Abstract
In this paper we investigate the vacuum stability of the non-minimally coupled Standard-Model Higgs during a phase of kinetic domination following the end of inflation. The non-minimal coupling to curvature stabilises the Higgs fluctuations during inflation while driving them towards the instability scale during kination, when they can classically overcome the potential barrier separating the false electroweak vacuum from the true one at super-Planckian field values. Avoiding the instability of the Standard-Model vacuum sets an upper bound on the inflationary scale that depends both on the strength of the non-minimal interaction and on the top quark Yukawa coupling. Classical vacuum stability is guaranteed if the gravitationally-produced energy density is smaller than the height of barrier in the effective potential. Interestingly enough, thanks to the explosive particle production in the tachyonic phase, the Higgs itself can be also appointed to the role of reheaton field responsible for the onset of the hot Big Bang era, setting an additional lower bound on the inflationary scale \( {\mathcal{H}}_{\textrm{inf}} \) ≳ 105.5 GeV. Overall, these constraints favour lower masses for the top quark, in agreement with the current measurements of the top quark pole mass. We perform our analysis semi-analytically in terms of the one-loop and three-loop running of the Standard-Model Higgs self-coupling and make use of lattice-based parametric formulas for studying the (re)heating phase derived in arXiv:2307.03774. For a specific choice of mt = 171.3 GeV we perform also an extensive numerical scanning of the parameter space via classical lattice simulations, identifying stable/unstable regions and supporting the previous analytical arguments. For this fiducial value, the heating of the Universe is achieved at temperatures in the range 10−2–109 GeV.
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Acknowledgments
G.L. and J.R. wish to thank Dario Bettoni, Andreas Mantziris and Matteo Piani for the interesting discussions during the preparation of this work. This work was partially supported by the Spanish Ministerio de Ciencia, Innovación y Universidades’ project PID2022-139841NBI00 (AEI/FEDER, UE). The numerical lattice simulations have been performed with the support of the Infraestrutura Nacional de Computação Distribuída (INCD) funded by the Fundação para a Ciência e a Tecnologia (FCT) and FEDER under the project 01/SAICT/2016 n° 022153. G.L. (ORCID 0000-0002-4739-4946) is supported by a fellowship from “la Caixa” Foundation (ID 100010434) with fellowship code LCF/BQ/DI21/11860024. G.L. thanks also FCT for the financial support to the Center for Astrophysics and Gravitation-CENTRA, Instituto Superior Técnico, Universidade de Lisboa, through the Project No. UIDB/00099/2020. J.R. (ORCID ID 0000-0001-7545-1533) is supported by a Ramón y Cajal contract of the Spanish Ministry of Science and Innovation with ref. RYC2020-028870-I.
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Laverda, G., Rubio, J. The rise and fall of the Standard-Model Higgs: electroweak vacuum stability during kination. J. High Energ. Phys. 2024, 339 (2024). https://doi.org/10.1007/JHEP05(2024)339
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DOI: https://doi.org/10.1007/JHEP05(2024)339