Ikjyot Singh Kohli

Dynamical systems approach to a Bianchi type I viscous magnetohydrodynamic model

We use the expansion-normalized variables approach to study the dynamics of a non-tilted Bianchi Type I cosmological model with both a homogeneous magnetic field and a viscous fluid. In our model the perfect magnetohydrodynamic approximation is made, and both bulk and shear viscous effects are retained. The dynamical system is studied in detail through a fixed-point analysis which determines the local sink and source behavior of the system. We show that the fixed points may be associated with Kasner-type solutions, a flat universe FLRW solution, and interestingly, a new solution to the Einstein Field equations involving non-zero magnetic fields, and non-zero viscous coefficients. It is further shown that for certain values of the bulk and shear viscosity and equation of state parameters, the model isotropizes at late times.

Mathematical issues in eternal inflation

In this paper, we consider the problem of existence and uniqueness of solutions to the Einstein field equations for a spatially flat FLRW universe in the context of stochastic eternal inflation where the stochastic mechanism is modelled by adding a stochastic forcing term representing Gaussian white noise to the Klein-Gordon equation. We show that under these considerations, the Klein-Gordon equation actually becomes a stochastic differential equation. Therefore, the existence and uniqueness of solutions to Einsteins equations depend on whether the coefficients of this stochastic differential equation obey Lipschitz continuity conditions. We show that for any choice of

Dynamics of a closed viscous universe

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Future asymptotic behavior of a nontilted Bianchi type IV viscous model

, the Einstein field equations are not globally well-posed, hence, any solution found to these equations is not guaranteed to be unique. Instead, the coefficients are at best locally Lipschitz continuous in the physical state space of the dynamical variables, which only exist up to a finite explosion time. We further perform Fellers explosion test for an arbitrary power-law inflaton potential and prove that all solutions to the EFE explode in a finite time with probability one. This implies that the mechanism of stochastic inflation thus considered cannot be described to be eternal, since the very concept of eternal inflation implies that the process continues indefinitely. We therefore argue that stochastic inflation based on a stochastic forcing term would not produce an infinite number of universes in some multiverse ensemble. In general, since the Einstein field equations in both situations are not well-posed, we further conclude that the existence of a multiverse via the stochastic eternal inflation mechanism considered in this paper is still very much an open question that will require much deeper investigation.

Stochastic Eternal Inflation in a Bianchi Type I Universe

We use a dynamical systems approach based on the method of orthonormal frames to study the dynamics of a nontilted Bianchi type IX cosmological model with a bulk and shear viscous fluid source. We begin by completing a detailed fixed-point analysis which give the local sinks, sources and saddles of the dynamical system. We then analyze the global dynamics by finding the

The osgood criterion and finite-time cosmological singularities

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Einstein’s field equations as a fold bifurcation

-and

An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game

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On Singularities in Cosmic Inflation

-limit sets which give an idea of the past and future asymptotic behavior of the system. The fixed points were found to be a flat Friedmann-LeMai\ifmmode \hat{}\else \^{}\fi{}tre-Robertson-Walker (FLRW) solution, Bianchi type II solution, Kasner circle, Jacobs disc, Bianchi type

Exploring Vacuum Energy in a Two-Fluid Bianchi Type I Universe

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