Abstract
Most of the inflationary models that are in agreement with the Planck data rely on the presence of non-renormalizable operators. If the connection to low energy particle physics is made, the renormalization group (RG) introduces a sensitivity to ultraviolet (UV) physics that can be crucial in determining the inflationary predictions. We analyse this effect for the Standard Model (SM) augmented with non-minimal derivative couplings to gravity. Our set-up reduces to the SM for small values of the Higgs field, and allows for inflation in the opposite large field regime. The one-loop beta functions in the inflationary region are calculated using a covariant approach that properly accounts for the non-trivial structure of the field space manifold. We run the SM parameters from the electroweak to the inflationary scale, matching the couplings of the different effective field theories at the boundary between the two regimes, where we also include threshold corrections that parametrize effects from UV physics. We then compute the spectral index and tensor-to-scalar ratio and find that RG flow corrections can be determinant: a scenario that is ruled out at tree level can be resurrected and vice versa.
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Planck collaboration, Planck 2018 results. X. Constraints on inflation, arXiv:1807.06211 [INSPIRE].
J. Martin, C. Ringeval and V. Vennin, Encyclopædia Inflationaris, Phys. Dark Univ. 5–6 (2014) 75 [arXiv:1303.3787] [INSPIRE].
E.J. Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart and D. Wands, False vacuum inflation with Einstein gravity, Phys. Rev. D 49 (1994) 6410 [astro-ph/9401011] [INSPIRE].
D. Baumann and L. McAllister, Inflation and String Theory, in Cambridge Monographs on Mathematical Physics , Cambridge University Press (2015) [arXiv:1404.2601] [INSPIRE].
C.P. Burgess, S.P. Patil and M. Trott, On the Predictiveness of Single-Field Inflationary Models, JHEP 06 (2014) 010 [arXiv:1402.1476] [INSPIRE].
J. Fumagalli and M. Postma, UV (in)sensitivity of Higgs inflation, JHEP 05 (2016) 049 [arXiv:1602.07234] [INSPIRE].
C. Germani and A. Kehagias, New Model of Inflation with Non-minimal Derivative Coupling of Standard Model Higgs Boson to Gravity, Phys. Rev. Lett. 105 (2010) 011302 [arXiv:1003.2635] [INSPIRE].
C. Germani, Spontaneous localization on a brane via a gravitational mechanism, Phys. Rev. D 85 (2012) 055025 [arXiv:1109.3718] [INSPIRE].
S. Di Vita and C. Germani, Electroweak vacuum stability and inflation via nonminimal derivative couplings to gravity, Phys. Rev. D 93 (2016) 045005 [arXiv:1508.04777] [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence, JHEP 10 (2013) 087 [arXiv:1308.2627] [INSPIRE].
F. Bezrukov, J. Rubio and M. Shaposhnikov, Living beyond the edge: Higgs inflation and vacuum metastability, Phys. Rev. D 92 (2015) 083512 [arXiv:1412.3811] [INSPIRE].
F. Bezrukov and M. Shaposhnikov, Higgs inflation at the critical point, Phys. Lett. B 734 (2014) 249 [arXiv:1403.6078] [INSPIRE].
V.-M. Enckell, K. Enqvist and S. Nurmi, Observational signatures of Higgs inflation, JCAP 07 (2016) 047 [arXiv:1603.07572] [INSPIRE].
F. Bezrukov, M. Pauly and J. Rubio, On the robustness of the primordial power spectrum in renormalized Higgs inflation, JCAP 02 (2018) 040 [arXiv:1706.05007] [INSPIRE].
J. Fumagalli, S. Mooij and M. Postma, Unitarity and predictiveness in new Higgs inflation, JHEP 03 (2018) 038 [arXiv:1711.08761] [INSPIRE].
F.L. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton, Phys. Lett. B 659 (2008) 703 [arXiv:0710.3755] [INSPIRE].
K. Kamada, T. Kobayashi, T. Takahashi, M. Yamaguchi and J. Yokoyama, Generalized Higgs inflation, Phys. Rev. D 86 (2012) 023504 [arXiv:1203.4059] [INSPIRE].
J. Rubio, Higgs inflation, Front. Astron. Space Sci. 5 (2019) 50 [arXiv:1807.02376] [INSPIRE].
F. Bezrukov and M. Shaposhnikov, Standard Model Higgs boson mass from inflation: Two loop analysis, JHEP 07 (2009) 089 [arXiv:0904.1537] [INSPIRE].
F. Bezrukov, A. Magnin, M. Shaposhnikov and S. Sibiryakov, Higgs inflation: consistency and generalisations, JHEP 01 (2011) 016 [arXiv:1008.5157] [INSPIRE].
A. De Simone, M.P. Hertzberg and F. Wilczek, Running Inflation in the Standard Model, Phys. Lett. B 678 (2009) 1 [arXiv:0812.4946] [INSPIRE].
A.O. Bärvinsky, A.Y. Kamenshchik and A.A. Starobinsky, Inflation scenario via the Standard Model Higgs boson and LHC, JCAP 11 (2008) 021 [arXiv:0809.2104] [INSPIRE].
A.O. Bärvinsky, A.Y. Kamenshchik, C. Kiefer, A.A. Starobinsky and C. Steinwachs, Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field, JCAP 12 (2009) 003 [arXiv:0904.1698] [INSPIRE].
A.O. Bärvinsky, A.Y. Kamenshchik, C. Kiefer, A.A. Starobinsky and C.F. Steinwachs, Higgs boson, renormalization group, and naturalness in cosmology, Eur. Phys. J. C 72 (2012) 2219 [arXiv:0910.1041] [INSPIRE].
D.P. George, S. Mooij and M. Postma, Quantum corrections in Higgs inflation: the real scalar case, JCAP 02 (2014) 024 [arXiv:1310.2157] [INSPIRE].
D.P. George, S. Mooij and M. Postma, Quantum corrections in Higgs inflation: the Standard Model case, JCAP 04 (2016) 006 [arXiv:1508.04660] [INSPIRE].
M.P. Hertzberg, Can Inflation be Connected to Low Energy Particle Physics?, JCAP 08 (2012) 008 [arXiv:1110.5650] [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].
J. Fumagalli, Renormalization Group independence of Cosmological Attractors, Phys. Lett. B 769 (2017) 451 [arXiv:1611.04997] [INSPIRE].
F. Bauer and D.A. Demir, Inflation with Non-Minimal Coupling: Metric versus Palatini Formulations, Phys. Lett. B 665 (2008) 222 [arXiv:0803.2664] [INSPIRE].
S. Räsänen and P. Wahlman, Higgs inflation with loop corrections in the Palatini formulation, JCAP 11 (2017) 047 [arXiv:1709.07853] [INSPIRE].
V.-M. Enckell, K. Enqvist, S. Räsänen and E. Tomberg, Higgs inflation at the hilltop, JCAP 06 (2018) 005 [arXiv:1802.09299] [INSPIRE].
S. Räsänen, Higgs inflation in the Palatini formulation with kinetic terms for the metric, Open J. Astrophys. 2 (2019) 1 [arXiv:1811.09514] [INSPIRE].
A. Racioppi, Non-Minimal (Self-)Running Inflation: Metric vs. Palatini Formulation, arXiv:1912.10038 [INSPIRE].
F. Bauer and D.A. Demir, Higgs-Palatini Inflation and Unitarity, Phys. Lett. B 698 (2011) 425 [arXiv:1012.2900] [INSPIRE].
A. Escrivà and C. Germani, Beyond dimensional analysis: Higgs and new Higgs inflations do not violate unitarity, Phys. Rev. D 95 (2017) 123526 [arXiv:1612.06253] [INSPIRE].
M. Galante, R. Kallosh, A. Linde and D. Roest, Unity of Cosmological Inflation Attractors, Phys. Rev. Lett. 114 (2015) 141302 [arXiv:1412.3797] [INSPIRE].
G.A. Vilkovisky, The Unique Effective Action in Quantum Field Theory, Nucl. Phys. B 234 (1984) 125 [INSPIRE].
J.-O. Gong and T. Tanaka, A covariant approach to general field space metric in multi-field inflation, JCAP 03 (2011) 015 [Erratum JCAP 02 (2012) E01] [arXiv:1101.4809] [INSPIRE].
J. Fumagalli, S. Renaux-Petel and J.W. Ronayne, Higgs vacuum (in)stability during inflation: the dangerous relevance of de Sitter departure and Planck-suppressed operators, JHEP 02 (2020) 142 [arXiv:1910.13430] [INSPIRE].
B.S. DeWitt, Dynamical theory of groups and fields, Conf. Proc. C 630701 (1964) 585 [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. Achucarro, J.-O. Gong, S. Hardeman, G.A. Palma and S.P. Patil, Features of heavy physics in the CMB power spectrum, JCAP 01 (2011) 030 [arXiv:1010.3693] [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space, Phys. Lett. B 754 (2016) 335 [arXiv:1511.00724] [INSPIRE].
R. Alonso, E.E. Jenkins and A.V. Manohar, Geometry of the Scalar Sector, JHEP 08 (2016) 101 [arXiv:1605.03602] [INSPIRE].
A. Helset, M. Paraskevas and M. Trott, Gauge fixing the Standard Model Effective Field Theory, Phys. Rev. Lett. 120 (2018) 251801 [arXiv:1803.08001] [INSPIRE].
R. Nagai, M. Tanabashi, K. Tsumura and Y. Uchida, Symmetry and geometry in a generalized Higgs effective field theory: Finiteness of oblique corrections versus perturbative unitarity, Phys. Rev. D 100 (2019) 075020 [arXiv:1904.07618] [INSPIRE].
A. Helset, A. Martin and M. Trott, The Geometric Standard Model Effective Field Theory, JHEP 03 (2020) 163 [arXiv:2001.01453] [INSPIRE].
R. Alonso, A covariant momentum representation for loop corrections in gravity, JHEP 05 (2020) 131 [arXiv:1912.09671] [INSPIRE].
C.F. Steinwachs and A.Y. Kamenshchik, Non-minimal Higgs Inflation and Frame Dependence in Cosmology, AIP Conf. Proc. 1514 (2013) 161 [arXiv:1301.5543] [INSPIRE].
K. Falls and M. Herrero-Valea, Frame (In)equivalence in Quantum Field Theory and Cosmology, Eur. Phys. J. C 79 (2019) 595 [arXiv:1812.08187] [INSPIRE].
K. Finn, S. Karamitsos and A. Pilaftsis, Frame Covariance in Quantum Gravity, Phys. Rev. D 102 (2020) 045014 [arXiv:1910.06661] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, On the New Definition of Off-shell Effective Action, Nucl. Phys. B 234 (1984) 509 [INSPIRE].
B.S. DeWitt, Quantum Theory of Gravity. 2. The Manifestly Covariant Theory, Phys. Rev. 162 (1967) 1195 [INSPIRE].
D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].
A.H. Hoang, The Top Mass: Interpretation and Theoretical Uncertainties, in proceedings of the 7th International Workshop on Top Quark Physics (TOP2014), Cannes, France, 28 September–3 October 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 (2019), pp. 123–151 [arXiv:1712.02796] [INSPIRE].
Particle Data Group, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [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].
A. Urbano, Inflation without gauge redundancy, JCAP 04 (2020) 040 [arXiv:2001.05480] [INSPIRE].
Planck collaboration, Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
M. Shaposhnikov, A. Shkerin and S. Zell, Quantum Effects in Palatini Higgs Inflation, JCAP 07 (2020) 064 [arXiv:2002.07105] [INSPIRE].
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Fumagalli, J., Postma, M. & van den Bout, M. Matching and running sensitivity in non-renormalizable inflationary models. J. High Energ. Phys. 2020, 114 (2020). https://doi.org/10.1007/JHEP09(2020)114
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DOI: https://doi.org/10.1007/JHEP09(2020)114