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.
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References
CMS collaboration, Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
P.Q. Hung, Vacuum Instability and New Constraints on Fermion Masses, Phys. Rev. Lett. 42 (1979) 873 [INSPIRE].
G. Isidori, G. Ridolfi and A. Strumia, On the metastability of the standard model vacuum, Nucl. Phys. B 609 (2001) 387 [hep-ph/0104016] [INSPIRE].
M. Sher, Precise vacuum stability bound in the standard model, Phys. Lett. B 317 (1993) 159 [Addendum ibid. B 331 (1994) 448] [hep-ph/9307342] [INSPIRE].
J.A. Casas, J.R. Espinosa and M. Quirós, Standard model stability bounds for new physics within LHC reach, Phys. Lett. B 382 (1996) 374 [hep-ph/9603227] [INSPIRE].
J. Ellis, J.R. Espinosa, G.F. Giudice, A. Hoecker and A. Riotto, The Probable Fate of the Standard Model, Phys. Lett. B 679 (2009) 369 [arXiv:0906.0954] [INSPIRE].
J. Elias-Miro, J.R. Espinosa, G.F. Giudice, G. Isidori, A. Riotto and A. Strumia, Higgs mass implications on the stability of the electroweak vacuum, Phys. Lett. B 709 (2012) 222 [arXiv:1112.3022] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
V. Branchina and E. Messina, Stability, Higgs Boson Mass and New Physics, Phys. Rev. Lett. 111 (2013) 241801 [arXiv:1307.5193] [INSPIRE].
V. Branchina, E. Bentivegna, F. Contino and D. Zappalà, Direct Higgs-gravity interaction and stability of our Universe, Phys. Rev. D 99 (2019) 096029 [arXiv:1905.02975] [INSPIRE].
T. Markkanen, A. Rajantie and S. Stopyra, Cosmological Aspects of Higgs Vacuum Metastability, Front. Astron. Space Sci. 5 (2018) 40 [arXiv:1809.06923] [INSPIRE].
J.R. Espinosa et al., The cosmological Higgstory of the vacuum instability, JHEP 09 (2015) 174 [arXiv:1505.04825] [INSPIRE].
W.E. East, J. Kearney, B. Shakya, H. Yoo and K.M. Zurek, Spacetime Dynamics of a Higgs Vacuum Instability During Inflation, Phys. Rev. D 95 (2017) 023526 [arXiv:1607.00381] [INSPIRE].
J.R. Espinosa, G.F. Giudice and A. Riotto, Cosmological implications of the Higgs mass measurement, JCAP 05 (2008) 002 [arXiv:0710.2484] [INSPIRE].
A. Kobakhidze and A. Spencer-Smith, Electroweak Vacuum (In)Stability in an Inflationary Universe, Phys. Lett. B 722 (2013) 130 [arXiv:1301.2846] [INSPIRE].
K. Enqvist, T. Meriniemi and S. Nurmi, Higgs Dynamics during Inflation, JCAP 07 (2014) 025 [arXiv:1404.3699] [INSPIRE].
A. Hook, J. Kearney, B. Shakya and K.M. Zurek, Probable or Improbable Universe? Correlating Electroweak Vacuum Instability with the Scale of Inflation, JHEP 01 (2015) 061 [arXiv:1404.5953] [INSPIRE].
J. Kearney, H. Yoo and K.M. Zurek, Is a Higgs Vacuum Instability Fatal for High-Scale Inflation?, Phys. Rev. D 91 (2015) 123537 [arXiv:1503.05193] [INSPIRE].
M. Jain and M.P. Hertzberg, Eternal Inflation and Reheating in the Presence of the Standard Model Higgs, arXiv:1910.04664 [INSPIRE].
G. Franciolini, G.F. Giudice, D. Racco and A. Riotto, Implications of the detection of primordial gravitational waves for the Standard Model, JCAP 05 (2019) 022 [arXiv:1811.08118] [INSPIRE].
M. Herranen, T. Markkanen, S. Nurmi and A. Rajantie, Spacetime curvature and Higgs stability after inflation, Phys. Rev. Lett. 115 (2015) 241301 [arXiv:1506.04065] [INSPIRE].
Y. Ema, K. Mukaida and K. Nakayama, Fate of Electroweak Vacuum during Preheating, JCAP 10 (2016) 043 [arXiv:1602.00483] [INSPIRE].
K. Kohri and H. Matsui, Higgs vacuum metastability in primordial inflation, preheating and reheating, Phys. Rev. D 94 (2016) 103509 [arXiv:1602.02100] [INSPIRE].
K. Enqvist, M. Karciauskas, O. Lebedev, S. Rusak and M. Zatta, Postinflationary vacuum instability and Higgs-inflaton couplings, JCAP 11 (2016) 025 [arXiv:1608.08848] [INSPIRE].
M. Postma and J. van de Vis, Electroweak stability and non-minimal coupling, JCAP 05 (2017) 004 [arXiv:1702.07636] [INSPIRE].
Y. Ema, M. Karciauskas, O. Lebedev and M. Zatta, Early Universe Higgs dynamics in the presence of the Higgs-inflaton and non-minimal Higgs-gravity couplings, JCAP 06 (2017) 054 [arXiv:1703.04681] [INSPIRE].
D.G. Figueroa, A. Rajantie and F. Torrenti, Higgs field-curvature coupling and postinflationary vacuum instability, Phys. Rev. D 98 (2018) 023532 [arXiv:1709.00398] [INSPIRE].
S. Renaux-Petel and K. Turzyński, Geometrical Destabilization of Inflation, Phys. Rev. Lett. 117 (2016) 141301 [arXiv:1510.01281] [INSPIRE].
S. Renaux-Petel, K. Turzyński and V. Vennin, Geometrical destabilization, premature end of inflation and Bayesian model selection, JCAP 11 (2017) 006 [arXiv:1706.01835] [INSPIRE].
S. Garcia-Saenz, S. Renaux-Petel and J. Ronayne, Primordial fluctuations and non-Gaussianities in sidetracked inflation, JCAP 07 (2018) 057 [arXiv:1804.11279] [INSPIRE].
O. Grocholski, M. Kalinowski, M. Kolanowski, S. Renaux-Petel, K. Turzyński and V. Vennin, On backreaction effects in geometrical destabilisation of inflation, JCAP 05 (2019) 008 [arXiv:1901.10468] [INSPIRE].
M. Herranen, T. Markkanen, S. Nurmi and A. Rajantie, Spacetime curvature and the Higgs stability during inflation, Phys. Rev. Lett. 113 (2014) 211102 [arXiv:1407.3141] [INSPIRE].
M. Fairbairn and R. Hogan, Electroweak Vacuum Stability in light of BICEP2, Phys. Rev. Lett. 112 (2014) 201801 [arXiv:1403.6786] [INSPIRE].
K. Kamada, Inflationary cosmology and the standard model Higgs with a small Hubble induced mass, Phys. Lett. B 742 (2015) 126 [arXiv:1409.5078] [INSPIRE].
O. Lebedev and A. Westphal, Metastable Electroweak Vacuum: Implications for Inflation, Phys. Lett. B 719 (2013) 415 [arXiv:1210.6987] [INSPIRE].
C. Ford, I. Jack and D.R.T. Jones, The Standard model effective potential at two loops, Nucl. Phys. B 387 (1992) 373 [Erratum ibid. B 504 (1997) 551] [hep-ph/0111190] [INSPIRE].
M.-x. Luo and Y. Xiao, Two loop renormalization group equations in the standard model, Phys. Rev. Lett. 90 (2003) 011601 [hep-ph/0207271] [INSPIRE].
L.N. Mihaila, J. Salomon and M. Steinhauser, Gauge Coupling β-functions in the Standard Model to Three Loops, Phys. Rev. Lett. 108 (2012) 151602 [arXiv:1201.5868] [INSPIRE].
K.G. Chetyrkin and M.F. Zoller, Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model, JHEP 06 (2012) 033 [arXiv:1205.2892] [INSPIRE].
T. Markkanen, S. Nurmi, A. Rajantie and S. Stopyra, The 1-loop effective potential for the Standard Model in curved spacetime, JHEP 06 (2018) 040 [arXiv:1804.02020] [INSPIRE].
M. Sasaki and E.D. Stewart, A General analytic formula for the spectral index of the density perturbations produced during inflation, Prog. Theor. Phys. 95 (1996) 71 [astro-ph/9507001] [INSPIRE].
S. Groot Nibbelink and B.J.W. van Tent, Scalar perturbations during multiple field slow-roll inflation, Class. Quant. Grav. 19 (2002) 613 [hep-ph/0107272] [INSPIRE].
A.A. Starobinsky, Stochastic de Sitter (inflationary) stage in the early universe, Lect. Notes Phys. 246 (1986) 107 [INSPIRE].
A.A. Starobinsky and J. Yokoyama, Equilibrium state of a selfinteracting scalar field in the de Sitter background, Phys. Rev. D 50 (1994) 6357 [astro-ph/9407016] [INSPIRE].
T. Fujita, M. Kawasaki and Y. Tada, Non-perturbative approach for curvature perturbations in stochastic δN formalism, JCAP 10 (2014) 030 [arXiv:1405.2187] [INSPIRE].
C.P. Burgess, R. Holman, G. Tasinato and M. Williams, EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum Fluctuations Go Classical, JHEP 03 (2015) 090 [arXiv:1408.5002] [INSPIRE].
V. Vennin and A.A. Starobinsky, Correlation Functions in Stochastic Inflation, Eur. Phys. J. C 75 (2015) 413 [arXiv:1506.04732] [INSPIRE].
C.P. Burgess, R. Holman and G. Tasinato, Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation, JHEP 01 (2016) 153 [arXiv:1512.00169] [INSPIRE].
V. Vennin, H. Assadullahi, H. Firouzjahi, M. Noorbala and D. Wands, Critical Number of Fields in Stochastic Inflation, Phys. Rev. Lett. 118 (2017) 031301 [arXiv:1604.06017] [INSPIRE].
I. Moss and G. Rigopoulos, Effective long wavelength scalar dynamics in de Sitter, JCAP 05 (2017) 009 [arXiv:1611.07589] [INSPIRE].
R.J. Hardwick, V. Vennin, C.T. Byrnes, J. Torrado and D. Wands, The stochastic spectator, JCAP 10 (2017) 018 [arXiv:1701.06473] [INSPIRE].
J. Grain and V. Vennin, Stochastic inflation in phase space: Is slow roll a stochastic attractor?, JCAP 05 (2017) 045 [arXiv:1703.00447] [INSPIRE].
H. Collins, R. Holman and T. Vardanyan, The quantum Fokker-Planck equation of stochastic inflation, JHEP 11 (2017) 065 [arXiv:1706.07805] [INSPIRE].
T. Prokopec and G. Rigopoulos, Functional renormalization group for stochastic inflation, JCAP 08 (2018) 013 [arXiv:1710.07333] [INSPIRE].
J. Tokuda and T. Tanaka, Statistical nature of infrared dynamics on de Sitter background, JCAP 02 (2018) 014 [arXiv:1708.01734] [INSPIRE].
R.J. Hardwick, Multiple spectator condensates from inflation, JCAP 05 (2018) 054 [arXiv:1803.03521] [INSPIRE].
J. Tokuda and T. Tanaka, Can all the infrared secular growth really be understood as increase of classical statistical variance?, JCAP 11 (2018) 022 [arXiv:1806.03262] [INSPIRE].
L. Pinol, S. Renaux-Petel and Y. Tada, Inflationary stochastic anomalies, Class. Quant. Grav. 36 (2019) 07LT01 [arXiv:1806.10126] [INSPIRE].
R.J. Hardwick, T. Markkanen and S. Nurmi, Renormalisation group improvement in the stochastic formalism, JCAP 09 (2019) 023 [arXiv:1904.11373] [INSPIRE].
T. Markkanen, A. Rajantie, S. Stopyra and T. Tenkanen, Scalar correlation functions in de Sitter space from the stochastic spectral expansion, JCAP 08 (2019) 001 [arXiv:1904.11917] [INSPIRE].
M. Jain and M.P. Hertzberg, Statistics of Inflating Regions in Eternal Inflation, Phys. Rev. D 100 (2019) 023513 [arXiv:1904.04262] [INSPIRE].
S. Winitzki and A. Vilenkin, Effective noise in stochastic description of inflation, Phys. Rev. D 61 (2000) 084008 [gr-qc/9911029] [INSPIRE].
S. Matarrese, M.A. Musso and A. Riotto, Influence of superhorizon scales on cosmological observables generated during inflation, JCAP 05 (2004) 008 [hep-th/0311059] [INSPIRE].
M. Liguori, S. Matarrese, M. Musso and A. Riotto, Stochastic inflation and the lower multipoles in the CMB anisotropies, JCAP 08 (2004) 011 [astro-ph/0405544] [INSPIRE].
Planck collaboration, Planck 2018 results. X. Constraints on inflation, arXiv:1807.06211 [INSPIRE].
N.G. van Kampen, Itô versus Stratonovich, J. Stat. Phys. 24 (1981) 175.
A. Riotto and M.S. Sloth, The probability equation for the cosmological comoving curvature perturbation, JCAP 10 (2011) 003 [arXiv:1103.5876] [INSPIRE].
G. Rigopoulos, Thermal Interpretation of Infrared Dynamics in de Sitter, JCAP 07 (2016) 035 [arXiv:1604.04313] [INSPIRE].
D. Cruces, C. Germani and T. Prokopec, Failure of the stochastic approach to inflation beyond slow-roll, JCAP 03 (2019) 048 [arXiv:1807.09057] [INSPIRE].
C. Pattison, V. Vennin, H. Assadullahi and D. Wands, Stochastic inflation beyond slow roll, JCAP 07 (2019) 031 [arXiv:1905.06300] [INSPIRE].
G.F. Giudice, E.W. Kolb and A. Riotto, Largest temperature of the radiation era and its cosmological implications, Phys. Rev. D 64 (2001) 023508 [hep-ph/0005123] [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
A.H. Hoang, The Top Mass: Interpretation and Theoretical Uncertainties, in Proceedings of 7th International Workshop on Top Quark Physics (TOP2014), Cannes France (2014) [arXiv:1412.3649] [INSPIRE].
P. Nason, The Top Mass in Hadronic Collisions, in From My Vast Repertoire ...: Guido Altarelli’s Legacy, A. Levy, S. Forte and G. Ridolfi eds., World Scientific, New York U.S.A. (2019), pg. 123 [arXiv:1712.02796] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001.
CMB-S4 collaboration, CMB-S4 Science Book, First Edition, arXiv:1610.02743 [INSPIRE].
J.R. Espinosa, D. Racco and A. Riotto, Cosmological Signature of the Standard Model Higgs Vacuum Instability: Primordial Black Holes as Dark Matter, Phys. Rev. Lett. 120 (2018) 121301 [arXiv:1710.11196] [INSPIRE].
C. Gross, A. Polosa, A. Strumia, A. Urbano and W. Xue, Dark Matter in the Standard Model?, Phys. Rev. D 98 (2018) 063005 [arXiv:1803.10242] [INSPIRE].
J.R. Espinosa, D. Racco and A. Riotto, Primordial Black Holes from Higgs Vacuum Instability: Avoiding Fine-tuning through an Ultraviolet Safe Mechanism, Eur. Phys. J. C 78 (2018) 806 [arXiv:1804.07731] [INSPIRE].
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Fumagalli, J., Renaux-Petel, S. & Ronayne, J.W. Higgs vacuum (in)stability during inflation. The dangerous relevance of de Sitter departure and Planck-suppressed operators. J. High Energ. Phys. 2020, 142 (2020). https://doi.org/10.1007/JHEP02(2020)142
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DOI: https://doi.org/10.1007/JHEP02(2020)142