Publication: Gravitational perturbations of the Higgs field
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2017-02-21
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Amer Physical Soc
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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 energymomentum 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 KleinGordon 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.
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© 2017 American Physical Society. This work has been supported by the Spanish MICINNs Consolider-Ingenio 2010 Programme under MultiDark Grant No. CSD2009-00064, MINECO Centro de Excelencia Severo Ochoa Programme under Grant No. SEV-2012-0249, and MINECO Grants No. FIS2014- 52837-P, AYA-2012-31101 and AYA2014-60641-C2-1-P. FDA acknowledges financial support from ‘la Caixa’- Severo Ochoa doctoral fellowship.