Higgs inflation with loop corrections in the Palatini formulation

Abstract

We compare Higgs inflation in the metric and Palatini formulations of general relativity, with loop corrections treated in a simple approximation. We consider Higgs inflation on the plateau, at a critical point, at a hilltop and in a false vacuum. In the last case there are only minor differences. Otherwise we find that in the Palatini formulation the tensor-to-scalar ratio is consistently suppressed, spanning the range 1×10 −13 < r < 7×10 −5 , compared to the metric case result 2×10 −5 < r < 0.2. Even when the values of n s and r overlap, the running and running of the running are different in the two formulations. Therefore, if Higgs is the inflaton, inflationary observables can be used to distinguish between different gravitational degrees of freedom, in this case to determine whether the connection is an independent variable. Non-detection of r in foreseeable future observations would not rule out Higgs inflation, only its metric variant. We conclude that in order to fix the theory of Higgs inflation, not only the particle physics UV completion but also the gravitational degrees of freedom have to be explicated. arXiv:1709.07853v2 [astro-ph.CO]

Axion dark matter from Higgs inflation with an intermediate H*

“…1 we show the potential for the Higgs field as a function of the field excursion χ/M P , in the metric case (blue dashed curve) and in the Palatini case (red solid curve). We have expressed the potential in units of λ φ M 4 P /(4ξ 2 φ ) and fixed ξ φ = 10 9 , consistently with the findings obtained in previous studies [57,62,76]. In the metric scenario, we have plotted the exact result for the quartic potential in Eq.…”

Tracing the high energy theory of gravity: an introduction to Palatini inflation

“…As further shown in Refs. [22,39], also the running, dn s /d lnk, and running of the running of the spectral index, d 2 n s /d(lnk) 2 , are different in the two theories. Therefore, if the SM Higgs indeed is the inflaton, detailed measurements of the inflationary observables can be used to distinguish between different gravitational degrees of freedom.…”

“…Refs. [22,58], it could be argued that the Palatini formulation is much simpler than the metric formulation, because there is no need to add a boundary term to the action, as it involves only first derivatives of the variables that are to be varied over. For this reason, the Palatini formalism is also sometimes called the "first order formalism", whereas the metric formulation is dubbed as the "second order formalism".…”

“…[93] for a recent review on metric Higgs inflation and Refs. [14,22,30,32,36,39,42,43,46,47,53] for recent studies on Palatini-Higgs inflation. The model is specified by…”

“…This is not totally unfounded, as recently studied in Refs. [22,53] in the context of Palatini-Higgs inflation. For other recent studies on quantum corrections in Higgs inflation, see Refs.…”