Is a Higgs vacuum instability fatal for high-scale inflation?

Abstract

We study the inflationary evolution of a scalar field h with an unstable potential for the case where the Hubble parameter H during inflation is larger than the instability scale Λ I of the potential.Quantum fluctuations in the field of size δh ∼ H 2π imply that the unstable part of the potential is sampled during inflation. We investigate the evolution of these fluctuations to the unstable regime, and in particular whether they generate cosmological defects or even terminate inflation.We apply the results of a toy scalar model to the case of the Standard Model (SM) Higgs boson, whose quartic evolves to negative values at high scales, and extend previous analyses of Higgs dynamics during inflation utilizing statistical methods to a perturbative and fully gauge-invariant formulation. We show that the dynamics are controlled by the renormalization group-improved quartic coupling λ(µ) evaluated at a scale µ = H, such that Higgs fluctuations are enhanced by the instability if H > Λ I . Even if H > Λ I , the instability in the SM Higgs potential does not end inflation; instead the universe slowly sloughs off crunching patches of space that never come to dominate the evolution. As inflation proceeds past 50 e-folds, a significant proportion of patches exit inflation in the unstable vacuum, and as much as 1% of the spacetime can rapidly evolve to a defect. Depending on the nature of these defects, however, the resulting universe could still be compatible with ours.

Spacetime Curvature and Higgs Stability after Inflation

“…It may therefore well be above the instability scale, in which case production of Higgs fluctuations could push the field over the potential barrier into the true Planck-scale vacuum [3]. This instability problem is exacerbated by spacetime curvature induced running of the couplings, which makes the Higgs selfcoupling negative even at low field values [4][5][6].Notably, vacuum stability can still be maintained even during inflation without any new physics coupled to the SM fields [4], thanks to the Higgs-curvature coupling ξRĤ †Ĥ . This coupling is inevitably generated by radiative corrections and when assuming the SM to be valid up to the Planck scale it is the only relevant new term when probing sub-Planckian scales.…”

“…It may therefore well be above the instability scale, in which case production of Higgs fluctuations could push the field over the potential barrier into the true Planck-scale vacuum [3]. This instability problem is exacerbated by spacetime curvature induced running of the couplings, which makes the Higgs selfcoupling negative even at low field values [4][5][6].…”

(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.…”