Quantum corrections in Higgs inflation: the real scalar case
  We present a critical discussion of quantum corrections, renormalisation, and
the computation of the beta functions and the effective potential in Higgs
inflation. In contrast with claims in the literature, we find no evidence for a
disagreement between the Jordan and Einstein frames, even at the quantum level.
For clarity of discussion we concentrate on the case of a real scalar Higgs. We
first review the classical calculation and then discuss the back reaction of
gravity. We compute the beta functions for the Higgs quartic coupling and
non-minimal coupling constant. Here, the mid-field regime is
non-renormalisable, but we are able to give an upper bound on the 1-loop
corrections to the effective potential. We show that, in computing the
effective potential, the Jordan and Einstein frames are compatible if all mass
scales are transformed between the two frames. As such, it is consistent to
take a constant cutoff in either the Jordan or Einstein frame, and both
prescriptions yield the same result for the effective potential. Our results
are extended to the case of a complex scalar Higgs.
