Higgs vacuum (in)stability during inflation. The dangerous relevance of de Sitter departure and Planck-suppressed operators

Abstract

The measured Standard Model parameters lie in a range such that the Higgs potential, once extrapolated up to high scales, develops a minimum of negative energy density. This has important cosmological implications. In particular, during inflation, quantum fluctuations could have pushed the Higgs field beyond its potential barrier, triggering the formation of anti-de Sitter regions, with fatal consequences for our universe. By requiring that this did not happen, one can in principle connect (and constrain) Standard Model parameters with the energy scale of inflation. In this context, we highlight the sensitivity of the fate of our vacuum to seemingly irrelevant physics. In particular, the departure of inflation from an exact de Sitter phase, as well as Planck-suppressed derivative operators, can, already and surprisingly, play a decisive role in (de)stabilizing the Higgs during inflation. Furthermore, in the stochastic dynamics, we quantify the impact of the amplitude of the noise differing from the one of a massless field, as well as of going beyond the slow-roll approximation by using a phase-space approach. On a general ground, our analysis shows that relating the period of inflation to precision particle physics requires a knowledge of these "irrelevant" effects.

On the inflationary massive field with a curved field manifold

“…But as discussed above (and also pointed out in Ref. [20,36,74] previously), this operator may give nontrivial corrections to the isocurvature mass. One can interpret this effect by the right diagram in Fig.…”

Matching and running sensitivity in non-renormalizable inflationary models

“…Note that, contrary to the conformal transformation used in Higgs inflation, the disformal transformation leads to the same Lagrangian eq. (2.7) both in the metric and Palatini formulation of general relativity (at first order in ε).5 If the Higgs boson is a spectator field during inflation, contrary to what is discussed here, derivative couplings between the inflaton and the Higgs leads to a non-trivial metric in field space that can play a crucial role in determining the fate of the vacuum instability during inflation[40].…”

Scalar correlation functions for a double-well potential in de Sitter space

“…For other techniques, see Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29] The stochastic approach has become increasingly popular in recent years, likely due to its great efficacy, and in this vein we note the recent works [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Often the focus is on the local probability distribution of the field or on local expectation values, even though the correlation of fluctutations over space is arguably the more relevant object physically.…”