Late-time constraints on dynamical dark energy models using DESI DR2, Type Ia supernova, and CC measurements

The ΛCDM model has successfully explained various cosmological phenomena, yet persistent discrepancies in the measured value of the Hubble constant ($H_0$) known as the “Hubble Tension” challenge its completeness. Early Universe measurements from the cosmic microwave background (CMB) suggest $H_0=67.4\pm 0.5$ km s⁻¹ Mpc⁻¹, whereas late-time measurements using the cosmic distance ladder yield $H_0=73.04\pm 1.04$ km s⁻¹ Mpc⁻¹, resulting in a tension of 4σ to 5.7σ. To address this issue, researchers have proposed a range of alternative cosmological models in recent years. These models are based on dynamic dark energy scenarios featuring various parameterization schemes of the equation of state $w\left(z\right)$. In this study, we investigate some well-known dark energy models employing both two-parameter and three-parameter parameterizations of the equation of state $w\left(z\right)$. Using observational data from Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations (BAO) including the latest release from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), we constrain key cosmological parameters such as the Hubble constant $H_0$ and the sound horizon at the baryon drag epoch $r_d$. We explore these parameterizations and their impact on the expansion history of the Universe, with particular emphasis on the late-time cosmic evolution. Our analysis employs Markov Chain Monte Carlo simulations and several statistical tests to estimate parameter values, evaluate model performance, and assess deviations from the ΛCDM model.