Logarithmic-Exponential Corrected Hubble Parameter Analysis of the Universe: Confronting Theory with Recent Observational Data

In this paper, we propose a logarithmic-exponential corrected power-law parametrization of the Hubble parameter, [Formula: see text], where [Formula: see text] is the present value Hubble constant and [Formula: see text] and [Formula: see text] are dimensionless free parameters. The model is constrained using 77 observational Hubble data (OHD) points, the Pantheon+ compilation of SN Ia data, and the baryon acoustic oscillation (BAO) measurements from the DESI Data Release 2 (DR2), both individually and in a joint analysis. The combined OHD+Pantheon++DESI DR2 analysis yields [Formula: see text], [Formula: see text], and [Formula: see text]. The dynamics of the Universe consistent with the observational data and closely mimics the [Formula: see text]CDM scenario. The cosmological dynamics of the model are further examined through the deceleration parameter, effective equation of state, [Formula: see text] diagnostic, and the evolution of the cosmological term. For the combined best fit values of the parameters, we obtain [Formula: see text] and a deceleration-to-acceleration transition at [Formula: see text], confirming that the Universe is presently undergoing accelerated expansion. The effective equation of state shows the quintessence like behaviour of the Universe at present epoch, with [Formula: see text] and [Formula: see text]. The [Formula: see text] diagnostic exhibits a departure from the constant [Formula: see text] behaviour and is consistent with quintessence like evolution at the present epoch. Furthermore, the reconstructed cosmological term remains positive and evolves with redshift, providing a dynamical extension of the standard cosmological constant scenario. Finally, this model provides a competitive description of the current expansion history with additional flexibility to describe the late time dynamics of the Universe.