Abstract
We study the ultraviolet behaviour of Higgs inflation models above the apparent unitarity violation scale arising from the large non minimal coupling to gravity, by computing on-shell 4-point scattering amplitudes in the presence of a large inflaton background, away from the electroweak vacuum. We find that all tree-level amplitudes are well behaved at high energies below the inflaton background that can thus take values up to the Planck scale. This result holds in both the metric and Palatini formulation, and is independent of the frame (Jordan or Einstein) as expected. The same result also holds if an R2 term is added to the action.
Highlights
Metric formulation in the Jordan frameIn what follows, concentrating on possible unitarity violation that arises from the nonminimal Higgs coupling, we ignore the potential and consider the action
Background which provides an effective cutoff against unitarity violation up to the Planck scale
We study the ultraviolet behaviour of Higgs inflation models above the apparent unitarity violation scale arising from the large non minimal coupling to gravity, by computing on-shell 4-point scattering amplitudes in the presence of a large inflaton background, away from the electroweak vacuum
Summary
In what follows, concentrating on possible unitarity violation that arises from the nonminimal Higgs coupling, we ignore the potential and consider the action. Note that because of the Ω2 coefficient that depends on position through φ1 and φ2, we will need the above expression in terms of the shifted graviton and before any integration by parts simplifications in order to compute. In order to obtain the graviton propagator for hμν (being the same as for hμν) we need to introduce gauge-fixing in the form of a term. The resulting Lkinh + Lgf term is ρ hμν δρσδαμδβν + (2α2 − 1)δρσημν ηαβ − 2(2α − 1)δβσηραημν At this order to point we decide to focus on the amplitude identify the interactions resulting from the for √. −gR aφn2d→√−φ1g,gφμν couplings we use the developed expressions given previously, including the extra interactions induced from the shifting of the graviton.
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