It has been claimed that the electroweak vacuum may be unstable during inflation due to large fluctuations of the order H in the case of a high inflationary scale as suggested by BICEP2. We compute the standard model Higgs effective potential including UV-induced curvature corrections at one-loop level. We find that for a high inflationary scale a large curvature mass is generated due to renormalization group running of nonminimal coupling ξ, which either stabilizes the potential against fluctuations for ξEW≳6×10(-2), or destabilizes it for ξEW≲2×10(-2) when the generated curvature mass is negative. Only in the narrow intermediate region may the effect of the curvature mass be significantly smaller.

We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the Standard Model only through the non-minimal gravitational coupling ξ of the Higgs field. Such a coupling is required by renormalisation of the Standard Model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for ξ 1, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.PACS numbers: 98.80. Cq, 04.62.+v The Standard Model (SM) of particle physics can be consistently extrapolated to the Planck scale without any new physics, but the current measurements of the Higgs boson and top quark masses suggest that the current vacuum state of the Universe would then not be stable. This instability depends sensitively on the top mass m t , which is subject to significant experimental and theoretical uncertainty [19], but for the best fit values, the Higgs potential turns negative above the instability scale Λ I ∼ 1011 GeV [21]. This implies that the current vacuum would eventually decay into a negative-energy Planck scale true vacuum, but its lifetime exceeds the age of the universe by a wide margin [1].Whether such a metastable universe could have survived the cosmological evolution, especially inflation, has recently attracted significant interest [3][4][5]. In most of the simplest models of inflation, the Hubble rate during inflation is comparable to the current upper bound H 9 × 10 13 GeV [8]. 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. The current experimental constraints are extremely weak, |ξ| 2.6×1015 [7]. With a positive coupling, this term increases the height of the potential barrier between the vacua, thereby increasing the lifetime of the metastable vacuum. Vacuum stability is maintained for all inflationary scales compatible with the tensor bound [8], provided the electroweak scale value of the running coupling ξ(µ) lies above ξ EW 0.1 [4].In this letter, we investigate the instability problem at the end of inflation, again assuming no new physics or higher-dimensional operators but taking the gravitational coupling ξ into account. In contrast with...

We investigate the dynamics of the Standard Model higgs with a minimal coupling to gravity during and after inflation. In the regime where the Standard Model vacuum is stable, we find that the higgs becomes a light spectator field after about 30 efolds of inflation, irrespectively of its initial value. Once the higgs has become light, its root-mean-square value h * relaxes to equilibrium in about 85 efolds for the inflationary scale of H * = 10 4 GeV and in 20 efolds for H * = 10 10 GeV. The equilibrium value is given by h * ∼ 0.36λ