Shape of Dark Energy: Constraining Its Evolution with a General Parametrization

We consider a general dark energy (DE) model parametrized by its equation-of-state (EoS), featuring three free parameters: $w_0$ (the present-day value of the DE EoS), $w_{\beta}$ (quantifying the dynamical nature of the DE EoS), and $\beta$ (governing various dynamical forms of the DE EoS). The key controlling parameter $\beta$ can recover several existing DE models in the literature, such as the Chevallier-Polarski-Linder (CPL) parametrization ($\beta = 1$), the logarithmic parametrization (in the limit $\beta \rightarrow 0$), and the linear parametrization ($\beta = -1$), alongside generate a class of new DE parametrizations for other values of $\beta$. The resulting DE scenario is constrained using a suite of the latest cosmological probes, including Cosmic Microwave Background (CMB) temperature and polarization anisotropies from three different experiments (Planck 2018 and Atacama Cosmology Telescope combined with WMAP), CMB lensing, Baryon Acoustic Oscillations from DESI Year 2, and PantheonPlus from Type Ia supernovae. Our analyses reveal that stringent constraints on the DE parameters are obtained only when all cosmological probes are combined; otherwise, some parameters remain unconstrained. The present-day value of the DE EoS remains in the quintessence regime according to our results, and no significant evidence for a dynamical DE EoS is found. However, based on the $\Delta \chi^2$ and Bayesian evidence analyses, we observe a mild preference for the present three-parameter DE parametrization over the CPL parametrization when all cosmological probes are taken into account. Nonetheless, the Bayesian evidence difference remains below the threshold for statistical significance according to the revised Jeffreys scale, indicating that both models are effectively equally preferred by the data.