Probing departures from $\Lambda$CDM by late-time datasets

Observational data play a pivotal role in identifying cosmological models that are both theoretically consistent and empirically viable. In this work, we investigate the level of preference for dynamical dark energy over a cosmological constant using current late-time observational datasets, including Cosmic Chronometers , Baryon Acoustic Oscillations from DESI DR2, and different Type Ia supernova catalogs (Pantheon$^+$, DES-Dovekie, Union3). We analyze various dynamical dark energy models, including $\omega$CDM, o$\omega$CDM, $\omega_0\omega_a$CDM, Logarithmic, Exponential, JBP, BA, and GEDE. In most cases, the o$\Lambda$CDM and o$\omega$CDM models favor an open Universe. For the o$\omega$CDM, the inclusion of DES-Dovekie or Union3 data together with CC and DESI DR2 favors a nearly flat geometry. Using the CC + DESI DR2 dataset, the preference for dynamical dark energy lies between the $1$-$2\sigma$ level. When different supernova catalogs (DES-Dovekie or Union3) are included, the deviation from $\Lambda$CDM in the $\omega$CDM, $\omega_0\omega_a$CDM, Logarithmic, JBP, BA, and GEDE models increases to the $2$-$2.74\sigma$ level, while the Pantheon$^{+}$ sample yields deviations below the $2\sigma$ level. We find consistent evidence for $\omega_0 > -1$ and $\omega_a < 0$ across all dark energy models, indicating a preference for dynamical dark energy characterized by a Quintom-B type scenario. The $\Lambda$CDM paradigm has long served as the standard framework of modern cosmology; however recent DESI DR2 results have exposed emerging tensions with the cosmological constant $\Lambda$, hinting at possible new physics in the dark energy sector. Even so, the currently available data are still not strong enough to definitively rule out the $\Lambda$CDM model.