Cosmic expansion beyond $Λ$CDM: Investigating power-law and logarithmic corrections

Abstract: The cosmic acceleration observed in the expansion of the Universe has sparked extensive research into the nature of dark energy, which is known to constitute approximately 70\% of the Universe's energy content. In this study, we explore two parametrizations of the Hubble parameter, namely power-law and logarithmic corrections, as alternatives to the standard $\Lambda$CDM model. Using observational data from Cosmic Chronometers (CC), Pantheon+, and the Baryonic Acoustic Oscillations (BAO) datasets, we investigate the dynamics of essential cosmological parameters, including the deceleration parameter, energy density, pressure, and equation of state (EoS) parameter. The $Om(z)$ diagnostic test is employed to classify different dark energy models. Our cosmological models, with the power-law and logarithmic corrections, are found to provide a good fit to the recent observational data and efficiently describe the cosmic expansion scenario.