Nonperturbative effects of vacuum energy on the recent expansion of the universe

Abstract

We show that the vacuum energy of a free quantized field of very low mass can significantly alter the recent expansion of the universe. The type of particle we consider is of spin-0, but a higher spin field, such as a graviton of ultralight mass, may well affect the expansion in the same way. The effective action of the theory is obtained from a non-perturbative sum of scalar curvature terms in the propagator. We renormalize this effective action and express it in terms of observable gravitational coupling constants. We numerically investigate the semiclassical Einstein equations derived from it. As a result of non-perturbative quantum effects, the scalar curvature of the matter-dominated universe stops decreasing and approaches a constant value. The universe in our model evolves from an open matter-dominated epoch to a mildly inflating de Sitter expansion. The Hubble constant during the present de Sitter epoch, as well as the time at which the transition occurs from matter-dominated to de Sitter expansion, are determined by the mass of the field and by the present matter density. The model provides a theoretical explanation of the observed recent acceleration of the universe, and gives a good fit to data from high-redshift type Ia supernovae, with a mass of about ${10}^{\ensuremath{-}33}\mathrm{eV},$ and a current ratio of matter density to critical density, ${\ensuremath{\Omega}}_{0}<0.4.$ The age of the universe then follows with no further free parameters in the theory, and turns out to be greater than 13 Gyr. The model is spatially open and consistent with the possibility of inflation in the very early universe. Furthermore, our model arises from the standard renormalizable theory of a free quantum field in curved spacetime, and does not require a cosmological constant or the associated fine-tuning.