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

TL;DR

This work tests whether a single dark-fluid characterized by a Lambert $W$-based equation of state can describe the Universe's expansion in light of Pantheon+ SNIa, DESI DR1 BAO, and H(z) data. The authors constrain the two EoS parameters $\theta_1$ and $\theta_2$ via a Bayesian MCMC analysis and compare the Lambert $W$ model to ΛCDM using AIC and BIC, while examining the evolution of $q(z)$, $j(z)$, $\omega_{ m eff}(z)$, and $Om(z)$. They find best-fit values $\theta_1\approx0.087$, $\theta_2\approx-3.36$, with $H_0\approx67.4$ km s$^{-1}$ Mpc$^{-1}$ and $r_d\approx146$ Mpc, and identify a transition from DM-like to quintessence-like behavior around $z\approx0.56$, alongside dynamical deviations in $j(z)$ and $Om(z)$. Although the AIC indicates the Lambert $W$ model is statistically similar to ΛCDM, the BIC disfavors it due to the extra parameters, suggesting caution in claiming superiority. Overall, the Lambert $W$ EoS provides a coherent and testable alternative for late-time acceleration and DM-DE unification, meriting further scrutiny with upcoming data and complementary probes.

Abstract

We investigate the hypothesis that the evolution of the Universe can be described by a single dark fluid whose effective equation of state (EoS), $ω_{\rm{eff}}$, is a linear combination of a logarithmic term and a power law term, both involving the Lambert $W$ function. This particular form of EoS was first proposed by S. Saha and K. Bamba in 2019 and has two parameters, $θ_1$ and $θ_2$, which must be determined from observations. To this end, we place limits on these parameters by combining recent baryon acoustic oscillation (BAO) data -- including measurements from the Dark Energy Spectroscopic Instrument (DESI) -- with Type Ia supernova observations from the Pantheon+ compilation, along with direct determinations of the Hubble parameter. From this combined analysis, we obtain a best-fit value for the Hubble parameter, $H_0 = 67.4 \pm 1.2~\text{km\,s}^{-1}\text{Mpc}^{-1}$, while current measurements of the sound horizon at the baryon drag epoch yield $r_d = 146\pm 2.5$~Mpc. Furthermore, we study the evolution of the deceleration parameter, the effective EoS, and the jerk parameter, and support our findings using the $Om(z)$ diagnostic. The model exhibits noticeable deviations from the predictions of the concordance $Λ$CDM model. Despite these differences, our results indicate that the model provides a coherent description of late-time cosmic evolution and the observed accelerated expansion of the Universe. Finally, we assess the observational viability of the model using information criteria, particularly the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), and compare these results with those obtained for the $Λ$CDM model, which serves as our reference.

Figures (8)

• Figure 1: Triangle plot showing the $1\sigma$ and $2\sigma$ confidence contours, along with the one-dimensional marginalized posterior distributions of the Lambert $W$ model parameters, obtained from the combined SNIa+BAO+OHD data set.
• Figure 2: Triangle plot showing the $1\sigma$ and $2\sigma$ confidence contours, along with the one-dimensional marginalized posterior distributions of the $\Lambda$CDM model parameters, obtained from the combined SNIa+BAO+OHD data set.
• Figure 3: The best-fit evolution of the Hubble parameter $H(z)$ for the Lambert $W$ model, obtained from the combined SNIa+BAO+OHD data set. The solid curve represents the best-fit $H(z)$ prediction of the Lambert $W$ model, while the observational data points with error bars correspond to the compiled measurements. For comparison, the predicted $H(z)$ evolution from the standard $\Lambda$CDM model is also shown.
• Figure 4: The best-fit evolution of the distance modulus $\mu(z)$ for the Lambert $W$ model, derived from the combined SNIa+BAO+OHD data set. The observational data points with corresponding uncertainties are shown for comparison, along with the predicted $\mu(z)$ evolution from the standard $\Lambda$CDM model.
• Figure 5: The best-fit curve of the deceleration parameter $q$ as a function of the redshift $z$ in the Lambert $W$ and $\Lambda$CDM models obtained from the combined SNIa+BAO+OHD data set. The horizontal line indicates the point where $q(z)=0$.