Pedagogic Null Tests of Dynamical Dark Energy Hints: Reconstructing LambdaCDM with Consistent BAO, CMB, and SNe Mocks

TL;DR

This work probes whether hints of dynamical dark energy are genuine or artifacts of likelihood geometry by constructing self-consistent mocks of DESI-like BAO, Planck-like CMB distance priors, and Pantheon+ SNe from a fiducial $\Lambda$CDM cosmology. Analyzing single, pairwise, and full three-probe likelihoods within the CPL framework reveals that individual probes and most two-probe combinations generate apparent deviations in $(w_0,w_a)$ due to misaligned degeneracy directions across redshift, while the complete BAO+CMB+SNe likelihood robustly recovers the fiducial $(-1,0)$ and the true $\Omega_{m0}$ and $H_0$. The results provide a transparent benchmark for interpreting future claims of $\omega(z) \neq -1$, highlighting the necessity of fully consistent multi-probe analyses and flexible priors on $H_0$ and $r_d$ to avoid misattributing geometric effects to physics. Overall, the paper emphasizes that, with current data covariances, genuine dynamical dark energy would imprint a coherent, cross-probe signal only when all probes are jointly analyzed, while partial analyses are prone to spurious features arising from likelihood geometry.

Abstract

Hints of a dynamical dark-energy equation of state have appeared in several combined cosmological probes. However, such indications may instead arise from the intrinsic likelihood geometry of individual datasets, residual inter-probe tension, or restrictive priors. These factors can mimic evidence for dynamical dark energy. To clarify these issues, we perform a controlled null test. We use realistic mock BAO, CMB, and Type~Ia supernova datasets generated from a common fiducial LambdaCDM cosmology. These mocks include the DESI~DR2 BAO covariance, the Planck~2018 distance-prior covariance, and the full Pantheon+ SH0ES supernova covariance. This setup isolates physical information from geometric or statistical effects in the CPL parametrization. We find that individual probes and most two-probe combinations show apparent deviations in the (w0,wa) plane. These could be mistaken for phantom crossing or evolving dark energy. Two-probe combinations including supernovae (BAO+SNe, CMB+SNe) recover values near (w0,wa)=(-1,0) but fail to reconstruct (Omegam0,H0), because SNe do not determine the absolute distance scale. Combinations without SNe (BAO+CMB), as well as any single dataset, retain strong degeneracy directions. These produce significant shifts driven purely by likelihood geometry. These behaviors arise because BAO, CMB, and SNe each constrain only one principal direction in (w0,wa) space. Their degeneracy ridges are misaligned due to distinct redshift sensitivities. In contrast, the full BAO+CMB+SNe likelihood with proper covariance breaks all degeneracies simultaneously. It cleanly recovers the fiducial cosmology, including (w0,wa)=(-1,0) and (Omegam0,H0). Our results provide a transparent benchmark for assessing future claims of omega(z) neq -1. They emphasize the need for complete multi-probe analyses with flexible H0 and rd priors.

Figures (11)

• Figure 1: BAO-only marginalized posteriors in $(\Omega_{m0}, h r_d, \omega_0,\,\omega_a)$, showing the characteristic degeneracies of BAO distances and their limited constraining power on DDE. The darker and lighter shaded regions indicate the 68% and 95% marginalized credible contours, respectively.
• Figure 2: CMB-only marginalized posteriors in $(\Omega_{m0}, H_0, \omega_0,\,\omega_a)$. Distance priors tightly constrain the high-redshift geometry but leave the late-time DE parameters weakly constrained, producing extended degeneracies in both $(H_0,\Omega_{m0})$ and $(\omega_0,\,\omega_a)$.
• Figure 3: Marginalized posteriors for the SNe-only mock dataset. Relative luminosity distances fix the Hubble diagram shape but not its normalization, yielding a pronounced $(H_0,M)$ degeneracy and an elongated ridge in $(\omega_0,\,\omega_a)$.
• Figure 4: Joint BAO+CMB posterior distributions for $(\Omega_{m0}, H_0, \omega_0,\,\omega_a, r_d)$ from the GetDist analysis. The Planck 2018 distance priors tighten the parameter constraints and produce the characteristic positive $\omega_0$–$\omega_a$ correlation associated with the CMB acoustic-scale degeneracy.
• Figure 5: GetDist triangle plot for the joint BAO+SNe posterior using BAO + SNe chains. The combination of intermediate-redshift BAO geometry with low-redshift supernova distances efficiently breaks the principal SNe degeneracy and yields significantly tighter contours than either dataset alone.