Easing the Hubble Tension in f(R,Lm) Gravity: A Bayesian MCMC Analysis with CC and Pantheon Plus & SH0ES Datasets

In this study, we explored the cosmological implications of the modified gravity framework f(R,Lm), taking the specific form f(R,Lm)=R2+Lmn, where n denotes the model parameter. The analysis was carried out within a spatially flat FLRW background by adopting the Barboza–Alcaniz (BA) parametrization for the dark energy equation of state, expressed as ω(z)=w0+w1z(1+z)1+z2. Based on this setup, an expression for the Hubble parameter H(z) was derived. The parameters (H0,n,w0,w1) were estimated using a Bayesian Markov Chain Monte Carlo (MCMC) technique, implemented via the emcee package, with Cosmic Chronometers (CC), Pantheon Plus & SH0ES (PPS) and DESI BAO datasets. For the CC+PPS+DESI BAO combination, the best-fit Hubble constant was obtained as H0=72.08−0.24+0.30kms−1Mpc−1, which shows better consistency with the local SH0ES measurement than with the Planck ΛCDM result, thereby reducing the Hubble tension. Furthermore, the dynamical evolution of the equation of state parameter ω, the deceleration parameter, the impact of various energy conditions, and the optimal model parameters were thoroughly examined. The study also investigated the behavior of the (Om) diagnostic and determined the present age of the universe predicted by this model.