Bulk viscous cosmological models with a cosmological constant: Observational constraints

TL;DR

This study assesses whether bulk viscous cold dark matter models can reduce the Hubble tension within a $\\Lambda$-dominated universe, using observational data and Bayesian inference, finding only partial alleviation and no definitive resolution.

Contribution

It introduces and constrains bulk viscous dark matter models with evolving viscosity, comparing their performance to $\\Lambda$CDM using current observational datasets.

Findings

Viscous models show partial tension alleviation (~1σ) with local $H_0$ measurements.

Current viscosity constrained to around 10^6 Pa s, consistent with thermodynamics.

Model selection favors $\\Lambda$CDM$, but some criteria mildly support viscous models.

Abstract

We investigate whether viscous cold dark matter (vCDM) in a $\Lambda$-dominated FLRW universe can alleviate the Hubble tension while satisfying thermodynamic constraints, examining both flat and curved geometries. We model vCDM with bulk viscosity $\zeta = \zeta_0\,(\Omega_{vc}/\Omega_{vc0})^m$, where $m$ determines the viscosity evolution and $\Omega_{vc}$ is the density parameter of vCDM. We explore two particular scenarios: constant viscosity ($m=0$), and variable viscosity ($m$ free). Using Bayesian inference, we constrain these models with the latest datasets: the Pantheon+ SN Ia sample (both with SH0ES calibration, PPS, and without it, PP), $H(z)$ measurements from CC and BAO as separate datasets, and a Gaussian prior on $H_0$ from 2022 SH0ES baseline, $H_0=73.04 \pm 1.04$ km/s/Mpc (R22 prior). We compare the models via information criteria such as AIC, BIC, DIC, and Bayesian evidence. Our results reveal that the Hubble tension persists, although it shows partial alleviation ($\sim 1\sigma$ tension) in all investigated scenarios when local measurements are included. For the flat $m=0$ case, the joint analysis yields $H_0 = 71.05^{+0.62}_{-0.60}$ km/s/Mpc. Curved model initially favors $\Omega_{K0} > 0$ (at more than $2\sigma$), but this preference shifts toward flatness once the PPS+R22 prior are included. Notably, the current viscosity is constrained to $\zeta_0 \sim 10^6$ Pa s in all scenarios, in agreement with the thermodynamic requirements. Although model selection via BIC and Bayesian evidence favors $\Lambda$CDM, AIC and DIC show mild support for viscous models in some datasets. Bulk viscous models moderately improve fits but neither resolve the Hubble tension nor outperform the $\Lambda$CDM model. To achieve more robust constraints, future analyses should incorporate CMB observations, which are expected to break parameter degeneracies involving $m$ and $\tilde{\zeta}_0$.