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Inverse nonmetricity in f(Q) gravity: Cosmology and observational constraints

Luís Atayde1,2,*, Simão Marques Nunes1,2,†, and Noemi Frusciante3,4,‡

  • 1Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, P-1749-016 Lisbon, Portugal
  • 2Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, P-1749-016 Lisbon, Portugal
  • 3Dipartimento di Fisica “E. Pancini”, Università degli Studi di Napoli “Federico II”, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy
  • 4INFN Sezione di Napoli, Università degli Studi di Napoli “Federico II”, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy

  • *Contact author: luisbbatayde@gmail.com
  • Contact author: simaomnunes@gmail.com
  • Contact author: noemi.frusciante@unina.it

Phys. Rev. D 114, 024056 – Published 22 July, 2026

DOI: https://doi.org/10.1103/ts4w-xn8v

Abstract

We study a minimal modified gravity scenario in the symmetric teleparallel (nonmetricity) formulation, focusing on an inverse nonmetricity term with f(Q)=Q+M4Q1. The model does not introduce additional free parameters relative to the standard cosmological model ΛCDM, but modifies the late-time expansion and linear growth via an enhanced effective gravitational coupling. We identify key signatures: an enhanced matter power spectrum and cosmic microwave background (CMB) lensing, alongside a reduced late-time integrated Sachs-Wolfe effect and a shift in CMB peak positions. We confront the model with CMB data alone and in combination with baryon acoustic oscillations, redshift-space distortions, supernovae Ia, and DES large-scale structure data, considering both fixed minimal neutrino mass and varying Σmν. We find that the model typically prefers higher H0 than ΛCDM, alleviating the H0 tension, while its boosted growth tends to increase clustering amplitudes unless offset by larger neutrino masses when Σmν is free. Overall, CMB-only data provide at most weak statistical support compared to ΛCDM, whereas late-time measurements impose tight restrictions that largely remove any improvement, positioning this model as a minimal yet strongly constrained alternative to dark energy.

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References (87)

  1. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020).
  2. S. Weinberg, in 4th International Symposium on Sources and Detection of Dark Matter in the Universe (DM 2000) (2000), pp. 18–26, arXiv:astro-ph/0005265.
  3. H. E. S. Velten, R. F. vom Marttens, and W. Zimdahl, Eur. Phys. J. C 74, 3160 (2014).
  4. P. Bull et al., Phys. Dark Universe 12, 56 (2016).
  5. E. Di Valentino et al. (CosmoVerse Network Collaboration), Phys. Dark Universe 49, 101965 (2025).
  6. A. H. Wright et al., Astron. Astrophys. 703, A158 (2025).
  7. A. G. Adame et al. (DESI Collaboration), J. Cosmol. Astropart. Phys. 02 (2025) 021.
  8. W. Giarè, V. Poulin, and T. L. Smith, J. Cosmol. Astropart. Phys. 10 (2024) 035.
  9. B. R. Dinda, J. Cosmol. Astropart. Phys. 09 (2024) 062.
  10. J. B. Jiménez, L. Heisenberg, and T. S. Koivisto, Phys. Rev. D 98, 044048 (2018).
  11. J. Beltrán Jiménez, L. Heisenberg, T. S. Koivisto, and S. Pekar, Phys. Rev. D 101, 103507 (2020).
  12. L. Heisenberg, Phys. Rep. 1107, 1 (2024).
  13. N. Frusciante, Phys. Rev. D 103, 044021 (2021).
  14. I. S. Albuquerque and N. Frusciante, Phys. Dark Universe 35, 100980 (2022).
  15. T. B. Gonçalves, L. Atayde, and N. Frusciante, Phys. Rev. D 109, 084003 (2024).
  16. S. Nojiri and S. D. Odintsov, Phys. Dark Universe 45, 101538 (2024).
  17. S. Nojiri and S. D. Odintsov, Phys. Dark Universe 49, 102001 (2025).
  18. R. Lázkoz, F. S. N. Lobo, M. a. Ortiz-Baños, and V. Salzano, Phys. Rev. D 100, 104027 (2019).
  19. L. Atayde and N. Frusciante, Phys. Rev. D 107, 124048 (2023).
  20. L. Atayde and N. Frusciante, Phys. Rev. D 104, 064052 (2021).
  21. I. Ayuso, R. Lazkoz, and V. Salzano, Phys. Rev. D 103, 063505 (2021).
  22. B. J. Barros, T. Barreiro, T. Koivisto, and N. J. Nunes, Phys. Dark Universe 30, 100616 (2020).
  23. C. G. Boiza, M. Petronikolou, M. Bouhmadi-López, and E. N. Saridakis, J. Cosmol. Astropart. Phys. 12 (2025) 011.
  24. G. G. L. Nashed, Eur. Phys. J. C 85, 183 (2025).
  25. S. Sahlu and A. Abebe, arXiv:2412.20831.
  26. Q. Wang, X. Ren, Y.-F. Cai, W. Luo, and E. N. Saridakis, Astrophys. J. 974, 7 (2024).
  27. J. Shi, Eur. Phys. J. C 83, 951 (2023).
  28. J. Ferreira, T. Barreiro, J. P. Mimoso, and N. J. Nunes, Phys. Rev. D 108, 063521 (2023).
  29. S. Mandal and P. K. Sahoo, Phys. Lett. B 823, 136786 (2021).
  30. M. Koussour, S. H. Shekh, A. Hanin, Z. Sakhi, S. R. Bhoyer, and M. Bennai, Classical Quantum Gravity 39, 195021 (2022).
  31. J. Ferreira, T. Barreiro, J. Mimoso, and N. J. Nunes, Phys. Rev. D 105, 123531 (2022).
  32. R. D’Agostino and R. C. Nunes, Phys. Rev. D 106, 124053 (2022).
  33. K. El Bourakadi, Z. Sakhi, and M. Bennai, arXiv:2302.11229.
  34. S. A. Narawade, S. H. Shekh, B. Mishra, W. Khyllep, and J. Dutta, Eur. Phys. J. C 84, 773 (2024).
  35. F. K. Anagnostopoulos, S. Basilakos, and E. N. Saridakis, Phys. Lett. B 822, 136634 (2021).
  36. O. Sokoliuk, S. Arora, S. Praharaj, A. Baransky, and P. K. Sahoo, Mon. Not. R. Astron. Soc. 522, 252 (2023).
  37. F. K. Anagnostopoulos, V. Gakis, E. N. Saridakis, and S. Basilakos, Eur. Phys. J. C 83, 58 (2023).
  38. N. Aggarwal, A. Pourmand, F. Shojai, and H. Parthasarathy, arXiv:2212.00312.
  39. M. Koussour and A. De, Eur. Phys. J. C 83, 400 (2023).
  40. J. A. Nájera, C. A. Alvarado, and C. Escamilla-Rivera, Mon. Not. R. Astron. Soc. 524, 5280 (2023).
  41. A. Oliveros and M. A. Acero, Int. J. Mod. Phys. D 33, 2450004 (2024).
  42. Z. Sakr and L. Schey, J. Cosmol. Astropart. Phys. 10 (2024) 052.
  43. A. K. Yadav, S. Bhoyar, M. Dhabe, S. Shekh, and N. Ahmad, J. High Energy Astrophys. 43, 114 (2024).
  44. S. Pradhan, R. Solanki, and P. K. Sahoo, J. High Energy Astrophys. 43, 258 (2024).
  45. L. K. Sharma, S. Parekh, and A. K. Yadav, Nucl. Phys. B1018, 117007 (2025).
  46. F. Oliveira, B. Ribeiro, W. S. Hipólito-Ricaldi, F. Avila, and A. Bernui, J. Cosmol. Astropart. Phys. 12 (2025) 007.
  47. A. Kolhatkar, S. S. Mishra, and P. K. Sahoo, Eur. Phys. J. C 85, 656 (2025).
  48. S. Sultanaa and S. Chattopadhyay, J. High Energy Astrophys. 48, 100422 (2025).
  49. P. Karmakar and S. Haridasu, arXiv:2509.07976.
  50. C. Li, X. Ren, Y. Yang, E. N. Saridakis, and Y.-F. Cai, arXiv:2512.16551.
  51. A. Paliathanasis, Phys. Dark Universe 49, 101993 (2025).
  52. A. Paliathanasis, J. High Energy Astrophys. 53, 100609 (2026).
  53. S. M. Carroll, V. Duvvuri, M. Trodden, and M. S. Turner, Phys. Rev. D 70, 043528 (2004).
  54. J. Lesgourgues and S. Pastor, Phys. Rep. 429, 307 (2006).
  55. A. Barreira, B. Li, C. Baugh, and S. Pascoli, Phys. Rev. D 90, 023528 (2014).
  56. J. Shim, J. Lee, and M. Baldi, arXiv:1404.3639.
  57. M. Baldi, F. Villaescusa-Navarro, M. Viel, E. Puchwein, V. Springel, and L. Moscardini, Mon. Not. R. Astron. Soc. 440, 75 (2014).
  58. J.-h. He, Phys. Rev. D 88, 103523 (2013).
  59. J. Dossett, B. Hu, and D. Parkinson, J. Cosmol. Astropart. Phys. 03 (2014) 046.
  60. A. Hojjati, L. Pogosian, and G.-B. Zhao, J. Cosmol. Astropart. Phys. 08 (2011) 005.
  61. H. Motohashi, A. A. Starobinsky, and J. Yokoyama, Phys. Rev. Lett. 110, 121302 (2013).
  62. B. Hu, M. Raveri, A. Silvestri, and N. Frusciante, Phys. Rev. D 91, 063524 (2015).
  63. N. Bellomo, E. Bellini, B. Hu, R. Jimenez, C. Pena-Garay, and L. Verde, J. Cosmol. Astropart. Phys. 02 (2017) 043.
  64. N. Frusciante and M. Benetti, Phys. Rev. D 103, 104060 (2021).
  65. M. Ballardini, M. Braglia, F. Finelli, D. Paoletti, A. A. Starobinsky, and C. Umiltà, J. Cosmol. Astropart. Phys. 10 (2020) 044.
  66. T. M. C. Abbott et al. (DES Collaboration), arXiv:2601.14559.
  67. J. Beltrán Jiménez, L. Heisenberg, and T. S. Koivisto, J. Cosmol. Astropart. Phys. 08 (2018) 039.
  68. J. Beltrán Jiménez, L. Heisenberg, and T. Koivisto, Phys. Rev. D 98, 044048 (2018).
  69. K. F. Dialektopoulos, T. S. Koivisto, and S. Capozziello, Eur. Phys. J. C 79, 606 (2019).
  70. L. Amendola, M. Kunz, and D. Sapone, J. Cosmol. Astropart. Phys. 04 (2008) 013.
  71. A. Silvestri, L. Pogosian, and R. V. Buniy, Phys. Rev. D 87, 104015 (2013).
  72. A. Zucca, L. Pogosian, A. Silvestri, and G.-B. Zhao, J. Cosmol. Astropart. Phys. 05 (2019) 001.
  73. I. Sawicki and E. Bellini, Phys. Rev. D 92, 084061 (2015).
  74. S. Peirone, K. Koyama, L. Pogosian, M. Raveri, and A. Silvestri, Phys. Rev. D 97, 043519 (2018).
  75. N. Frusciante, S. Peirone, S. Casas, and N. A. Lima, Phys. Rev. D 99, 063538 (2019).
  76. A. Lewis, J. Cosmol. Astropart. Phys. 08 (2025) 025.
  77. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A5 (2020).
  78. A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. Burden, and M. Manera, Mon. Not. R. Astron. Soc. 449, 835 (2015).
  79. F. Beutler, C. Blake, M. Colless, D. H. Jones, L. Staveley-Smith, L. Campbell, Q. Parker, W. Saunders, and F. Watson, Mon. Not. R. Astron. Soc. 416, 3017 (2011).
  80. S. Alam et al. (BOSS Collaboration), Mon. Not. R. Astron. Soc. 470, 2617 (2017).
  81. M. Betoule et al. (SDSS Collaboration), Astron. Astrophys. 568, A22 (2014).
  82. T. M. C. Abbott et al. (DES Collaboration), Phys. Rev. D 98, 043526 (2018).
  83. T. M. C. Abbott et al. (DES Collaboration), Phys. Rev. D 99, 123505 (2019).
  84. P. A. R. Ade et al. (Planck Collaboration), Astron. Astrophys. 594, A14 (2016).
  85. N. Frusciante, S. Peirone, L. Atayde, and A. De Felice, Phys. Rev. D 101, 064001 (2020).
  86. A. G. Riess et al., Astrophys. J. Lett. 934, L7 (2022).
  87. D. J. Spiegelhalter, N. G. Best, B. P. Carlin, and A. Linde, J. R. Stat. Soc. Ser. B 76, 485 (2014).

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