Thawing Quintessence: Priors, evidence, and likely trajectories

TL;DR

This work evaluates whether thawing quintessence, described by a Padé-w parameterization with two physically meaningful parameters $\epsilon_0$ and $\eta_0$, provides a better description of cosmic expansion than $\Lambda$CDM when informed by theory-based priors. It performs a Bayesian model comparison using DESI DR2 BAO, Planck+ACT CMB, and multiple Type Ia SN catalogs, and contrasts Bayesian evidence with information criteria (AIC, BIC, DIC). The main finding is that thawing quintessence is favored when SN data are included, with evidence improvements up to ~10, and that DIC tracks Bayesian evidence more reliably than AIC or BIC; without SN data the preference weakens. Additionally, the paper reconstructs observationally compatible thawing trajectories from marginal likelihoods, assesses the impact of priors, and discusses implications for future extensions to more elaborate dark energy scenarios and phantom-crossing models.

Abstract

We perform a Bayesian comparison between thawing quintessence and a cosmological constant, incorporating theoretically motivated priors on the phenomenological Padé-w parameters used to model thawing dynamics. We find that thawing quintessence is consistently preferred over a cosmological constant when combining BAO data from DESI DR2 and CMB data from Planck+ACT with any of the major supernova compilations, including the recently updated DES-Dovekie sample. This preference is not sensitive to our choice of prior, but it is contingent on the inclusion of supernovae in the analysis. We comment on the consistency between various information criteria and Bayesian evidence ratios, finding that the Deviance Information Criterion (DIC) tracks the Bayesian evidence more reliably than either the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC). Finally, we use observational likelihoods to identify which thawing trajectories are compatible with the available data, independently of theoretical priors.

Figures (3)

• Figure 1: MCMC posterior densities for the Padé-w parameters $\epsilon_0$ and $\eta_0$ according to combinations of DESI and CMB data with different supernova samples. The linear scaling in $\sqrt{\epsilon_0}$ and the nonlinear scaling in $\eta_0$ are adopted so that the informed priors from Eqs. (\ref{['e_prioreps']}-\ref{['e_prioreta']}) appear uniform on the parameter space, allowing posteriors to directly represent marginal observational likelihoods. We include a twin axis with (nonlinear) values of $w_0 = \frac{2}{3}\epsilon_0-1$ for ease of interpretation. Contours drawn in solid black contain 68% and 95% of the posterior mass, while contours drawn in dashed gray identify level sets with 32% and 5% of the maximum posterior density. Note that the $\Lambda$CDM limit of this parameterization corresponds to the one-dimensional boundary $\epsilon_0 = 0$. $^*$The DES-SN5YR supernova sample has recently been re-analyzed and superseded by DES-Dovekie. Results are shown for both samples in the interest of comparison.
• Figure 2: High-likelihood evolutions of the dark energy equation of state $\epsilon(z)$ or $w(z) = \frac{2}{3}\epsilon(z)-1$ according to combinations of DESI and CMB data with different supernova samples. From darkest to lightest, the shaded regions are reconstructed from $(\epsilon_0, \eta_0)$ combinations with $\geq 90\%$, $\geq 32\%$, and $\geq 5\%$ of the maximum marginal likelihood. The boundaries of the 32% and 5% regions correspond to the dashed gray contours on the Padé-w parameter space shown in Fig. \ref{['f_posteriors']}. $^*$The DES-SN5YR supernova sample has recently been re-analyzed and superseded by DES-Dovekie. Results are shown for both samples in the interest of comparison.
• Figure 3: MCMC results showing marginalized posteriors and joint 68% and 95% credible regions for the Padé-w parameters $\{\epsilon_0, \eta_0\}$, the Hubble constant $H_0$ (in km/s/Mpc), and the matter fraction $\Omega_m$. The linear scaling in $\sqrt{\epsilon_0}$ and the nonlinear scaling in $\eta_0$ are adopted so that the informed priors from Eqs. (\ref{['e_prioreps']}-\ref{['e_prioreta']}) appear uniform on the Padé-w parameter space, as explained in the text. $^*$The DES-SN5YR supernova sample has recently been re-analyzed and superseded by DES-Dovekie. Results are shown for both samples in the interest of comparison.