Quantum gravitational corrections from the Wheeler-DeWitt equation for scalar-tensor theories

Abstract

We perform the canonical quantization of a general scalar-tensor theory and derive the first quantum gravitational corrections following from a semi-classical expansion of the Wheeler-DeWitt equation. The non-minimal coupling of the scalar field to gravity induces a derivative coupling between the scalar field and the gravitational degrees of freedom, which prevents a direct application of the expansion scheme. We address this technical difficulty by transforming the theory from the Jordan frame to the Einstein frame. We find that a large non-minimal coupling can have strong effects on the quantum gravitational correction terms. We briefly discuss these effects in the context of the specific model of Higgs inflation.

33 pages, no figures, typos corrected, comments and references added, published in CQG

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• Quantum gravitational corrections to the inflationary power spectra in scalar-tensor theories
• Beyond semiclassical time
• Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario
• Mode coupling on a geometrodynamical quantization of an inflationary universe