Gravitational perturbations of the Higgs field

TL;DR

This paper investigates how classical gravitational backgrounds influence the Higgs field, focusing on the effective potential and energy-momentum tensor in a perturbed FRW metric, using adiabatic and dimensional regularization methods.

Contribution

It provides a detailed analysis of gravitational effects on the Higgs field's effective potential and energy-momentum tensor, including explicit solutions and regularization techniques.

Findings

Gravitational perturbations do not affect the leading order of the Higgs effective potential.

Regularized effective potential retains flat spacetime divergences, allowing standard renormalization.

Explicit expressions for the energy-momentum tensor in a perturbed metric are derived.

Abstract

We study the possible effects of classical gravitational backgrounds on the Higgs field through the modifications induced in the one-loop effective potential and the vacuum expectation value of the energy-momentum tensor. We concentrate our study on the Higgs self-interaction contribution in a perturbed FRW metric. For weak and slowly varying gravitational fields, a complete set of mode solutions for the Klein-Gordon equation is obtained to leading order in the adiabatic approximation. Dimensional regularization has been used in the integral evaluation and a detailed study of the integration of nonrational functions in this formalism has been presented. As expected, the regularized effective potential contains the same divergences as in flat spacetime, which can be renormalized without the need of additional counterterms. We find that, in contrast with other regularization methods, even though metric perturbations affect the mode solutions, they do not contribute to the leading adiabatic order of the potential. We also obtain explicit expressions of the complete energy-momentum tensor for general nonminimal coupling in terms of the perturbed modes. The corresponding leading adiabatic contributions are also obtained.