  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, $\phi$, and the Brans--Dicke parameter, $\omega(\phi)$, at late times in
spatially curved as well as flat universes. We also discuss the corresponding
solutions in the conformally related Einstein metric.
