Cosmological Dynamics and Observational Constraints of a Logarithmic Herglotz $f(R,T)$ Gravity

Abstract

We investigate the cosmological dynamics and observational viability of a logarithmic Herglotz-type $f(R,T)$ gravity model described by $f(R,T)=R+β\ln(-T/T_0)$. Assuming a spatially flat Friedmann--Lemaître--Robertson--Walker background and pressureless matter, the modified field equations are formulated as a coupled dynamical system involving the Herglotz field and the normalized matter density. A phenomenological closure relation is adopted for the effective Herglotz sector, allowing the background evolution to be determined numerically. The model is constrained using Cosmic Chronometer measurements, the DESI DR2 baryon acoustic oscillation compilation, and the Union3 supernova sample, considering both individual and combined datasets within a Bayesian Markov-chain Monte Carlo framework. The combined analysis provides a statistically consistent description of the background expansion. The reconstructed expansion history yields a present-day effective equation of state $w_{\rm eff,0}\simeq-0.702$ and exhibits the expected transition from accelerated expansion at late times toward decelerated expansion at higher redshifts. We further investigate the $Om(z)$ diagnostic and statefinder parameter. These results indicate that the logarithmic Herglotz model provides a consistent phenomenological description of the homogeneous and isotropic late-time expansion history, while allowing departures from the standard $Λ$CDM background.