Exact solutions of Brans-Dicke cosmology with decaying vacuum density

TL;DR

This paper explores exact solutions in Brans-Dicke cosmology where vacuum energy and gravitational constant decay with the Hubble parameter, addressing the cosmological constant problem and the cosmic coincidence issue.

Contribution

It presents new exact solutions with decaying vacuum and gravitational constant, including models consistent with observations and solutions addressing the coincidence problem.

Findings

Models with constant deceleration match observed matter density and universe age.

Some solutions predict future singularities like big-rip.

One solution offers a potential explanation for the cosmic coincidence problem.

Abstract

We investigate cosmological solutions of Brans-Dicke theory with both the vacuum energy density and the gravitational constant decaying linearly with the Hubble parameter. A particular class of them, with constant deceleration factor, sheds light on the cosmological constant problems, leading to a presently small vacuum term, and to a constant ratio between the vacuum and matter energy densities. By fixing the only free parameter of these solutions, we obtain cosmological parameters in accordance with observations of both the relative matter density and the universe age. In addition, we have three other solutions, with Brans-Dicke parameter w = -1 and negative cosmological term, two of them with a future singularity of big-rip type. Although interesting from the theoretical point of view, two of them are not in agreement with the observed universe. The third one leads, in the limit of large times, to a constant relative matter density, being also a possible solution to the cosmic coincidence problem.