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What we have not learned about the dark energy equation of state

Savvas Nesseris1,*, Yashar Akrami1,2,3,†, and Glenn D. Starkman2,‡

  • *Contact author: savvas.nesseris@csic.es
  • Contact author: yashar.akrami@csic.es
  • Contact author: glenn.starkman@case.edu

Phys. Rev. D 114, L041305 – Published 21 August, 2026

DOI: https://doi.org/10.1103/q2gb-n61g

Abstract

We show that using a Taylor expansion for the dark energy equation-of-state parameter and limiting it to the zeroth and first-order terms, i.e., the so-called Chevallier-Polarski-Linder (CPL) parametrization in regimes where it has been shown to fail as a physics-based two-parameter model, instead of allowing for higher-order terms and then marginalizing over them, adds extra information not present in the data and leads to markedly different and potentially misleading conclusions. Fixing the higher-order terms to zero, one concludes that vacuum energy that is currently nondynamical (e.g., the cosmological constant) is excluded at several σ significance as the explanation of cosmic acceleration, even in Dark Energy Spectroscopic Survey (DESI) DR1 data. Meanwhile, instead marginalizing over the higher-order terms shows that we know neither the current dark energy equation of state nor its current rate of change well enough to make such a claim. The CPL parametrization also implies that dark energy exhibits phantom behavior at high redshifts, while we show that by allowing the higher-order terms—which is required in order to capture the behavior of the dark energy equation of state in regimes beyond the validity of the CPL parametrization—the evidence for this phantomlike dark energy significantly weakens. This is not an argument for the higher-order phenomenological parametrizations, but rather a caution regarding such parametrizations in general. This issue has become more prominent now with the recent release of high-quality Stage IV galaxy survey data. The results of analyses using simple parametrizations should be interpreted with great care.

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References (34)

  1. S. Perlmutter et al. (Supernova Cosmology Project Collaboration), Measurements of Ω and Λ from 42 high redshift supernovae, Astrophys. J. 517, 565 (1999).
  2. A. G. Riess et al. (Supernova Search Team Collaboration), Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116, 1009 (1998).
  3. J. Martin, Everything you always wanted to know about the cosmological constant problem (but were afraid to ask), C.R. Phys. 13, 566 (2012).
  4. C. P. Burgess, The cosmological constant problem: Why it’s hard to get dark energy from micro-physics, in 100e Ecole d’Ete de Physique: Post-Planck Cosmology (2015), pp. 149–197, .
  5. W. Nernst, Über einen Versuch, von quantentheoretischen Betrachtungen zur Annahme stetiger Energieänderungen zurückzukehren, Verh. Dtsch. Phys. Ges. 18, 83 (1916).
  6. S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61, 1 (1989).
  7. E. J. Copeland, M. Sami, and S. Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15, 1753 (2006).
  8. G. Obied, H. Ooguri, L. Spodyneiko, and C. Vafa, De Sitter space and the swampland, arXiv:1806.08362.
  9. M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter, Int. J. Mod. Phys. D 10, 213 (2001).
  10. E. V. Linder, Exploring the expansion history of the universe, Phys. Rev. Lett. 90, 091301 (2003).
  11. E. V. Linder, The dynamics of quintessence, the quintessence of dynamics, Gen. Relativ. Gravit. 40, 329 (2008).
  12. E. V. Linder, Interpreting dark energy data away from Λ, arXiv:2410.10981.
  13. D. Huterer and G. Starkman, Parameterization of dark-energy properties: A principal-component approach, Phys. Rev. Lett. 90, 031301 (2003).
  14. P. Bansal and D. Huterer, Expansion-history preferences of DESI and external data, arXiv:2502.07185.
  15. A. N. Ormondroyd, W. J. Handley, M. P. Hobson, and A. N. Lasenby, Nonparametric reconstructions of dynamical dark energy via flexknots, arXiv:2503.08658.
  16. M. Berti, E. Bellini, C. Bonvin, M. Kunz, M. Viel, and M. Zumalacarregui, Reconstructing the dark energy density in light of DESI BAO observations, arXiv:2503.13198.
  17. A. N. Ormondroyd, W. J. Handley, M. P. Hobson, and A. N. Lasenby, Comparison of dynamical dark energy with ΛCDM in light of DESI DR2, arXiv:2503.17342.
  18. A. G. Adame et al. (DESI Collaboration), DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 02 (2024) 021.
  19. We could have used the supernova data provided by the Dark Energy Survey (DES) Collaboration, which supersede the Pantheon+data. DES-SN5YR presented substantial new high-redshift supernova data and improved the techniques from Pantheon+, while DES-Dovekie further improved the cross-calibration between low- and high-redshift supernovae and made analysis improvements. However, as our paper primarily focuses on the limitations of the CPL parameterization it is not necessary to use the latest data set. Since all of the supernova data sets are consistent with each other, the results of this paper would not substantially change.

  20. D. Scolnic et al., The Pantheon+Analysis: The full data set and light-curve release, Astrophys. J. 938, 113 (2022).
  21. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  22. Z. Zhai and Y. Wang, Robust and model-independent cosmological constraints from distance measurements, J. Cosmol. Astropart. Phys. 07 (2018) 005.
  23. S. Brieden, H. Gil-Marín, and L. Verde, A tale of two (or more) h’s, J. Cosmol. Astropart. Phys. 04 (2022) 023.
  24. N. Schöneberg, The 2024 BBN baryon abundance update, J. Cosmol. Astropart. Phys. 06 (2024) 006.
  25. R. Trotta, Bayes in the sky: Bayesian inference and model selection in cosmology, Contemp. Phys. 49, 71 (2008).
  26. K. Lodha et al., Extended dark energy analysis using DESI DR2 BAO measurements, arXiv:2503.14743.
  27. J. T. Nielsen, A. Guffanti, and S. Sarkar, Marginal evidence for cosmic acceleration from type Ia supernovae, Sci. Rep. 6, 35596 (2016).
  28. A. Sah, M. Rameez, S. Sarkar, and C. Tsagas, Anisotropy in Pantheon+Supernovae, arXiv:2411.10838.
  29. U. Alam, V. Sahni, T. D. Saini, and A. A. Starobinsky, Rejoinder to ’No evidence of dark energy metamorphosis’, astro-ph/040468, arXiv:astro-ph/0406672.
  30. S. Nesseris and L. Perivolaropoulos, Comparison of the legacy and gold snia dataset constraints on dark energy models, Phys. Rev. D 72, 123519 (2005).
  31. Y. Akrami, G. Alestas, and S. Nesseris, Has DESI detected exponential quintessence?, arXiv:2504.04226.
  32. S. Anselmi, P.-S. Corasaniti, A. G. Sanchez, G. D. Starkman, R. K. Sheth, and I. Zehavi, Cosmic distance inference from purely geometric BAO methods: Linear point standard ruler and correlation function model fitting, Phys. Rev. D 99, 123515 (2019).
  33. S. Anselmi, G. D. Starkman, and A. Renzi, Cosmological forecasts for future galaxy surveys with the linear point standard ruler: Toward consistent BAO analyses far from a fiducial cosmology, Phys. Rev. D 107, 123506 (2023).
  34. M. Abdul Karim et al. (DESI Collaboration), DESI DR2 results II: Measurements of baryon acoustic oscillations and cosmological constraints, arXiv:2503.14738.

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