The universe dominated by oscillating scalar with non-minimal derivative coupling to gravity

We study the expansion law of the universe dominated by the oscillating scalar field with non-minimal derivative coupling to gravity as G^{\mu \nu} \partial_{\mu} \phi \partial_{\nu} \phi. In this system the Hubble parameter oscillates with a frequency of the effective mass of the scalar field, which formerly caused a difficulty in analyzing how the universe expands. We find an analytical solution for power law potentials and interpret the solution in an intuitive way by using a new invariant of the system. As a result, we find marginally accelerated expansion for the quadratic potential and no accelerated expansion for the potential with higher power.