Abstract
It is shown that a positive non-minimal coupling of the Higgs field to gravity can solve the two problems in inflation models in which postinflationary universe is dominated by an energy with stiff equation of state such as a kination, namely, overproduction of gravitons in gravitational reheating scenario, and overproduction of curvature perturbation from Higgs condensation. Furthermore, we argue that the non-minimal coupling parameter can be constrained more stringently with the progress in observations of large-scale structure and cosmic microwave background.
Highlights
If the equation of state parameter w is larger than 1/3 after inflation [1], the energy density of the inflaton decreases more quickly than radiation
One of the candidates is the standard Higgs field as it may acquire a condensation of long-wave quantum fluctuations which are generated if it is minimally coupled to gravity so that its effective mass is much smaller than the Hubble parameter during inflation [7]. If it has a typical amplitude around the root-mean-square in the domain corresponding to our Universe, its energy density is of the same order of radiation energy created by gravitational particle production just after inflation [8]
Since the graviton satisfies the same equation of motion as a massless minimally coupled scalar field, its energy density is twice as large as that given by Eq (3), reflecting their two polarization states [6]
Summary
If the equation of state parameter w is larger than 1/3 after inflation [1], the energy density of the inflaton decreases more quickly than radiation. One of the candidates is the standard Higgs field as it may acquire a condensation of long-wave quantum fluctuations which are generated if it is minimally coupled to gravity so that its effective mass is much smaller than the Hubble parameter during inflation [7] If it has a typical amplitude around the root-mean-square in the domain corresponding to our Universe, its energy density is of the same order of radiation energy created by gravitational particle production just after inflation [8].
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