Non-minimal (self-)running inflation: metric vs. Palatini formulation

Antonio Racioppi

doi:10.1007/jhep01(2021)011

Abstract

We consider a model of quartic inflation where the inflaton is coupled non-minimally to gravity and the self-induced radiative corrections to its effective potential are dominant. We perform a comparative analysis considering two different formulations of gravity, metric or Palatini, and two different choices for the renormalization scale, widely known as prescription I and II. Moreover we comment on the eventual compatibility of the results with the final data release of the Planck mission.

Highlights

We consider a model of quartic inflation where the inflaton is coupled nonminimally to gravity and the self-induced radiative corrections to its effective potential are dominant
It has been demonstrated that radiative corrections to inflationary potentials may play a relevant role [64,65,66,67], dynamically generating the Planck scale [68, 69], predicting super-heavy dark matter [70, 71] and leading to linear inflation predictions when a non-minimal coupling to gravity is added [57, 58, 69, 72,73,74]
The second part of eq (2.5) is the contribution coming from the Coleman-Weinberg (CW) 1-loop correction [108] to the effective potential, while the first one comes from the renormalization group equation (RGE) [109, 110] of the quartic coupling, whose solution is λ(μ) =

Summary

Model building and effective potential

Where MP is the reduced Planck mass, R is the Ricci scalar constructed from a connection Γ and Veff (φ) is the effective potential of the inflaton scalar. The second part of eq (2.5) is the contribution coming from the Coleman-Weinberg (CW) 1-loop correction [108] to the effective potential, while the first one comes from the renormalization group equation (RGE) [109, 110] of the quartic coupling, whose solution is λ(μ) =. Prescription I [116] is the choice motivated by the scaleinvariant quantization in the Jordan frame, while prescription II [86,87,88] corresponds to the usual quantization in the Jordan frame and it is convenient because it cancels explicitly the CW part of (2.7), moving all the loop correction into the running of the quartic coupling.

Non-minimal gravity

Inflationary results

U d2U dχ2

Conclusions

A More details about the running of ξ