Covariant one-loop quantum gravity and Higgs inflation

The quantisation of scalar field theory and Einstein gravity is investigated using a fully covariant background field formalism, including Vilkovisky-DeWitt corrections. The one-loop divergences, which are relevant for the consistency of the low-energy effective theory, differ substantially from non-covariant calculations. The results are applied to the effective action of Higgs inflation, with a non-minimal gravity coupling parameter $ξ$, where the use of a formalism which is independent of field redefinitions is particularly important. Consistency of the one-loop effective action requires the cut-off $Λ<M_p/\sqrtξ$ in the small field and $Λ<M_p$ in the large field limit.

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