General relativity in hyperextended chaotic inflation

Abstract

We address the question of whether general relativity (GR) is an “attractor” in a universe governed by hyperextended chaotic inflation (HCI). HCI results from the combination of chaotic inflation and a theory of gravity that is equivalent to Brans-Dicke (BD) gravity within the horizon scale. Globally it differs from BD gravity in that ω is a dynamical parameter that depends on the BD field Φ. As is well known, GR is recovered from BD gravity in the limit ω → ∞ and large values of Φ. A substantial difficulty in studying HCI is to find and adequate model for the functional dependence of ω. In this paper we employ the analogy between the BD field in HCI and the dilaton field in string theory to construct an ansatz for ω(Φ). The string theory analogy is based on the principle of least coupling of Polyakov and Damour which states that the dilaton and metric fields decouple asymptotically. Based on this principle, we investigate the question of whether a large value of ω is predominant in most regions of the universe, which would then lead to the conclusion that the theory of gravity in a typical region is GR, in other words, that GR is an “attractor”. Previous authors have come up with an affirmative answer to this question, in the case Φ < ∞. We find that the resulting scenario is in fact more complex. We show that, whereas it is indeed possible to concoct inflaton potentials for which GR is a typical theory, this conclusion is not generic and GR is not in fact generically an “attractor”, even within the class of HCI theories for which Φ < ∞. We describe the conditions required on a potential to predict that GR is typical in HCI.