Exact solutions of Brans–Dicke cosmology with decaying vacuum density

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 ω = −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.

Modified Brans–Dicke theory in arbitrary dimensions

“…We should also note that in [17], the inducing procedure has been started from a very general BD field equations, rather than the vacuum space-time. 3 For example, assuming the BD coupling parameter ω as a function of the time [20], or introducing a time-dependent cosmological term [21] and/or adding a particular kind of scalar potential to the Lagrangian (or without considering any scalar potential) by assuming a fluid with dissipative pressure [22,23]. Further, in [24], the authors derived the accelerating universe in the BD theory by assuming a scalar potential compatible with the power-law expansion of the universe.…”

Expansion history with decaying vacuum: a complete cosmological scenario

“…Λ = Λ(t). There are a number of interesting Λ-variable models in the old literature (Ozer & Taha 1986, 1987Bertolami 1986;Freese et al 1987;Peebles & Ratra 1988;Carvalho, Lima & Waga 1992;Lima & Maia 1994;Lima 1996;Lima & Trodden 1996;Overduin & Cooperstock 1998) and even more recently (Shapiro & Solà 2000;Shapiro & Solà 2002;Alcaniz & Maia 2003;Opher & Pellison 2004;Bauer 2005;Carneiro & Lima 2005;Alcaniz & Lima 2005;Barrow & Clifton 2006;Montenegro & Carneiro 2007;Shapiro & Solà 2009;Solà &Štefančić 2005Solà &Štefančić , 2006Basilakos 2009;Solà 2011 and references therein). The functional form of Λ(t) in most of them has usually been proposed on phenomenological grounds, as it occurs with the vast majority of DE models (Carvalho et al 2006).…”

Noncommutative minisuperspace, gravity-driven acceleration, and kinetic inflation

“…At a classical level, to obtain results in agreement with observational data, for an early as well as a late time universe, other extended versions of the BD theory (scalartensor theories) have been applied. In these theories, in contrary to the standard version of the BD theory, it has been assumed that either the BD coupling parameter should be a general function of the BD scalar field [3], and/or a scalar potential [4] (which is also a function of * Electronic address: mrasouli@ubi.pt † Electronic address: pmoniz@ubi.pt φ) must be added by hand. 1 It is also established that the BD theory not only can provide observational consequences to convince the original aims of the theory, but also it is possible to construct interesting quantum cosmological models, which may present appropriate scenarios to study the inflationary universe [7,8].…”