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 Δm_e/m_e << 10^{-11} for the electron and Δm_p/m_p << 10^{-15} for the proton since redshift z~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 non-minimal gravitational couplings involving arbitrarily high powers of the curvature scalar R, indicating that quintessence entails modified gravity effects.