To CPL, or not to CPL? What we have not learned about the dark energy equation of state

Abstract

We show that using a Taylor expansion for the dark energy equation-of-state parameter and limiting it to the zeroth and first-order terms, i.e., the so-called Chevallier-Polarski-Linder (CPL) parametrization in regimes where it has been shown to fail as a physics-based two-parameter model, instead of allowing for higher-order terms and then marginalizing over them, adds extra information not present in the data and leads to markedly different and potentially misleading conclusions. Fixing the higher-order terms to zero, one concludes that vacuum energy that is currently non-dynamical (e.g., the cosmological constant) is excluded at several $σ$ significance as the explanation of cosmic acceleration, even in Dark Energy Spectroscopic Survey (DESI) DR1 data. Meanwhile, instead marginalizing over the higher-order terms shows that we know neither the current dark energy equation of state nor its current rate of change well enough to make such a claim. The CPL parametrization also implies that dark energy exhibits phantom behavior at high redshifts, while we show that by allowing the higher-order terms -- which is required in order to capture the behavior of the dark energy equation of state in regimes beyond the validity of the CPL parametrization -- the evidence for this phantom-like dark energy significantly weakens. This is not an argument for the higher-order phenomenological parametrizations, but rather a caution regarding such parametrizations in general. This issue has become more prominent now with the recent release of high-quality Stage IV galaxy survey data. The results of analyses using simple parametrizations should be interpreted with great care.