Investigating the H0 − r tension in f(R,T) gravity using cosmological observations

The ongoing Hubble tension, a significant discrepancy between early- and late-universe measurements of the Hubble constant H0, challenges the foundations of modern cosmology. A closely related issue, the H0−rd tension, arises from the dependency of BAO-based inferences of H0 on the assumed sound horizon at the drag epoch rd. In this work, we investigate the cosmological implications of the f(R,T)=R+2λT gravity model, which introduces a direct coupling between the Ricci scalar (R) and the trace of the energy-momentum tensor (T). By utilizing a Markov Chain Monte Carlo (MCMC) analysis with observational datasets, such as Baryon Acoustic Oscillations (BAO), Cosmic Chronometers (CC), and Standard Candles (SC), we constrain the model parameters and assess their compatibility with current cosmological observations. Our findings indicate a strong correlation between H0 and rd, confirming that different dataset combinations lead to systematically varying constraints on these parameters. The inclusion of the Riess 2019 prior (R19) results in higher values of H0, reinforcing the Hubble tension, while BAO-only data favors lower values, consistent with early-universe measurements. Additionally, we analyze the evolution of the main cosmologic parameters such as the deceleration parameter q(z) and the equation of state parameter ω(z). Our results suggest that the f(R,T) model exhibits a quintessence-like behavior, with ω(z)>−1 at present, indicating a dynamical dark energy component rather than a simple cosmological constant. Furthermore, we confirm that the present-day values of the matter and dark energy density parameters, Ωm≈0.3 and ΩΛ≈0.7, remain consistent with a spatially flat universe. These results highlight the role of modified gravity in addressing key tensions in cosmology and demonstrate that the f(R,T) framework provides a natural extension of ΛCDM.