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.
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