Acceleration of the universe, vacuum metamorphosis, and the large-time asymptotic form of the heat kernel

We investigate the possibility that the late acceleration observed in the rate of expansion of the universe is due to vacuum quantum effects arising in curved spacetime. The theoretical basis of the vacuum cold dark matter (VCDM), or vacuum metamorphosis, cosmological model of Parker and Raval is revisited and improved. We show, by means of a manifestly nonperturbative approach, how the infrared behavior of the propagator (related to the large-time asymptotic form of the heat kernel) of a free scalar field in curved spacetime causes the vacuum expectation value of its energy-momentum tensor to exhibit a resonance effect when the scalar curvature R of the spacetime reaches a particular value related to the mass of the field. we show that the back reaction caused by this resonance drives the universe through a transition to an accelerating expansion phase, very much in the same way as originally proposed by Parker and Raval. Our analysis includes higher derivatives that were neglected in the earlier analysis, and takes into account the possible runaway solutions that can follow from these higher-derivative terms. We find that the runaway solutions do not occur if the universe was described by the usual classical FRW solution prior to the growth of vacuum energy-density and negative pressure (i.e., vacuum metamorphosis) that causes the transition to an accelerating expansion of the universe in this theory