Gravitational perturbations of the Higgs field

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.

15 pages. Version accepted for publication in PRD. Error corrected in the angular integration in Appendix B. Conclusions changed. New section included

References in corpus (8)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• Vacuum energy as dark matter
• Higgs-induced spectroscopic shifts near strong gravity sources
• The large-scale structure of vacuum
• Higgs shifts from electron-positron annihilations near neutron stars
• Higgs effective potential in a perturbed Robertson-Walker background

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• Thermal and nonthermal scaling of the Casimir-Polder interaction in a black hole spacetime
• Electroweak Vacuum Instability and Renormalized Vacuum Field Fluctuations in Friedmann-Lemaitre-Robertson-Walker Background
• Finite temperature corrections to the energy-momentum tensor at one-loop in static space-times