Raychaudhuri Equation in an Anisotropic Universe with Anisotropic Sources

In this paper we investigate the fate of the universe with an anisotropic background sourced by anisotropic matter. We see the behaviour of the Raychaudhuri Equation and investigate wheather a congrurence of time like geodesics focus to a point in a universe with Bianchi I background which is dictated by anisotropic sources like cosmic strings, domain walls, magnetic field and lorentz violating magnetic field each separately. Thus, Focussing theorem has been checked both for initially contracting and diverging universe with each of these anisotropic sources.Comment: 6 pages, 10 figure

Energetics of complex phase diagram in a tunable bilayer graphene probed by quantum capacitance

Bilayer graphene provides a unique platform to explore the rich physics in quantum Hall effect. The unusual combination of spin, valley and orbital degeneracy leads to interesting symmetry broken states with electric and magnetic field. Conventional transport measurements like resistance measurements have been performed to probe the different ordered states in bilayer graphene. However, not much work has been done to directly map the energetics of those states in bilayer graphene. Here, we have carried out the magneto capacitance measurements with electric and magnetic field in a hexagonal boron nitride encapsulated dual gated bilayer graphene device. At zero magnetic field, using the quantum capacitance technique we measure the gap around the charge neutrality point as a function of perpendicular electric field and the obtained value of the gap matches well with the theory. In presence of perpendicular magnetic field, we observe Landau level crossing in our magneto-capacitance measurements with electric field. The gap closing and reopening of the lowest Landau level with electric and magnetic field shows the transition from one ordered state to another one. Further more we observe the collapsing of the Landau levels near the band edge at higher electric field ($\bar D > 0.5$ V/nm), which was predicted theoretically. The complete energetics of the Landau levels of bilayer graphene with electric and magnetic field in our experiment paves the way to unravel the nature of ground states of the system

Pre-inflationary dynamics in loop quantum cosmology: Power-law potentials

In this paper, we study the pre-inflationary dynamics for the power-law potential $(V(\phi) \propto \phi^n)$ with $n<2$ in the framework of loop quantum cosmology. In the case where the kinetic energy of the inflaton dominates at the initial, the evolution of the universe can always be divided into three different phases prior to preheating: {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution of the expansion factor is independent not only on the initial conditions but also the inflationary potentials, and is given explicitly by an analytical solution. In contrast, for the potential energy dominated initial conditions, this universality is lost. We also obtain total number of e-folds during the slow-roll inflation, whereby physically viable models are identified. In addition, we present phase space analysis for the inflationary potentials under consideration and compare our results with the ones obtained previously for different potentials.Comment: revtex4, 11 figure and 4 tables. Some typos are corrected, and new references are added. Phys. Rev. D96 (2017) 12353