Alleviating the H₀ tension in Rastall gravity

The tension between measurements of the Hubble constant H₀ locally and the value inferred from Planck satellite have provided a strong motivation to explore theoretical frameworks beyond the standard cosmological model ($Λ$CDM). To this aim, we investigate the H₀ tension in the Rastall $Λ$CDM model (R-$Λ$CDM), formulated within the Rastall gravity framework as a phenomenological extension of General Relativity featuring a non-conserved energy-momentum tensor. To constrain the cosmological parameters, we employ a comprehensive combined dataset including Big Bang Nucleosynthesis (BBN), Hubble parameter $H(z)$, Type Ia supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB) anisotropies, and the growth rate of cosmic structures f(z)σ₈(z). The estimation of model parameters is performed via Markov Chain Monte Carlo (MCMC) sampling within a Bayesian statistical framework. Our results show that the R-$Λ$CDM model, especially in closed geometry, reduces the H₀ tension, bringing the discrepancy with the local SH0ES measurements down to $1.97σ$ to $2.18σ$. However, the tension related to the σ₈ parameter remains unresolved.