Empirical Validation: Investigating the $\Lambda_s $CDM Model with new DESI BAO Observations

The $\Lambda$CDM model has long served as the cornerstone of modern cosmology, offering an elegant and successful framework for interpreting a wide range of cosmological observations. However, the rise of high-precision datasets has revealed statistically significant tensions, most notably the Hubble tension and the $S_8$ discrepancy, which challenge the completeness of this standard model. In this context, we explore the $\Lambda_{\rm s}$CDM model-an extension of $\Lambda$CDM featuring a single additional parameter, $z_\dagger$, corresponding to a sign-switching cosmological constant. This minimal modification aims to alleviate key observational tensions without compromising the model's overall coherence. Recent findings present in the literature indicate that the $\Lambda_{\rm s}$CDM model not only provides a better fit to Lyman-$\alpha$ forest data for $z_\dagger < 2.3$, but also accommodates both the SH0ES measurement of $H_0$ and the angular diameter distance to the last scattering surface when 2D BAO data are included. We present a comprehensive analysis combining the full Planck 2018 CMB data, the Pantheon Type Ia Supernovae sample, and the recently released Baryon Acoustic Oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI). Our finding reveal that the Preliminary DESI results, a possible $3.9\sigma$ deviation from $\Lambda$CDM expectations, reinforce the importance of exploring such dynamic dark energy frameworks. In sum, our study underscores the potential of $\Lambda_{\rm s}$CDM to reconcile multiple cosmological tensions and sheds light on the role of upcoming high-precision observations in reshaping our understanding of the universe's expansion history and the nature of dark energy.