isotropic neutrino emission. As a result, in our models for iron-core SNe, collective flavor conversions have a negligible impact on the characterization of the observable neutrino signal during the accretion phase. Instead, for a low-mass O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, collective conversions are possible also at early times.