Spacetime dynamics of a Higgs vacuum instability during inflation

Abstract

A remarkable prediction of the Standard Model is that, in the absence of corrections lifting the energy density, the Higgs potential becomes negative at large field values. If the Higgs field samples this part of the potential during inflation, the negative energy density may locally destabilize the spacetime.We use numerical simulations of the Einstein equations to study the evolution of inflation-induced Higgs fluctuations as they grow towards the true (negative-energy) minimum. These simulations show that forming a single patch of true vacuum in our past light cone during inflation is incompatible with the existence of our Universe; the boundary of the true vacuum region grows outward in a causally disconnected manner from the crunching interior, which forms a black hole. We also find that these black hole horizons may be arbitrarily elongated-even forming black strings-in violation of the hoop conjecture. By extending the numerical solution of the Fokker-Planck equation to the exponentially suppressed tails of the field distribution at large field values, we derive a rigorous correlation between a future measurement of the tensor-to-scalar ratio and the scale at which the Higgs potential must receive stabilizing corrections in order for the Universe to have survived inflation until today.

(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].…”

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

“…The fate of a spacetime region in which a scalar field is falling towards a negative energy vacuum, as well as the fate of an AdS patch embedded in a de Sitter geometry, represent non-trivial general relativity problems. As a matter of fact, these issues were not well understood until very recently [14,15]. Thus, before starting, we briefly brush over the current understanding of these phenomena.…”

“…As inflation proceeds, initially sub-Hubble fluctuations of the Higgs field exit the Hubble radius and feed its infrared dynamics [44,45]. This stochastic evolution is usually modeled by the simple Langevin equation 15) where here and in the remainder of this paper, h denotes the super-Hubble coarse-grained part of the Higgs field. N is the number of e-folds of inflation, and η is a Gaussian white noise with variance the power spectrum of the Higgs fluctuations when they join the IR sector (more about the factor f below in section 2.3.2):…”

“…Even if today the lifetime of our vacuum is much larger than the age of our Universe, assuming a period of inflation implies that, in the very early Universe, the Higgs (when it is not the inflaton) behaved as a test scalar field in a (quasi) de Sitter background. There, stochastic kicks could have pushed it beyond the potential barrier towards the true vacuum, until the point of forming anti de Sitter (AdS) regions fatal for our universe [14,15]. For good reasons (e.g.…”

On the catalysis of the electroweak vacuum decay by black holes at high temperature

“…This issue is crucial for the decay of the electroweak vacuum, because of the extreme sensitivity of the Higgs potential to the Higgs and top masses [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The fact that the a e-mail: ntetrad@phys.uoa.gr gravitational effects are significant during inflation has led to an extensive investigation of the stability of the electroweak vacuum during this era, leading to bounds on the inflationary scale [14,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] in order to avoid a catastrophic singularity characterized as the AdS crunch [1,31,36].…”