How Complex is Dark Energy? A Bayesian Analysis of CPL Extensions with Recent DESI BAO Measurements

TL;DR

This study assesses whether dark energy evolution is better described by the CPL parametrization and its extensions using a joint analysis of DESI DR2 BAO, Planck CMB distance priors, and SN Ia data from PantheonPlus or Union3. It employs a robust Bayesian framework alongside MLE and AIC to compare CPL, CPL^+, CPL^{++}, Quadratic, Cubic, and w0w_a two-parameter forms, finding that CPL and the two-parameter models improve over ΛCDM while higher-order CPL extensions do not require additional complexity. The results are consistent across SN Ia datasets, indicating a dynamical DE description captured effectively by two parameters, with no statistical justification for more complex CPL forms. Overall, the paper reinforces evolving DE signals while advocating against unnecessary model complexity beyond the two-parameter w0w_a framework. The analysis highlights the balance between data fit and model simplicity achieved by CPL and related two-parameter families in current cosmological observations, particularly when incorporating DESI BAO and CMB information.

Abstract

The nature of dark energy is one of the big puzzling issues in cosmology. While $Λ$CDM provides a good fit to the observational data, evolving dark energy scenarios, such as the CPL parametrization, offer a compelling alternative. In this paper, we present a Bayesian model comparison of various dark energy parametrizations using a joint analysis of Cosmic Microwave Background data, DESI Baryon Acoustic Oscillation measurements, and the PantheonPlus (or Union3) Supernovae type Ia sample. We find that while the $Λ$CDM model is initially favored over a constant $w$CDM model, the CPL parametrization is significantly preferred over $w$CDM, reinforcing recent evidence for an evolving dark energy component, consistent with DESI collaboration findings. Crucially, when testing higher-order CPL extensions, the so-called CPL$^+$ and CPL$^{++}$, our Bayesian analysis shows that the observational data do not favor these more complex scenarios compared to the standard CPL. This result indicates that adding excessive complexity to the CPL form is unwarranted by current observations. Interestingly, similar to the CPL parametrization, alternative two-parameter forms, specifically $w_{de}(a) = w_0 + w_b(1-a)^2$ and $w_{de}(a) = w_0 + w_c(1-a)^3$, yield a better fit to observational data than the standard $Λ$CDM cosmology. Our results challenge the necessity for overly complex CPL extensions and confirm that well-chosen two-parameter $w_0w_a$ parametrizations effectively capture DE evolution with current cosmological data, supporting the recent signals for dynamical dark energy by DESI collaboration.

Figures (2)

• Figure 1: Two-dimensional marginalized posteriors within 1–2–3$\sigma$ confidence levels for different DE parameters ($w_0$, $w_a$, $w_b$, $w_c$) from CMB + DESI BAO (DR2) + PantheonPlus combination.
• Figure 2: Same as Fig. \ref{['fig:corner_pan']}, But for CMB + DESI BAO (DR2) + Union3 combination.