Varying Fundamental Constants: A Dynamical Systems Approach

Abstract

Theory of dynamical systems offers a possibility of investigating the space of all possible solutions. In the context of simple cosmological models such like Varying Speed of Light FriedmanRobertson-Walker (VSL FRW) models there exists a systematic method of reducing field equations to certain two-dimensional dynamical system. One of the features of this reduction is the possibility of representing the model as a Hamiltonian system in which the properties of the potential function V (X) can serve as a tool for qualitative classification of possible evolutions of a(t). Some important features like resolution of the flatness problem, existence of event horizons near the singularity can be visualized as domains on the phase-space. Then one is able to see how large is the class of solutions (labelled by the initial conditions) leading to the desired property.