Quantum corrections in quintessence models

Abstract

We investigate the impact of quantum fluctuations on a light rolling quintessence field from three different sources, namely, from a coupling to the standard model and dark matter, from its self-couplings, and from its coupling to gravity. We derive bounds for time-varying masses from the change of vacuum energy, finding $\ensuremath{\Delta}{m}_{e}/{m}_{e}\ensuremath{\ll}{10}^{\ensuremath{-}11}$ for the electron and $\ensuremath{\Delta}{m}_{p}/{m}_{p}\ensuremath{\ll}{10}^{\ensuremath{-}15}$ for the proton since redshift $z\ensuremath{\sim}2$, whereas the neutrino masses could change of order one. Mass-varying dark matter is also constrained. Next, the self-interactions are investigated. For inverse power law potentials, the effective potential does not become infinitely large at small field values, but saturates at a finite maximal value. We discuss implications for cosmology. Finally, we show that one-loop corrections induce nonminimal gravitational couplings involving arbitrarily high powers of the curvature scalar $R$, indicating that quintessence entails modified gravity effects.