Bulk viscous cosmological models with a cosmological constant: Observational constraints

¹ Departamento de Astronomía, Universidad de La Serena, Raúl Bitrán 1305 La Serena, Chile
² Departamento de Física, Universidad de La Serena, Avenida Juan Cisternas 1200, La Serena, Chile
³ Departamento de Física, Universidad de Santiago de Chile, Avenida Víctor Jara 3493, Estación Central, 9170124 Santiago, Chile
⁴ Center for Interdisciplinary Research in Astrophysics and Space Exploration (CIRAS), Universidad de Santiago de Chile, Avenida Libertador Bernardo O’Higgins 3363 Estación Central, Chile
⁵ Instituto de Astrofísica de Canarias, E-38200 La Laguna, Tenerife, Spain
⁶ Departamento de Astrofísica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain

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Received: 16 August 2025
Accepted: 10 February 2026

Abstract

Aims. We investigate whether viscous cold dark matter (vCDM) in a Λ-dominated Friedmann-Lemaître-Robertson-Walker (FLRW) universe can alleviate the Hubble tension, while satisfying thermodynamic constraints. Here, we examine both flat and curved geometries.

Methods. We modeled a vCDM cosmology with a bulk viscosity ζ = ζ₀ (Ω_vc/Ω_vc0)^m, where m determines the viscosity evolution and Ω_vc is the density parameter of vCDM. We explored two particular scenarios: (i) constant viscosity ζ = ζ₀ (m = 0) and (ii) variable viscosity ζ = ζ(Ω_vc) (m free). Using Bayesian inference, we constrained these models with the latest datasets: the Pantheon+ Type Ia supernova sample (with a SH0ES calibration, PPS, and without, PP), Hubble parameter measurements, H(z), from cosmic chronometers and baryon acoustic oscillations (BAO) as independent datasets, including DESI DR2, and a Gaussian prior on H₀ from the SH0ES measurement, H₀ = 73.04 ± 1.04 km s⁻¹ Mpc⁻¹ (R22 prior). We compared the models via Akaike, Bayesian, and deviance information criteria (AIC, BIC, and DIC), and with Bayesian evidence.

Results. Our results indicate that the Hubble tension persists, although it shows partial alleviation (∼1σ tension) in all investigated scenarios when local measurements are included. For the flat m = 0 case, the joint analysis yields H₀ = 71.05^+0.62_−0.60 km s⁻¹ Mpc⁻¹. Curved models initially favor Ω_K0 > 0 (at more than 2σ), but this preference shifts toward flatness once the PPS + R22 prior is included. Notably, the current viscosity is constrained to ζ₀ ∼ 10⁶ Pa s in all scenarios, in agreement with the thermodynamic requirements. Although the model selection via BIC and Bayesian evidence favors ΛCDM, the AIC and DIC show mild support for viscous models in some datasets.

Conclusions. Bulk viscous models moderately improve the fits, but they can neither resolve the Hubble tension nor outperform the ΛCDM model. To achieve more robust constraints, future analyses should incorporate CMB observations, which are expected to break parameter degeneracies involving m and ζ∼₀.