Addressing the H₀ tension through matter with pressure and no early dark energy

¹ Università di Camerino, Via Madonna delle Carceri Camerino 62032, Italy
² INAF – Osservatorio Astronomico di Brera, Milano, Italy
³ Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia 06123, Italy
⁴ SUNY Polytechnic affiliation, 13502 Utica New York, USA
⁵ Al-Farabi Kazakh National University, Al-Farabi av. 71 050040, Almaty, Kazakhstan
⁶ ICRANet, Piazza della Repubblica 10 65122 Pescara, Italy

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Received: 22 June 2025
Accepted: 3 February 2026

Abstract

Context. We propose that the Hubble tension arises due to an unaccounted-for additional component that behaves as matter with pressure.

Aims. We aim to demonstrate that this fluid remains subdominant compared to both dust and radiation throughout the entire expansion history of the Universe. Specifically, the additional fluid satisfies the Zel’dovic limit with a constant equation of state, ω_s > 0, and quite a small normalized energy density, Ω_s.

Methods. This component modifies both the sound horizon and the background expansion rate, acting quite differently from early dark-energy models, without significantly affecting the other cosmological parameters. To show this, we performed a Markov chain Monte Carlo analysis of our model, hereafter dubbed the Λ_ωs cold dark matter (Λ_ωsCDM) paradigm, using the publicly available CLASS Boltzmann code.

Results. Our results confirm the presence of this fluid, with properties that closely resemble those of radiation. We find best-fit values that satisfy ω_s ≲ ω_γ and a relative energy density of Ω_s/Ω_γ = 0.33, with ω_γ and Ω_γ being the equation of state and density of photons, respectively. The additional fluid may be interpreted either as a thermalized scalar field, plausibly associated with the quasi-quintessence model, or as Proca-type vector fields, albeit we did not exclude a priori more exotic possibilities, i.e., dark radiation, axions, and so on. Physical implications of our results were analyzed in detail, indicating a statistical preference for the Λ_ωsCDM scenario over the conventional ΛCDM background.