  We consider the dynamics of a scalar field non-minimally coupled to gravity
in the context of cosmology. It is demonstrated that there exists a new phase
for the scalar field, in addition to the inflationary and dust-like (reheating
period) phases. Analytic expressions for the scalar field and the Hubble
parameter, which describe the new phase are given. The Hubble parameter
indicates an accelerating expanding Universe. We explicitly show that the
scalar field oscillates with time- dependent frequency. Moreover, an
interaction between the scalar field in the new phase and other fields is
discussed. It turns out that the parametric resonance is absent, which is
another crucial difference between the dynamics of the scalar field in the new
phase and dust-like phase.
