Pressure parametrization of dark energy: first and second-order constraints with latest cosmological data
Hanyu Cheng, Eleonora Di Valentino, Luis A. Escamilla, Anjan A. Sen, Luca Visinelli
Abstract
Abstract We explore an extension of the ΛCDM model in which the pressure p of the dark energy (DE) fluid evolves with the expansion of the Universe, expressed as a function of the scale factor a . The corresponding energy density ρ is derived from the continuity equation, resulting in a dynamical equation-of-state parameter w ≡ p / ρ during the late-time expansion of the Universe. The pressure is modeled using a Taylor expansion around the present epoch ( a = 1), introducing deviations from a cosmological constant within the dynamical dark energy (DDE) framework. At first order, a single new parameter Ω 1 captures linear deviations, while a second-order parameter, Ω 2 , accounts for quadratic evolution in the pressure. We constrain the first- and second-order DDE models using multiple observational datasets and compare their performance against ΛCDM and the CPL parameterization. A joint analysis of Planck CMB, DESI, and DESY5 data yields the strongest evidence for DDE, with a 2.7 σ deviation in the first-order model and over 4 σ in the second-order model — providing strong statistical support for a departure from a cosmological constant. The reconstructed DE evolution in the second-order case reveals a distinctive non-monotonic behavior in both energy density and w DE ( a ), including clear phantom-crossing phenomena. Notably, the late-time evolution of w DE ( a ) remains consistent across datasets and shows strong agreement with the CPL parameterization, underscoring the robustness of the pressure-based approach.