Higgs effective potential in a perturbed Robertson-Walker background

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Prada, Francisco
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We calculate the one-loop effective potential of a scalar field in a Robertson-Walker background with scalar metric perturbations. A complete set of orthonormal solutions of the perturbed equations is obtained by using the adiabatic approximation for comoving observers. After analyzing the problem of renormalization in inhomogeneous backgrounds, we get the explicit contribution of metric perturbations to the effective potential. We apply these results to the Standard Model Higgs field and evaluate the effects of metric perturbations on the Higgs mass and on its vacuum expectation value. Space-time variations are found, which are proportional to the gravitational slip parameter, with a typical amplitude of the order of Δϕ/ϕ ≃ 10−11 on cosmological scales. We also discuss possible astrophysical signatures in the Solar System and in the MilkyWay that could open new possibilities to explore the symmetry breaking sector of the electroweak interactions.
© 2014 American Physical Society. We would like to thank S. Odintsov and E. Elizalde for useful comments. This work has been supported by MICINN (Spain) Projects No. FIS2011-23000, No. AYA2010-21231-C02-01, Consolider-Ingenio MULTIDARK CSD2009-00064, and Centro de Excelencia Severo Ochoa Programme under Grant No. SEV-2012-0249.
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