Probable or improbable universe? Correlating electroweak vacuum instability with the scale of inflation

Abstract

Measurements of the Higgs boson and top quark masses indicate that the Standard Model Higgs potential becomes unstable around Λ I ∼ 10 11 GeV. This instability is cosmologically relevant since quantum fluctuations during inflation can easily destabilize the electroweak vacuum if the Hubble parameter during inflation is larger than Λ I (as preferred by the recent BICEP2 measurement). We perform a careful study of the evolution of the Higgs field during inflation, obtaining different results from those currently in the literature. We consider both tunneling via a Coleman-de Luccia or Hawking-Moss instanton, valid when the scale of inflation is below the instability scale, as well as a statistical treatment via the Fokker-Planck equation appropriate in the opposite regime. We show that a better understanding of the post-inflation evolution of the unstable AdS vacuum regions is crucial for determining the eventual fate of the universe. If these AdS regions devour all of space, a universe like ours is indeed extremely unlikely without new physics to stabilize the Higgs potential; however, if these regions crunch, our universe survives, but inflation must last a few e-folds longer to compensate for the lost AdS regions. Lastly, we examine the effects of generic Planck-suppressed corrections to the Higgs potential, which can be sufficient to stabilize the electroweak vacuum during inflation.

Measurement of beauty and charm production in deep inelastic scattering at HERA and measurement of the beauty-quark mass

“…This helps to push the Higgs potential towards the stability regime, making it less uncomfortable. Moreover, the recent Bicep2 discovery [25], if confirmed, suggests that the EW vacuum in which we live in would have already decayed [26][27][28][29][30][31] in a universe where the SM holds up to the instability scale Λ = 10 9÷11 GeV. In this case, unless Planck suppressed corrections stabilise the vacuum during inflation [31], some new physics making the quartic Higgs coupling larger than zero would be needed.…”

(Higgs) vacuum decay during inflation

“…The Higgs field can fluctuate towards values a few orders of magnitude below the Planck scale, for which its potential can be deeper than for the electroweak vacuum [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. If vacuum decay happens during inflation, the regions of true vacuum expand and engulf the whole space [2,18,24].…”

Indirect determinations of the top quark mass

“…The measured SM parameters lie so close to the critical condition for the formation of the large-field minimum that the instability scale can fluctuate from 10 10 GeV to the Planck scale with a variation of M t of merely 2 GeV [1][2][3][4]. Any such small change in M t can have a substantial effect in the evolution of the universe at the inflationary epoch [5][6][7][8][9][10][11][12] and determine the viability of scenarios of Higgs inflation [13]. A more precise determination of M t will add important information to our knowledge of particle physics and cosmology.…”

“…The situation is expected to improve greatly in the future. By 2025 the error budget will be 9) assuming that the errors from higher-order effects will be significantly reduced.…”