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
  • Open Access

Reconciling Starobinsky inflation with ACT data

Loris Del Grosso1,*, Alfredo Urbano2,3,†, and Marcello Ziccolella2,3,‡

  • *Contact author: ldelgro1@jh.edu
  • †Contact author: alfredo.urbano@uniroma1.it
  • ‡Contact author: marcello.ziccolella@uniroma1.it

Phys. Rev. D 114, 083522 – Published 13 October, 2026

DOI: https://doi.org/10.1103/1znv-zjgd

Abstract

Recent Atacama Cosmology Telescope (ACT) observations, combined with Planck, favor a scalar spectral index in tension with Starobinsky inflation. Two main strategies have been proposed to reconcile Starobinsky inflation with these data: (i) including higher-curvature operators in the gravitational action and (ii) modifying the postinflationary reheating dynamics. We critically reexamine both approaches. When higher-curvature corrections are included, dimensional-analysis arguments allow introducing a second mass scale suppressing higher-dimensional operators, resulting in a one-coupling, two-scale effective theory. We show that fitting the Planck+ACT data drives this class of effective theories toward a regime of stronger sensitivity to UV physics, potentially implying fine-tuning of the inflationary observables. We illustrate our general point with two concrete models, namely, no-scale supergravity and metric-affine gravity, showing that they provide different realizations of the same underlying f(R) theory. On the reheating side, requiring the CMB modes to reenter the horizon before recombination leads to stringent constraints on the reheating equation of state, and fitting the Planck+ACT data favors an exotic reheating phase with ωreh>1/3, incompatible with inflaton oscillations about the minimum of the standard Starobinsky potential. Finally, we explore the possibility that a phase of cosmological stasis, driven by a tower of decaying massive states, could play the role of the postinflationary epoch. We find that accommodating ACT-preferred ns in this setup requires a tower of states with negative energy density. Taken together, our results suggest that reconciling Starobinsky inflation with the Planck+ACT data demands ingredients that are challenging to motivate from the perspective of UV-complete theories, undermining the minimality of the original Starobinsky model.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (95)

  1. A. A. Starobinsky, Sov. Astron. Lett. 9, 302 (1983).
  2. Y. Akrami et al. (Planck Collaboration), Astron. Astrophys. 641, A10 (2020).
  3. T. Louis et al. (ACT Collaboration), arXiv:2503.14452.
  4. E. Calabrese et al. (ACT Collaboration), arXiv:2503.14454.
  5. T. Louis et al. (Atacama Cosmology Telescope Collaboration), J. Cosmol. Astropart. Phys. 11 (2025) 062.
  6. C. Dioguardi, A. J. Iovino, and A. Racioppi, Phys. Lett. B 868, 139664 (2025).
  7. I. Antoniadis, J. Ellis, W. Ke, D. V. Nanopoulos, and K. A. Olive, J. Cosmol. Astropart. Phys. 08 (2025) 090.
  8. A. Salvio, Phys. Rev. D 112, L061301 (2025).
  9. N. Shobcha, N. Sidik Risdianto, and R. H. S. Budhi, arXiv:2606.24131.
  10. S. D. Odintsov and V. K. Oikonomou, Phys. Lett. B 880, 140805 (2026).
  11. S. D. Odintsov and V. K. Oikonomou, Phys. Lett. B 870, 139907 (2025).
  12. S. D. Odintsov and V. K. Oikonomou, Phys. Lett. B 870, 139909 (2025).
  13. Yogesh, A. Mohammadi, Q. Wu, and T. Zhu, J. Cosmol. Astropart. Phys. 10 (2025) 010.
  14. A. Mohammadi, Yogesh, and A. Wang, Phys. Lett. B 872, 140054 (2026).
  15. Yogesh, I. A. Bhat, M. R. Gangopadhyay, and M. Sami, J. Cosmol. Astropart. Phys. 09 (2026) 064.
  16. A. Mohammadi, Yogesh, H. Tan, and M. Sami, arXiv:2607.06112.
  17. I. D. Gialamas, T. Katsoulas, and K. Tamvakis, J. Cosmol. Astropart. Phys. 09 (2025) 060.
  18. T. Katsoulas and K. Tamvakis, Phys. Rev. D 113, 124010 (2026).
  19. J. Bezerra-Sobrinho and L. G. Medeiros, Eur. Phys. J. C 86, 416 (2026).
  20. A. Addazi, Y. Aldabergenov, and S. V. Ketov, Phys. Lett. B 869, 139883 (2025).
  21. S. V. Ketov, E. O. Pozdeeva, and S. Y. Vernov, J. Cosmol. Astropart. Phys. 12 (2025) 040.
  22. J. Kim, X. Wang, Y.-l. Zhang, and Z. Ren, J. Cosmol. Astropart. Phys. 09 (2025) 011.
  23. M. Drees and Y. Xu, Phys. Lett. B 867, 139612 (2025).
  24. L. Liu, Z. Yi, and Y. Gong, Sci. China Phys., Mech. Astron. 69, 280413 (2026).
  25. D. S. Zharov, O. O. Sobol, and S. I. Vilchinskii, Phys. Rev. D 112, 023544 (2025).
  26. G. C. Dorsch, L. P. C. Leão, L. M. B. Alves, L. C. A. Miranda, and B. M. D. Sena, arXiv:2606.28502.
  27. I. D. Gialamas, Phys. Rev. D 113, 084027 (2026).
  28. I. D. Gialamas and K. Tamvakis, J. Cosmol. Astropart. Phys. 03 (2023) 042.
  29. A. R. Liddle and S. M. Leach, Phys. Rev. D 68, 103503 (2003).
  30. L. Sebastiani, G. Cognola, R. Myrzakulov, S. D. Odintsov, and S. Zerbini, Phys. Rev. D 89, 023518 (2014).
  31. R. Myrzakulov, S. Odintsov, and L. Sebastiani, Phys. Rev. D 91, 083529 (2015).
  32. T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010).
  33. S. Nojiri and S. D. Odintsov, Phys. Rep. 505, 59 (2011).
  34. S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, Phys. Rep. 692, 1 (2017).
  35. M. Brinkmann, M. Cicoli, and P. Zito, J. High Energy Phys. 09 (2023) 038.
  36. F. Farakos, A. Kehagias, and A. Riotto, Nucl. Phys. B876, 187 (2013).
  37. S. Ferrara, R. Kallosh, A. Linde, and M. Porrati, J. Cosmol. Astropart. Phys. 11 (2013) 046.
  38. S. A. Appleby, R. A. Battye, and A. A. Starobinsky, J. Cosmol. Astropart. Phys. 06 (2010) 005.
  39. D. Y. Cheong, M. G. Park, and S. C. Park, Phys. Lett. B 873, 140217 (2026).
  40. Z.-C. Qiu, Y.-H. Pang, and Q.-G. Huang, Sci. China Phys., Mech. Astron. 69, 260413 (2026).
  41. C. P. Burgess, H. M. Lee, and M. Trott, J. High Energy Phys. 09 (2009) 103.
  42. M. P. Hertzberg, J. High Energy Phys. 11 (2010) 023.
  43. C. P. Burgess, H. M. Lee, and M. Trott, J. High Energy Phys. 07 (2010) 007.
  44. A. Kehagias, A. Moradinezhad Dizgah, and A. Riotto, Phys. Rev. D 89, 043527 (2014).
  45. D. Y. Cheong, H. M. Lee, and S. C. Park, Phys. Lett. B 805, 135453 (2020).
  46. M. He, K. Kamada, and K. Mukaida, Phys. Rev. Lett. 132, 191501 (2024).
  47. A. D. Linde and A. Westphal, J. Cosmol. Astropart. Phys. 03 (2008) 005.
  48. D. Chakraborty, M. Hai, S. T. Jahan, A. R. Kamal, and M. S. J. Shuvo, J. Cosmol. Astropart. Phys. 06 (2026) 025.
  49. E. Cremmer, S. Ferrara, C. Kounnas, and D. V. Nanopoulos, Phys. Lett. 133B, 61 (1983).
  50. J. R. Ellis, A. B. Lahanas, D. V. Nanopoulos, and K. Tamvakis, Phys. Lett. 134B, 429 (1984).
  51. J. R. Ellis, C. Kounnas, and D. V. Nanopoulos, Nucl. Phys. B241, 406 (1984).
  52. J. R. Ellis, C. Kounnas, and D. V. Nanopoulos, Nucl. Phys. B247, 373 (1984).
  53. J. R. Ellis, C. Kounnas, and D. V. Nanopoulos, Phys. Lett. 143B, 410 (1984).
  54. A. B. Lahanas and D. V. Nanopoulos, Phys. Rep. 145, 1 (1987).
  55. J. Ellis, M. A. G. Garcia, N. Nagata, N. D. V., K. A. Olive, and S. Verner, Int. J. Mod. Phys. D 29, 2030011 (2020).
  56. J. Ellis, D. V. Nanopoulos, and K. A. Olive, Phys. Rev. Lett. 111, 111301 (2013); 111, 129902(E) (2013).
  57. V. R. Ivanov, S. V. Ketov, E. O. Pozdeeva, and S. Y. Vernov, J. Cosmol. Astropart. Phys. 03 (2022) 058.
  58. P. A. R. Ade et al. (BICEP Collaboration and Keck Collaboration), Phys. Rev. Lett. 127, 151301 (2021).
  59. G. Pradisi and A. Salvio, Eur. Phys. J. C 82, 840 (2022).
  60. A. Racioppi, J. Cosmol. Astropart. Phys. 04 (2025) 084; 08 (2025) E01(E).
  61. M. He, M. Hong, and K. Mukaida, J. Cosmol. Astropart. Phys. 05 (2024) 107.
  62. I. D. Gialamas, T. Katsoulas, and K. Tamvakis, Phys. Rev. D 112, 9 (2025).
  63. R. H. Dicke, Phys. Rev. 125, 2163 (1962).
  64. M. Postma and M. Volponi, Phys. Rev. D 90, 103516 (2014).
  65. V. Faraoni and S. Nadeau, Phys. Rev. D 75, 023501 (2007).
  66. A. Di Marco, E. Orazi, and G. Pradisi, Eur. Phys. J. C 84, 146 (2024).
  67. C. Di Benedetto, A. Di Marco, E. Orazi, and G. Pradisi, arXiv:2605.09571.
  68. G. W. Anderson and D. J. Castano, Phys. Lett. B 347, 300 (1995).
  69. R. Barbieri and G. F. Giudice, Nucl. Phys. B306, 63 (1988).
  70. A. J. Iovino and A. Riotto, J. Cosmol. Astropart. Phys. 07 (2026) 047.
  71. J. B. Munoz and M. Kamionkowski, Phys. Rev. D 91, 043521 (2015).
  72. S. Allegrini, L. Del Grosso, A. J. Iovino, and A. Urbano, Phys. Rev. D 111, 123557 (2025).
  73. E. Calabrese et al. (Atacama Cosmology Telescope Collaboration), J. Cosmol. Astropart. Phys. 11 (2025) 063.
  74. P. Saha, S. Anand, and L. Sriramkumar, Phys. Rev. D 102, 103511 (2020).
  75. M. S. Turner, Phys. Rev. D 28, 1243 (1983).
  76. J. de Haro and L. A. Saló, Galaxies 9, 73 (2021).
  77. K. R. Dienes, L. Heurtier, F. Huang, D. Kim, T. M. P. Tait, and B. Thomas, Phys. Rev. D 105, 023530 (2022).
  78. D. S. Gorbunov and A. G. Panin, Phys. Lett. B 700, 157 (2011).
  79. A. A. Starobinsky, Phys. Lett. 91B, 99 (1980).
  80. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 1982).
  81. D. Lüst, J. Masias, B. Muntz, and M. Scalisi, J. High Energy Phys. 07 (2024) 186.
  82. P. G. Catinari, L. Del Grosso, L. Di Giovanni, and A. Urbano, Phys. Rev. D 112, L121302 (2025).
  83. K. N. Abazajian et al. (CMB-S4 Collaboration), arXiv:1610.02743.
  84. E. Allys et al. (LiteBIRD Collaboration), Prog. Theor. Exp. Phys. 2023, 042F01 (2023).
  85. E. G. M. Ferreira, E. McDonough, L. Balkenhol, R. Kallosh, L. Knox, and A. Linde, Phys. Rev. D 113, 043524 (2026).
  86. S. Chang and M. A. Luty, J. High Energy Phys. 03 (2020) 140.
  87. F. Abu-Ajamieh, S. Chang, M. Chen, and M. A. Luty, J. High Energy Phys. 07 (2021) 056.
  88. A. Falkowski and R. Rattazzi, J. High Energy Phys. 10 (2019) 255.
  89. T. Cohen, N. Craig, X. Lu, and D. Sutherland, J. High Energy Phys. 12 (2021) 003.
  90. T. Steingasser, M. P. Hertzberg, and D. I. Kaiser, arXiv:2505.20386.
  91. R. Kleiss, W. J. Stirling, and S. D. Ellis, Comput. Phys. Commun. 40, 359 (1986).
  92. P. Creminelli, S. Renaux-Petel, G. Tambalo, and V. Yingcharoenrat, J. Cosmol. Astropart. Phys. 01 (2026) 064.
  93. G. K. Karananas, M. Shaposhnikov, A. Shkerin, and S. Zell, Phys. Rev. D 104, 064036 (2021).
  94. I. L. Shapiro, Phys. Rep. 357, 113 (2002).
  95. D. Diakonov, A. G. Tumanov, and A. A. Vladimirov, Phys. Rev. D 84, 124042 (2011).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation