- Open Access
When dark matter heats up: A model-independent search for noncold behavior
Phys. Rev. D 112, 123537 – Published 23 December, 2025
DOI: https://doi.org/10.1103/r8sv-1g4q
Abstract
This article questions the common assumption of cold dark matter (DM) by exploring the possibility of a nonzero equation of state (EOS) without relying on any parametric approach. In standard cosmological analyses, DM is typically modeled as pressureless dust with , an assumption that aligns with large-scale structure formation, supports the empirical success of the -cold dark matter model, and simplifies cosmological modeling. However, there is no fundamental reason to exclude a nonzero from the cosmological framework. In this work, we explore this possibility through nonparametric and parametric reconstructions based on Gaussian process regression. The reconstructions use Hubble parameter measurements from cosmic chronometers, the of Type Ia supernovae, and baryon acoustic oscillation (BAO) data from DESI DR1 and DR2. Our findings suggest that a dynamical EOS for DM, although only mildly supported statistically, cannot be conclusively ruled out. Notably, we observe a mild tendency () toward a negative at the present epoch, which is most likely due to inconsistencies between the BAO data from DESI and other datasets.
Physics Subject Headings (PhySH)
Article Text
References (81)
- L. Verde, T. Treu, and A. G. Riess, Tensions between the early and the late Universe, Nat. Astron. 3, 891 (2019).
- Leandros Perivolaropoulos and Foteini Skara, Challenges for : An update, New Astron. Rev. 95, 101659 (2022).
- Elcio Abdalla et al., Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies, J. High Energy Astrophys. 34, 49 (2022).
- Eleonora Di Valentino et al., The CosmoVerse white paper: Addressing observational tensions in cosmology with systematics and fundamental physics, Phys. Dark Universe 49, 101965 (2025).
- Eleonora Di Valentino, Olga Mena, Supriya Pan, Luca Visinelli, Weiqiang Yang, Alessandro Melchiorri, David F. Mota, Adam G. Riess, and Joseph Silk, In the realm of the Hubble tension—A review of solutions, Classical Quantum Gravity 38, 153001 (2021).
- Nils Schöneberg, Guillermo Franco Abellán, Andrea Pérez Sánchez, Samuel J. Witte, Vivian Poulin, and Julien Lesgourgues, The Olympics: A fair ranking of proposed models, Phys. Rep. 984, 1 (2022).
- Marc Kamionkowski and Adam G. Riess, The Hubble tension and early dark energy, Annu. Rev. Nucl. Part. Sci. 73, 153 (2023).
- Ali Rida Khalife, Maryam Bahrami Zanjani, Silvia Galli, Sven Günther, Julien Lesgourgues, and Karim Benabed, Review of Hubble tension solutions with new SH0ES and SPT-3G data, J. Cosmol. Astropart. Phys. 04 (2024) 059.
- Eleonora Di Valentino et al., Snowmass2021—Letter of interest cosmology intertwined II: The Hubble constant tension, Astropart. Phys. 131, 102605 (2021).
- Paul Shah, Pablo Lemos, and Ofer Lahav, A buyer’s guide to the Hubble constant, Astron. Astrophys. Rev. 29, 9 (2021).
- Eleonora Di Valentino, Challenges of the standard cosmological model, Universe 8, 399 (2022).
- William Giarè, CMB anomalies and the Hubble tension, in The Hubble Constant Tension (Springer, Singapore, 2024).
- Jian-Ping Hu and Fa-Yin Wang, Hubble tension: The evidence of new physics, Universe 9, 94 (2023).
- Licia Verde, Nils Schöneberg, and Héctor Gil-Marín, A tale of many , Annu. Rev. Astron. Astrophys. 62, 287 (2024).
- The Hubble Constant Tension, edited by Eleonora Di Valentino and Dillon Brout, Springer Series in Astrophysics and Cosmology (Springer, New York, 2024).
- Leandros Perivolaropoulos, Hubble tension or distance ladder crisis?, Phys. Rev. D 110, 123518 (2024).
- Supriya Pan, Weiqiang Yang, Eleonora Di Valentino, David F. Mota, and Joseph Silk, IWDM: The fate of an interacting non-cold dark matter—vacuum scenario, J. Cosmol. Astropart. Phys. 07 (2023) 064.
- Christian M. Muller, Cosmological bounds on the equation of state of dark matter, Phys. Rev. D 71, 047302 (2005).
- Erminia Calabrese, Marina Migliaccio, Luca Pagano, Grazia De Troia, Alessandro Melchiorri, and Paolo Natoli, Cosmological constraints on the matter equation of state, Phys. Rev. D 80, 063539 (2009).
- Suresh Kumar and Lixin Xu, Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck, Phys. Lett. B 737, 244 (2014).
- Cristian Armendariz-Picon and Jayanth T. Neelakanta, How cold is cold dark matter?, J. Cosmol. Astropart. Phys. 03 (2014) 049.
- Kari Enqvist, Seshadri Nadathur, Toyokazu Sekiguchi, and Tomo Takahashi, Decaying dark matter and the tension in , J. Cosmol. Astropart. Phys. 09 (2015) 067.
- Riccardo Murgia, Alexander Merle, Matteo Viel, Maximilian Totzauer, and Aurel Schneider, “Non-cold” dark matter at small scales: A general approach, J. Cosmol. Astropart. Phys. 11 (2017) 046.
- Stefano Gariazzo, Miguel Escudero, Roberta Diamanti, and Olga Mena, Cosmological searches for a noncold dark matter component, Phys. Rev. D 96, 043501 (2017).
- Michael Kopp, Constantinos Skordis, Daniel B. Thomas, and Stéphane Ilić, Dark matter equation of state through cosmic history, Phys. Rev. Lett. 120, 221102 (2018).
- Riccardo Murgia, Vid Iršič, and Matteo Viel, Novel constraints on noncold, nonthermal dark matter from Lyman- forest data, Phys. Rev. D 98, 083540 (2018).
- Aurel Schneider, Constraining noncold dark matter models with the global 21-cm signal, Phys. Rev. D 98, 063021 (2018).
- Nikodem J. Popławski, Non-particle dark matter from Hubble parameter, Eur. Phys. J. C 79, 734 (2019).
- Stéphane Ilić, Michael Kopp, Constantinos Skordis, and Daniel B. Thomas, Dark matter properties through cosmic history, Phys. Rev. D 104, 043520 (2021).
- Sebastián Nájera and Roberto A. Sussman, Non-comoving cold dark matter in a background, Eur. Phys. J. C 81, 374 (2021).
- Emilio Elizalde, Janusz Gluza, and Martiros Khurshudyan, An approach to cold dark matter deviation and the tension problem by using machine learning, arXiv:2104.01077.
- Krishna Naidoo, Mariana Jaber, Wojciech A. Hellwing, and Maciej Bilicki, A dark matter solution to the and tensions, and the integrated Sachs-Wolfe void anomaly, Phys. Rev. D 109, 083511 (2024).
- Emil Brinch Holm, Thomas Tram, and Steen Hannestad, Decaying warm dark matter revisited, J. Cosmol. Astropart. Phys. 08 (2022) 044.
- Martiros Khurshudyan, Swampland criteria and neutrino generation in a non-cold dark matter universe, Astrophysics (Engl. Transl.) 66, 423 (2023).
- Yan-Hong Yao, Jun-Chao Wang, and Xin-He Meng, Observational constraints on noncold dark matter and phenomenological emergent dark energy, Phys. Rev. D 109, 063502 (2024).
- Martiros Khurshudyan and Emilio Elizalde, Constraints on prospective deviations from the cold dark matter model using a Gaussian process, Galaxies 12, 31 (2024).
- Weiqiang Yang, Supriya Pan, Eleonora Di Valentino, Olga Mena, David F. Mota, and Subenoy Chakraborty, Probing the cold nature of dark matter, Phys. Rev. D 111, 103509 (2025).
- Utkarsh Kumar, Abhijith Ajith, and Amresh Verma, Evidence for non-cold dark matter from DESI DR2 measurements, arXiv:2504.14419.
- Deng Wang, Evidence for dynamical dark matter, arXiv:2504.21481.
- Xingang Chen and Abraham Loeb, Evolving dark energy or evolving dark matter?, J. Cosmol. Astropart. Phys. 07 (2025) 059.
- Tian-Nuo Li, Yi-Min Zhang, Yan-Hong Yao, Peng-Ju Wu, Jing-Fei Zhang, and Xin Zhang, Is non-zero equation of state of dark matter favored by DESI DR2?, arXiv:2506.09819.
- Matteo Braglia, Xingang Chen, and Abraham Loeb, Exotic dark matter and the DESI anomaly, J. Cosmol. Astropart. Phys. 11 (2025) 064.
- Nils Schöneberg, The 2024 BBN baryon abundance update, J. Cosmol. Astropart. Phys. 06 (2024) 006.
- Marina Seikel, Chris Clarkson, and Mathew Smith, Reconstruction of dark energy and expansion dynamics using Gaussian processes, J. Cosmol. Astropart. Phys. 06 (2012) 036.
- Carl Edward Rasmussen and Christopher K. I. Williams, Gaussian Processes for Machine Learning, Adaptive Computation and Machine Learning (MIT Press, Cambridge, MA, 2006), pp. I–XVIII, 1–248.
- Purba Mukherjee and Narayan Banerjee, Nonparametric reconstruction of interaction in the cosmic dark sector, Phys. Rev. D 103, 123530 (2021).
- José de Jesús Velázquez, Luis A. Escamilla, Purba Mukherjee, and J. Alberto Vázquez, Non-parametric reconstruction of cosmological observables using Gaussian processes regression, Universe 10, 464 (2024).
- Christopher Williams, Prediction with Gaussian processes: From linear regression to linear prediction and beyond, in Learning in Graphical Models, NATO ASI Series D: Behavioural and Social Sciences (Springer, Netherlands, 1997), pp. 599–621.
- Bikash R. Dinda and Roy Maartens, Model-agnostic assessment of dark energy after DESI DR1 BAO, J. Cosmol. Astropart. Phys. 01 (2025) 120.
- John Skilling, Nested sampling, AIP Conf. Proc., 735, 395 (2004).
- Francesca Gerardi, Matteo Martinelli, and Alessandra Silvestri, Reconstruction of the dark energy equation of state from latest data: The impact of theoretical priors, J. Cosmol. Astropart. Phys. 07 (2019) 042.
- Luis A. Escamilla, Ozgur Akarsu, Eleonora Di Valentino, and J. Alberto Vazquez, Model-independent reconstruction of the interacting dark energy kernel: Binned and Gaussian process, J. Cosmol. Astropart. Phys. 11 (2023) 051.
- A. Slosar and J. A. Vazquez, https://github.com/ja-vazquez/SimpleMC.
- Joshua S. Speagle, dynesty: A dynamic nested sampling package for estimating Bayesian posteriors and evidences, Mon. Not. R. Astron. Soc. 493, 3132 (2020).
- J. Speagle, https://dynesty.readthedocs.io/en/stable/index.html.
- Dillon Brout et al., The analysis: Cosmological constraints, Astrophys. J. 938, 110 (2022).
- Chan-Gyung Park, Javier de Cruz Perez, and Bharat Ratra, Using non-DESI data to confirm and strengthen the DESI 2024 spatially-flat cosmological parameterization result, Phys. Rev. D 110, 123533 (2024).
- A. G. Adame et al. (DESI Collaboration), DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 02 (2025) 021.
- M. Abdul Karim et al. (DESI Collaboration), DESI DR2 results II: Measurements of baryon acoustic oscillations and cosmological constraints, Phys. Rev. D 112, 083515 (2025).
- A. L. Ratsimbazafy, S. I. Loubser, S. M. Crawford, C. M. Cress, B. A. Bassett, R. C. Nichol, and P. Väisänen, Age-dating luminous red galaxies observed with the southern African Large Telescope, Mon. Not. R. Astron. Soc. 467, 3239 (2017).
- Kang Jiao, Nicola Borghi, Michele Moresco, and Tong-Jie Zhang, New observational H(z) data from full-spectrum fitting of cosmic chronometers in the LEGA-C survey, Astrophys. J. Suppl. Ser. 265, 48 (2023).
- Cong Zhang, Han Zhang, Shuo Yuan, Tong-Jie Zhang, and Yan-Chun Sun, Four new observational data from luminous red galaxies in the Sloan Digital Sky Survey data release seven, Res. Astron. Astrophys. 14, 1221 (2014).
- Michele Moresco, Lucia Pozzetti, Andrea Cimatti, Raul Jimenez, Claudia Maraston, Licia Verde, Daniel Thomas, Annalisa Citro, Rita Tojeiro, and David Wilkinson, A 6% measurement of the Hubble parameter at : Direct evidence of the epoch of cosmic re-acceleration, J. Cosmol. Astropart. Phys. 05 (2016) 014.
- Raul Jimenez, Licia Verde, Tommaso Treu, and Daniel Stern, Constraints on the equation of state of dark energy and the Hubble constant from stellar ages and the CMB, Astrophys. J. 593, 622 (2003).
- Daniel Stern, Raul Jimenez, Licia Verde, Marc Kamionkowski, and S. Adam Stanford, Cosmic chronometers: Constraining the equation of state of dark energy. I: H(z) measurements, J. Cosmol. Astropart. Phys. 02 (2010) 008.
- Michele Moresco, Licia Verde, Lucia Pozzetti, Raul Jimenez, and Andrea Cimatti, New constraints on cosmological parameters and neutrino properties using the expansion rate of the Universe to , J. Cosmol. Astropart. Phys. 07 (2012) 053.
- Joan Simon, Licia Verde, and Raul Jimenez, Constraints on the redshift dependence of the dark energy potential, Phys. Rev. D 71, 123001 (2005).
- Michele Moresco, Raising the bar: New constraints on the Hubble parameter with cosmic chronometers at , Mon. Not. R. Astron. Soc. 450, L16 (2015).
- Yuhang Yang, Qingqing Wang, Chunyu Li, Peibo Yuan, Xin Ren, Emmanuel N. Saridakis, and Yi-Fu Cai, Gaussian-process reconstructions and model building of quintom dark energy from latest cosmological observations, J. Cosmol. Astropart. Phys. 08 (2025) 050.
- Marina Seikel and Chris Clarkson, Optimising Gaussian processes for reconstructing dark energy dynamics from supernovae, arXiv:1311.6678.
- Seung-gyu Hwang, Benjamin L’Huillier, Ryan E. Keeley, M. James Jee, and Arman Shafieloo, How to use GP: Effects of the mean function and hyperparameter selection on Gaussian process regression, J. Cosmol. Astropart. Phys. 02 (2023) 014.
- Guo-Jian Wang, Xiao-Jiao Ma, and Jun-Qing Xia, Machine learning the cosmic curvature in a model-independent way, Mon. Not. R. Astron. Soc. 501, 5714 (2021).
- Shadab Alam et al. (eBOSS Collaboration), Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory, Phys. Rev. D 103, 083533 (2021).
- Nikki Arendse et al., Cosmic dissonance: Are new physics or systematics behind a short sound horizon?, Astron. Astrophys. 639, A57 (2020).
- N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
- Will Handley, fgivenx: A python package for functional posterior plotting, J. Open Source Software 3, 849 (2018).
- Y. Mellier et al. (Euclid Collaboration), Euclid. I. Overview of the Euclid mission, Astron. Astrophys. 697, A1 (2025).
- Robert T. Zellem et al., Nancy Grace Roman Space telescope coronagraph instrument observation calibration plan, in Astronomical Telescopes + Instrumentation (2022). arXiv:2202.05923.
- Rachel Mandelbaum et al. (LSST Dark Energy Science Collaboration), The LSST Dark Energy Science Collaboration (DESC) science requirements document, 10.2172/1471560.
- Andrea Cozzumbo, Ulyana Dupletsa, Rodrigo Calderón, Riccardo Murgia, Gor Oganesyan, and Marica Branchesi, Model-independent cosmology with joint observations of gravitational waves and -ray bursts, J. Cosmol. Astropart. Phys. 05 (2025) 021.
- Robert E. Kass and Adrian E. Raftery, Bayes factors, J. Am. Stat. Assoc. 90, 773 (1995).