Quantum gravitational corrections to the inflationary power spectra in scalar–tensor theories

Abstract

We derive the first quantum gravitational corrections to the inflationary power spectra for a general single-field scalar–tensor theory which includes a non-minimal coupling to gravity, a non-standard scalar kinetic term and an arbitrary potential of the scalar field. We obtain these corrections from a semiclassical expansion of the Wheeler–DeWitt equation, which, in turn, governs the full quantum dynamics in the canonical approach to quantum gravity. We discuss the magnitude and relevance of these corrections, as well as their characteristic signature in the inflationary spectral observables. We compare our results to similar calculations performed for a minimally coupled scalar field with a canonical kinetic term and discuss the impact of the non-minimal coupling on the quantum gravitational corrections.