Massless Fileds in Scalar-Tensor Cosmologies

Abstract

We derive exact Friedmann--Robertson--Walker cosmological solutions in general scalar--tensor gravity theories, including Brans--Dicke gravity, for stiff matter or radiation. These correspond to the long or short wavelength modes respectively of massless scalar fields. If present, the long wavelength modes of such fields would be expected to dominate the energy density of the universe at early times and thus these models provide an insight into the classical behaviour of these scalar--tensor cosmologies near an initial singularity, or bounce. The particularly simple exact solutions also provide a useful example of the possible evolution of the Brans--Dicke (or dilaton) field, $ϕ$, and the Brans--Dicke parameter, $ω(ϕ)$, at late times in spatially curved as well as flat universes. We also discuss the corresponding solutions in the conformally related Einstein metric.