The cosmic coincidence in Brans–Dicke cosmologies

Abstract

Among the suggested solutions to the cosmological constant problem, we nd 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 e ective Brans{Dicke theory in the spatially at FLRW spacetime, nding 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 x the only free parameter of our solutions, obtaining a relative matter density in the range 0:25 < m < 0:4. In particular, for Ht = 1 we obtain m = 1=3. This constitutes a possible explanation for another problem related to the cosmological term, the cosmic coincidence problem.