Viscous matter in modified $f(R)$-gravity: Hubble tension attenuation with DESI and SH0ES data

Abstract

We study the late-time dynamics of the Universe in a modified metric $f(R)$ gravity model formulated in the Jordan frame. The standard $Λ$CDM model is additionally deformed to include a non-equilibrium effect on matter dynamics, represented via a bulk viscosity coefficient. We impose an additional condition on the cosmological dynamics that allows the matter energy density, the non-minimally coupled scalar field, and its non-constant potential to be treated as dynamical variables. In this way, the form of the $f(R)$ model is not specified \emph{a priori}, but is instead dynamically reconstructed from the evolution of the system. The resulting model contains five free parameters and is tested against Type Ia supernova and DESI data, using the SH0ES calibration for the supernova sample and a Planck calibration for the sound horizon. We find that the data mainly constrain the standard cosmological parameters $H_0$ and $Ω_{m0}$, while the three additional parameters remain only weakly constrained and are further restricted by imposing the physical viability conditions of the model. Our main result is that the model can accommodate SN Ia and DESI observations while allowing a larger value of $H_0$ than in the corresponding $Λ$CDM analysis and keeping the acoustic horizon close to the Planck value.