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Title: 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, the quartic of which 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 Standard Model Higgs potential does not end inflation; instead the universe slowly sloughs off crunching patches of space that never come to dominate the evolution. Asmore » inflation proceeds past 50 e-folds, a significant proportion of patches exits 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.« less

Authors:
 [1];  [2];  [2]
  1. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1226319
Alternate Identifier(s):
OSTI ID: 1198521
Report Number(s):
FERMILAB-PUB-15-090-T
Journal ID: ISSN 1550-7998; PRVDAQ; arXiv eprint number arXiv:1503.05193
Grant/Contract Number:
AC02-07CH11359; AC02-05CH11231; SC0007859
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. D, Particles, Fields, Gravitation and Cosmology
Additional Journal Information:
Journal Volume: 91; Journal Issue: 12; Journal ID: ISSN 1550-7998
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Kearney, John, Yoo, Hojin, and Zurek, Kathryn M. Is a Higgs vacuum instability fatal for high-scale inflation?. United States: N. p., 2015. Web. doi:10.1103/PhysRevD.91.123537.
Kearney, John, Yoo, Hojin, & Zurek, Kathryn M. Is a Higgs vacuum instability fatal for high-scale inflation?. United States. doi:10.1103/PhysRevD.91.123537.
Kearney, John, Yoo, Hojin, and Zurek, Kathryn M. Thu . "Is a Higgs vacuum instability fatal for high-scale inflation?". United States. doi:10.1103/PhysRevD.91.123537. https://www.osti.gov/servlets/purl/1226319.
@article{osti_1226319,
title = {Is a Higgs vacuum instability fatal for high-scale inflation?},
author = {Kearney, John and Yoo, Hojin and Zurek, Kathryn M.},
abstractNote = {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 ΛI 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, the quartic of which 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 > ΛI. Even if H > ΛI, the instability in the Standard Model 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 exits 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.},
doi = {10.1103/PhysRevD.91.123537},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 12,
volume = 91,
place = {United States},
year = {Thu Jun 25 00:00:00 EDT 2015},
month = {Thu Jun 25 00:00:00 EDT 2015}
}

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  • 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. Here, 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. Our 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; themore » 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. Furthermore, 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.« less
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  • We investigate the possibility of using the only known fundamental scalar, the Higgs, as an inflaton with minimal coupling to gravity. The peculiar appearance of a plateau or a false vacuum in the renormalised effective scalar potential suggests that the Higgs might drive inflation. For the case of a false vacuum we use an additional singlet scalar field, motivated by the strong CP problem, and its coupling to the Higgs to lift the barrier allowing for a graceful exit from inflation by mimicking hybrid inflation. We find that this scenario is incompatible with current measurements of the Higgs mass andmore » the QCD coupling constant and conclude that the Higgs can only be the inflaton in more complicated scenarios.« less