The Cosmological Higgstory of the Vacuum Instability
SLAC-PUB-16698 CERN-PH-TH-2015/119 IFUP-TH/2015 The cosmological Higgstory of the vacuum instability Jos´eR. Espinosaa;b, Gian F. Giudicec, Enrico Morganted, Antonio Riottod, Leonardo Senatoree, Alessandro Strumiaf;g, Nikolaos Tetradish a IFAE, Universitat Aut´onomade Barcelona, 08193 Bellaterra, Barcelona b ICREA, Instituci´oCatalana de Recerca i Estudis Avan¸cats,Barcelona, Spain c CERN, Theory Division, Geneva, Switzerland d D´epartement de Physique Th´eoriqueand Centre for Astroparticle Physics (CAP), Universit´ede Gen`eve,Geneva, Switzerland e Stanford Institute for Theoretical Physics and Kavli Institute for Particle Astrophysics and Cosmology, Physics Department and SLAC, Stanford, CA 94025, USA f Dipartimento di Fisica dell’Universit`adi Pisa and INFN, Italy g National Institute of Chemical Physics and Biophysics, Tallinn, Estonia h Department of Physics, University of Athens, Zographou 157 84, Greece Abstract The Standard Model Higgs potential becomes unstable at large field values. After clarifying the issue of gauge dependence of the effective potential, we study the cosmological evolution of the Higgs field in presence of this instability throughout inflation, reheating and the present epoch. We conclude that anti-de Sitter patches in which the Higgs field lies at its true vacuum are lethal for our universe. From this result, we derive upper bounds on the arXiv:1505.04825v2 [hep-ph] 4 Sep 2015 Hubble constant during inflation, which depend on the reheating temperature and on the Higgs coupling to the scalar curvature or to the inflaton. Finally we study how a speculative link between Higgs meta-stability and consistence of quantum gravity leads to a sharp prediction for the Higgs and top masses, which is consistent with measured values.
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