Uncovering the bias in the evidence for dynamical dark energy through minimal and generalized modeling approaches

In this letter we argue that the CPL parameterisation for the dark energy equation of state is biased towards preferring such model over the constant $w$ while the latter bounds are still compatible with LCDM. For that we compare constraints on the EoS parameters $w_0$ and early time type $w_a$ (CPL) against those with a late time parameterisation on $w_a$ (LZ) and the constant $w$ model, using CMB, Supernovae and BAO from DESI datasets. We found, the same as was the case with CPL model, preference for dynamical dark energy within the LZ model, but for values almost symmetrically distributed with respect to their LCDM limits. This is due to the fact that the presence of $w_0$ allows to recast each parametrisation into making it compensate the preference for $w\sim -1$ in the opposite direction. To further test our hypothesis, we fixed $w_0$ to -1 and followed a minimal approach by considering models that deviates by one free parameter, or we extend to more general models that either group both late and early effects, or allow the presence of two dark energy fluid alike and constant alike component. We found that all the variants, except the original CPL are still compatible with LCDM, with likelihoods peaking close to $w_0 = -1$, $w_a = 0$, or 0.68 for $\Omega_{\rm CC}$, with the constant $w$ and the late time $w_a$ having the smallest constraints. Although we found that the evidence from CPL is stronger than those for the more minimal cases, however the preference increases further for the more generalized parameterizations, while still staying compatible with LCDM in terms of the significance levels. We conclude that considering CPL model is not sufficient to test deviation from the standard model and that it is necessary to conduct further minimal or more general approaches to better understand the outcomes from model testing and inference methods.(abridged)