A GREAT model comparison against the cosmological constant

Recently, a covariant formulation of non-equilibrium phenomena in the context of General Relativity was proposed in order to explain from first principles the observed accelerated expansion of the Universe, without the need for a cosmological constant, leading to the GREA theory. Here, we confront the GREA theory against the latest cosmological data, including type Ia supernovae, baryon acoustic oscillations, the cosmic microwave background (CMB) radiation, Hubble rate data from the cosmic chronometers and the recent $H_0$ measurements. We perform Markov Chain Monte Carlo analyses and a Bayesian model comparison, by estimating the evidence via thermodynamic integration, and find that when all the aforementioned data are included, but no prior on $H_0$, the difference in the log-evidence is $\sim -9$ in favor of GREA, thus resulting in overwhelming support for the latter over the cosmological constant and cold dark matter model ($\Lambda$CDM). When we also include priors on $H_0$, either from Cepheids or the Tip of the Red Giant Branch measurements, then due to the tensions with CMB data the GREA theory is found to be statistically equivalent with $\Lambda$CDM.