One-parameter dynamical dark energy: Hints for oscillations

There is mounting evidence from multiple cosmological probes that dark energy may be dynamical, with an equation of state that evolves over cosmic time. While this evidence is typically quantified using the Chevallier-Polarski-Linder (CPL) parametrization, based on a linear expansion of $w(a)$ in the scale factor, non-parametric reconstructions frequently suggest non-linear features, particularly at late times. In this work, we investigate four minimal one-parameter models of dark energy with non-linear dependence on the scale factor. These models are constrained using Cosmic Microwave Background (CMB) data from Planck, lensing reconstruction from ACT-DR6, Baryon Acoustic Oscillation (BAO) measurements from DESI-DR2, and three Type-Ia supernovae (SNe) samples (PantheonPlus, DESY5, and Union3), considered independently. Although our conclusions depend on the choice of SNe sample, we consistently find a preference, as measured by the chi-squared statistic and the Bayesian evidence, for these dynamical dark energy models over the standard $\Lambda$CDM model. Notably, with the PantheonPlus dataset, one model shows strong Bayesian evidence ($\Delta \ln B \simeq 4.5$) against CPL, favoring an equation of state that peaks near $a \simeq 0.7$ and oscillates near the present day. These results highlight the impact of SNe selection and contribute to the growing collection of evidence for late-time deviations from $\Lambda$CDM.