The cosmic coincidence in Brans-Dicke cosmologies

TL;DR

This paper explores a Brans-Dicke cosmological model with a decaying vacuum energy density, proposing a solution to the cosmic coincidence problem by naturally maintaining a constant matter-to-vacuum energy ratio.

Contribution

It introduces a late-time solution in an effective Brans-Dicke framework where the matter and vacuum energy densities remain proportional, addressing the cosmic coincidence problem.

Findings

Relative matter density ranges from 0.25 to 0.4.

For Ht=1, matter density is approximately 1/3.

The model aligns with observed universe age constraints.

Abstract

Among the suggested solutions to the cosmological constant problem, we find the idea of a dynamic vacuum, with an energy density decaying with the universe expansion. We investigate the possibility of a variation in the gravitational constant as well, induced, at the cosmological scale, by the vacuum decay. We consider an effective Brans-Dicke theory in the spatially flat FLRW spacetime, finding late time solutions characterized by a constant ratio between the matter and vacuum energy densities. By using the observed limits for the universe age, we fix the only free parameter of our solutions, obtaining a relative matter density in the range 0.25-0.4. In particular, for Ht = 1 we obtain a relative matter density equals to 1/3. This constitutes a possible explanation for another problem related to the cosmological term, the cosmic coincidence problem.