The Lambert $W$ equation of state in light of DESI BAO

Abstract

We investigate a unified dark-fluid model whose effective equation of state (EoS) is described by logarithmic and power-law terms involving the Lambert $W$ function. The model parameters are constrained using BAO data, including DESI measurements, together with Pantheon+ Type Ia supernova observations and direct Hubble parameter measurements. The analysis yields $\theta_{1}=0.087\pm 0.011$, $\theta_{2}=-3.35\pm 0.13$, $r_d = 146\pm 2.5$~Mpc, and $H_0 = 67.4 \pm 1.2~\text{km\,s}^{-1}\text{Mpc}^{-1}$. The inferred Hubble constant, $H_{0}$, is consistent with the Planck 2018 measurement and remains in tension with local determinations, thereby reflecting the Hubble tension. We further examine the evolution of deceleration, effective EoS, and jerk parameters, complemented by the $Om(z)$ diagnostic. Our analysis reveals that the model provides a consistent description of late-time cosmic acceleration. Finally, the observational viability of the model is assessed using Akaike and Bayesian information criteria and compared with that of the standard $\Lambda$CDM model.