An entropy-driven cosmic expansion

Abstract

We examine the evolution of the Friedman Universe within our recent model of space-time identified with an elastic continuous medium whose deformations are described by a vector field constrained to obey a generalized four-dimensional version of the equilibrium equations of standard elasticity. It is found that the demand that the entropy associated with such elastic deformations be always extremal during the expansion of such a Universe turns these equilibrium equations into a single differential equation governing the evolution of the Hubble parameter H. The solution to the resulting dynamics admits both a power-law expansion, analogous to the one induced by an inflaton field, as well as a power-law expansion analogous to the one induced by a phantom field. Analyzing both types of expansions via the induced elastic energy and pressure permits to assign the former to the early Universe and the latter to its late-time expansion. It is argued, however, that the present model does not exclude a phantom-like inflation for the early Universe. We discuss the possible way for the dynamics to avoid the Big Rip singularity that would otherwise result. We succinctly discuss the possible way to avoid also the Big Bang singularity and how to obtain the large scale structure of the Universe from the present model.