Abstract
We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the R2 term and the tracker solution for dark energy at late times can be realized for the Rp+1 term with −1 < p < 0. We also discuss the implications of Higgs-sigma interactions for the inflation and the vacuum stability in the Standard Model.
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F. L. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton, Phys. Lett. B 659 (2008) 703 [arXiv:0710.3755] [INSPIRE].
A. A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
Planck collaboration, Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641 (2020) A10 [arXiv:1807.06211] [INSPIRE].
C. P. Burgess, H. M. Lee and M. Trott, Power-counting and the Validity of the Classical Approximation During Inflation, JHEP 09 (2009) 103 [arXiv:0902.4465] [INSPIRE].
J. L. F. Barbón and J. R. Espinosa, On the Naturalness of Higgs Inflation, Phys. Rev. D 79 (2009) 081302 [arXiv:0903.0355] [INSPIRE].
C. P. Burgess, H. M. Lee and M. Trott, Comment on Higgs Inflation and Naturalness, JHEP 07 (2010) 007 [arXiv:1002.2730] [INSPIRE].
M. P. Hertzberg, On Inflation with Non-minimal Coupling, JHEP 11 (2010) 023 [arXiv:1002.2995] [INSPIRE].
G. F. Giudice and H. M. Lee, Unitarizing Higgs Inflation, Phys. Lett. B 694 (2011) 294 [arXiv:1010.1417] [INSPIRE].
H. M. Lee, Running inflation with unitary Higgs, Phys. Lett. B 722 (2013) 198 [arXiv:1301.1787] [INSPIRE].
G. F. Giudice and H. M. Lee, Starobinsky-like inflation from induced gravity, Phys. Lett. B 733 (2014) 58 [arXiv:1402.2129] [INSPIRE].
O. Lebedev and H. M. Lee, Higgs Portal Inflation, Eur. Phys. J. C 71 (2011) 1821 [arXiv:1105.2284] [INSPIRE].
H. M. Lee, Light inflaton completing Higgs inflation, Phys. Rev. D 98 (2018) 015020 [arXiv:1802.06174] [INSPIRE].
S.-M. Choi, Y.-J. Kang, H. M. Lee and K. Yamashita, Unitary inflaton as decaying dark matter, JHEP 05 (2019) 060 [arXiv:1902.03781] [INSPIRE].
J. L. F. Barbón, J. A. Casas, J. Elias-Miro and J. R. Espinosa, Higgs Inflation as a Mirage, JHEP 09 (2015) 027 [arXiv:1501.02231] [INSPIRE].
Y. Ema, Higgs Scalaron Mixed Inflation, Phys. Lett. B 770 (2017) 403 [arXiv:1701.07665] [INSPIRE].
D. Gorbunov and A. Tokareva, Scalaron the healer: removing the strong-coupling in the Higgs- and Higgs-dilaton inflations, Phys. Lett. B 788 (2019) 37 [arXiv:1807.02392] [INSPIRE].
M. He, R. Jinno, K. Kamada, S. C. Park, A. A. Starobinsky and J. Yokoyama, On the violent preheating in the mixed Higgs-R2 inflationary model, Phys. Lett. B 791 (2019) 36 [arXiv:1812.10099] [INSPIRE].
D. Y. Cheong, H. M. Lee and S. C. Park, Beyond the Starobinsky model for inflation, Phys. Lett. B 805 (2020) 135453 [arXiv:2002.07981] [INSPIRE].
Y. Ema, K. Mukaida and J. van de Vis, Higgs inflation as nonlinear sigma model and scalaron as its σ-meson, JHEP 11 (2020) 011 [arXiv:2002.11739] [INSPIRE].
Y. Ema, K. Mukaida and J. Van De Vis, Renormalization group equations of Higgs-R2 inflation, JHEP 02 (2021) 109 [arXiv:2008.01096] [INSPIRE].
T. P. Sotiriou and V. Faraoni, f (R) Theories Of Gravity, Rev. Mod. Phys. 82 (2010) 451 [arXiv:0805.1726] [INSPIRE].
J. M. Ezquiaga and M. Zumalacárregui, Dark Energy After GW170817: Dead Ends and the Road Ahead, Phys. Rev. Lett. 119 (2017) 251304 [arXiv:1710.05901] [INSPIRE].
E. J. Copeland, A. R. Liddle and D. Wands, Exponential potentials and cosmological scaling solutions, Phys. Rev. D 57 (1998) 4686 [gr-qc/9711068] [INSPIRE].
P. G. Ferreira and M. Joyce, Cosmology with a primordial scaling field, Phys. Rev. D 58 (1998) 023503 [astro-ph/9711102] [INSPIRE].
S. Tsujikawa, Quintessence: A Review, Class. Quant. Grav. 30 (2013) 214003 [arXiv:1304.1961] [INSPIRE].
A. Banerjee, H. Cai, L. Heisenberg, E. Ó. Colgáin, M. M. Sheikh-Jabbari and T. Yang, Hubble sinks in the low-redshift swampland, Phys. Rev. D 103 (2021) L081305 [arXiv:2006.00244] [INSPIRE].
E. O. Colgáin, M. M. Sheikh-Jabbari and L. Yin, Can dark energy be dynamical?, Phys. Rev. D 104 (2021) 023510 [arXiv:2104.01930] [INSPIRE].
H. M. Lee, Chaotic inflation in Jordan frame supergravity, JCAP 08 (2010) 003 [arXiv:1005.2735] [INSPIRE].
I. L. Buchbinder, S. D. Odintsov and I. L. Shapiro, Effective action in quantum gravity, IOP, Bristol, U.K. (1992) [INSPIRE].
J. Elias-Miro, J. R. Espinosa, G. F. Giudice, H. M. Lee and A. Strumia, Stabilization of the Electroweak Vacuum by a Scalar Threshold Effect, JHEP 06 (2012) 031 [arXiv:1203.0237] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
F. Denef, A. Hebecker and T. Wrase, de Sitter swampland conjecture and the Higgs potential, Phys. Rev. D 98 (2018) 086004 [arXiv:1807.06581] [INSPIRE].
H. Murayama, M. Yamazaki and T. T. Yanagida, Do We Live in the Swampland?, JHEP 12 (2018) 032 [arXiv:1809.00478] [INSPIRE].
K. Choi, D. Chway and C. S. Shin, The dS swampland conjecture with the electroweak symmetry and QCD chiral symmetry breaking, JHEP 11 (2018) 142 [arXiv:1809.01475] [INSPIRE].
C. Han, S. Pi and M. Sasaki, Quintessence Saves Higgs Instability, Phys. Lett. B 791 (2019) 314 [arXiv:1809.05507] [INSPIRE].
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Lee, H.M., Menkara, A.G. Cosmology of linear Higgs-sigma models with conformal invariance. J. High Energ. Phys. 2021, 18 (2021). https://doi.org/10.1007/JHEP09(2021)018
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DOI: https://doi.org/10.1007/JHEP09(2021)018