In this letter we argue that the commonly adopted Chevallier-Polarski-Linder (CPL) parametrization for the dark energy equation of state (EoS) is biased toward preferring such model over the constant $w$ while the latter bounds are still compatible with their $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) values. For that we compare constraints on the EoS parameters $w_0$ and early type $w_a$ (CPL) against those with a late-time parametrization on $w_a$ (hereafter LZ) and the constant $w$ model, using cosmic microwave background, Supernovae, and baryonic acoustic oscillations from Dark Energy Spectroscopic Instrument datasets. We found, the same as was the case with the CPL model, preference for dynamical dark energy within the LZ model, but for values almost symmetrically distributed with respect to their $\mathrm{\Lambda }\mathrm{CDM}$ limits. This is due to the fact that the presence of $w_0$ allows to recast each parametrization 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 investigation approach by considering models that deviate only by one free parameter following the same previous parametrizations, making them now genuinely different from each other. On the other hand, we extend our models to more general ones by either incorporating parametrizations that group both late and early $w_a$ effects, which we name the generalized dark energy equation of state (GEoS) model, or by allowing the presence of two dark energy components, fluidlike ${\mathrm{\Omega }}_{\mathrm{DE}}$ and constantlike ${\mathrm{\Omega }}_{\mathrm{CC}}$. We also complement conclusions drawn from the significance levels from the resulting confidence contours with that of the Bayes factor calculation. We found that all the variants, except the original CPL or LZ, are still compatible with $\mathrm{\Lambda }\mathrm{CDM}$, with likelihoods peaking close to $w_0=-1$, $w_a=0$, or 0.68 for ${\mathrm{\Omega }}_{\mathrm{CC}}$, with the constant $w$ and the late time $w_a$ (minimal LZ) being the ones with the tightest constraints. Although we found that the evidence from CPL or LZ is stronger than those for the more minimal cases, however, the preference increases further for the more generalized parametrizations, instead of penalizing the addition of the extra degrees of freedom, while still staying compatible with $\mathrm{\Lambda }\mathrm{CDM}$ in terms of the significance levels. We conclude that considering the CPL model is not sufficient on its own to test deviations from the simple cosmological constant model, and that it is necessary to conduct further minimal or more general approaches when confronting models to observations, so as to localize biases, if they exist, or to better understand the outcomes from model testing and inference methods.

Note that the word “bias” here is considered to mean any artifact effect in general and not specifically only a shift in the parameter confidence contours.

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• Cosmological parameters
• Dark energy
• Evolution of the Universe
• General relativity
• Large scale structure of the Universe