Beyond Two Parameters: Revisiting Dark Energy with the Latest Cosmic Probes

Abstract

Dark energy (DE) models with many free parameters are often considered excessive, as constraining all parameters poses a significant challenge. While such models offer greater flexibility to probe the DE sector in more detail. With the rapid advancement of astronomical surveys and the availability of diverse datasets, it is timely to examine whether current combined observations can effectively constrain an extended parameter space in DE models. This article investigates a four-parameter dynamical DE model that spans a broad region of the universe's expansion history through four key parameters: present-day value of the DE equation of state ($w_0$), its initial value ($w_m$), scale factor depicting transition from $w_m$ to $w_0$ ($a_t$), and steepness of this transition ($\Delta_{\rm de}$). We constrain the model using cosmic microwave background data from Planck, BAO from DESI DR2, and three distinct compilations of Type Ia Supernovae: PantheonPlus, DESY5, and Union3. Our results show that constraining all four parameters remains challenging: $a_t$ is not constrained by any dataset, constraints on $w_m$ and $\Delta_{\rm de}$ remain weak, only $w_0$ is well constrained across all datasets. The results further show that $w_0 > -1$, while $w_m$ is negative, indicating a phantom-like behaviour at early times. Interestingly, despite its larger parameter space, the proposed model shows a preference over the $\Lambda$CDM and $w_0w_a$CDM scenarios for certain combined datasets, according to both $\Delta \chi^2$ and Bayesian evidence, although this preference is not strong.