- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Luminal scalar-tensor theories for a not so dark dark energy

S. Mironov1,2,3,*, A. Shtennikova1,2,†, and M. Valencia-Villegas2,1,‡

  • *Contact author: sa.mironov_1@physics.msu.ru
  • †Contact author: shtennikova@inr.ru
  • ‡Contact author: mvalenciavillegas@itmp.msu.ru
PDF

Phys. Rev. D 111, L101501 – Published 7 May, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L101501

Abstract

In general the speed of gravitational waves (GWs) in scalar-tensor modifications of Einstein’s gravity is different from the speed of light. Nevertheless, it has been measured that their speeds are nearly the same. For the most general scalar-tensor theories classified to date that do propagate a graviton—DHOST, including Horndeski and beyond Horndeski (BH) theories—we show that, remarkably, up to five self-consistent couplings of the scalar of dark energy (DE) to the photon are enough to make their GWs luminal in a wide set of cases. We find at least one luminal BH theory for which the GW decay into DE is suppressed in any cosmological background.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (41)

  1. B. P. Abbott et al., GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
  2. A. Goldstein et al., An ordinary short gamma-ray burst with extraordinary implications: Fermi-GBM detection of GRB 170817A, Astrophys. J. Lett. 848, L14 (2017).
  3. V. Savchenko et al., INTEGRAL detection of the first prompt gamma-ray signal coincident with the gravitational-wave event GW170817, Astrophys. J. Lett. 848, L15 (2017).
  4. P. Brax and C. Burrage, Constraining disformally coupled scalar fields, Phys. Rev. D 90, 104009 (2014).
  5. S. Mironov, A. Shtennikova, and M. Valencia-Villegas, Reviving Horndeski after GW170817 by Kaluza-Klein compactifications, Phys. Lett. B 858, 139058 (2024).
  6. D. Bettoni, J. M. Ezquiaga, K. Hinterbichler, and M. Zumalacárregui, Speed of gravitational waves and the fate of scalar-tensor gravity, Phys. Rev. D 95, 084029 (2017).
  7. J. M. Ezquiaga and M. Zumalacárregui, Dark energy after GW170817: Dead ends and the road ahead, Phys. Rev. Lett. 119, 251304 (2017).
  8. J. Sakstein and B. Jain, Implications of the neutron star merger GW170817 for cosmological scalar-tensor theories, Phys. Rev. Lett. 119, 251303 (2017).
  9. T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller, and I. Sawicki, Strong constraints on cosmological gravity from GW170817 and GRB 170817A, Phys. Rev. Lett. 119, 251301 (2017).
  10. P. Creminelli and F. Vernizzi, Dark energy after GW170817 and GRB170817A, Phys. Rev. Lett. 119, 251302 (2017).
  11. D. Langlois, R. Saito, D. Yamauchi, and K. Noui, Scalar-tensor theories and modified gravity in the wake of GW170817, Phys. Rev. D 97, 061501 (2018).
  12. A. G. Adame et al., DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 02 (2025) 021.
  13. G. Ye, M. Martinelli, B. Hu, and A. Silvestri, Non-minimally coupled gravity as a physically viable fit to DESI 2024 BAO, arXiv:2407.15832.
  14. W. J. Wolf, C. García-García, D. J. Bartlett, and P. G. Ferreira, Scant evidence for thawing quintessence, Phys. Rev. D 110, 083528 (2024).
  15. E. O. Colgáin and M. M. Sheikh-Jabbari, DESI and SNe: Dynamical dark energy, Ωm tension or systematics?, arXiv:2412.12905.
  16. E. O. Colgáin, M. G. Dainotti, S. Capozziello, S. Pourojaghi, M. M. Sheikh-Jabbari, and D. Stojkovic, Does DESI 2024 confirm ΛCDM?, arXiv:2404.08633.
  17. D. Shlivko and P. J. Steinhardt, Assessing observational constraints on dark energy, Phys. Lett. B 855, 138826 (2024).
  18. M. Cortês and A. R. Liddle, Interpreting DESI’s evidence for evolving dark energy, J. Cosmol. Astropart. Phys. 12 (2024) 007.
  19. V. Patel, A. Chakraborty, and L. Amendola, The prior dependence of the DESI results, arXiv:2407.06586.
  20. W. J. Wolf, P. G. Ferreira, and C. García-García, Matching current observational constraints with nonminimally coupled dark energy, Phys. Rev. D 111, L041303 (2025).
  21. D. Langlois and K. Noui, Degenerate higher derivative theories beyond Horndeski: Evading the Ostrogradski instability, J. Cosmol. Astropart. Phys. 02 (2016) 034.
  22. J. Ben Achour, M. Crisostomi, K. Koyama, D. Langlois, K. Noui, and G. Tasinato, Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order, J. High Energy Phys. 12 (2016) 100.
  23. D. Langlois, M. Mancarella, K. Noui, and F. Vernizzi, Effective description of higher-order scalar-tensor theories, J. Cosmol. Astropart. Phys. 05 (2017) 033.
  24. D. Langlois, Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review, Int. J. Mod. Phys. D 28, 1942006 (2019).
  25. S. Mironov and V. Volkova, Non-singular cosmological scenarios in scalar-tensor theories and their stability: A review, Usp. Fiz. Nauk 195, 163 (2025).
  26. P. Creminelli, M. Lewandowski, G. Tambalo, and F. Vernizzi, Gravitational wave decay into dark energy, J. Cosmol. Astropart. Phys. 12 (2018) 025.
  27. G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10, 363 (1974).
  28. C. Deffayet, X. Gao, D. A. Steer, and G. Zahariade, From k-essence to generalised Galileons, Phys. Rev. D 84, 064039 (2011).
  29. J. Gleyzes, D. Langlois, F. Piazza, and F. Vernizzi, Healthy theories beyond Horndeski, Phys. Rev. Lett. 114, 211101 (2015).
  30. J. Gleyzes, D. Langlois, F. Piazza, and F. Vernizzi, Exploring gravitational theories beyond Horndeski, J. Cosmol. Astropart. Phys. 02 (2015) 018.
  31. T. Kaluza, Zum Unitätsproblem der Physik, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1921, 966 (1921).
  32. S. Mironov, A. Shtennikova, and M. Valencia-Villegas, Higher derivative scalar-vector-tensor theories from Kaluza-Klein reductions of Horndeski theory, Phys. Rev. D 111, 024028 (2025).
  33. S. Mironov, M. Sharov, and V. Volkova, Linear stability of a time-dependent, spherically symmetric background in beyond Horndeski theory and the speed of gravity waves, Eur. Phys. J. C 85, 50 (2025).
  34. S. Mironov, M. Sharov, and V. Volkova, Time-dependent, spherically symmetric background in Kaluza-Klein compactified Horndeski theory and the speed of gravity waves, arXiv:2408.06329.
  35. E. Babichev, C. Charmousis, B. Muntz, A. Padilla, and I. D. Saltas, Horndeski speed tests with scalar-photon couplings, J. Cosmol. Astropart. Phys. 01 (2025) 041.
  36. P. Brax, C. Burrage, and C. Englert, Disformal dark energy at colliders, Phys. Rev. D 92, 044036 (2015).
  37. A. Joyce, B. Jain, J. Khoury, and M. Trodden, Beyond the cosmological standard model, Phys. Rep. 568, 1 (2015).
  38. K. Koyama, G. Niz, and G. Tasinato, Effective theory for the Vainshtein mechanism from the Horndeski action, Phys. Rev. D 88, 021502 (2013).
  39. T. Kobayashi, Y. Watanabe, and D. Yamauchi, Breaking of Vainshtein screening in scalar-tensor theories beyond Horndeski, Phys. Rev. D 91, 064013 (2015).
  40. T. Kobayashi, Horndeski theory and beyond: A review, Rep. Prog. Phys. 82, 086901 (2019).
  41. https://rscf.ru/project/24-72-10110/.

Outline

Information

Phys. Rev. D 111, L101501– Published 7 May, 2025
  • Received 22 January 2025
  • Accepted 18 April 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation