Dynamical System Approach to Cosmological Models with a Varying Speed of Light

TL;DR

This paper applies dynamical systems methods to analyze cosmological models with a varying speed of light, revealing solutions that address horizon and flatness problems, and exploring quantum tunneling effects.

Contribution

It introduces two reduction methods to planar Hamiltonian systems for VSL cosmologies with dynamic equations of state, enabling detailed phase space analysis.

Findings

Models with negative curvature solve horizon and flatness problems.

New evolution types near the initial singularity caused by VSL.

Highest tunnelling rate occurs for constant speed of light when c(a) ∝ a^n with -1 < n ≤ 0.

Abstract

Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state. The solutions are analyzed on two-dimensional phase space in the variables $(x, \dot{x})$ where $x$ is a function of a scale factor $a$. Then we show how the horizon problem may be solved on some evolutional paths. It is shown that the models with negative curvature overcome the horizon and flatness problems. The presented method of reduction can be adopted to the analysis of dynamics of the universe with the general form of the equation of state $p=\gamma(a)\epsilon$. This is demonstrated using as an example the dynamics of VSL models filled with a non-interacting fluid. We demonstrate a new type of evolution near the initial singularity caused by a varying speed of light. The singularity-free oscillating universes are also admitted for positive cosmological constant. We consider a quantum VSL FRW closed model with radiation and show that the highest tunnelling rate occurs for a constant velocity of light if $c(a) \propto a^n$ and $-1 < n \le 0$. It is also proved that the considered class of models is structurally unstable for the case of $n < 0$.