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    Parametrizing dark energy at the density level: A two-parameter alternative to the Chevallier-Polarski-Linder parametrization

    Gabriele Montefalcone1,* and Richard Stiskalek2,†

    • 1Texas Center for Cosmology and Astroparticle Physics, Weinberg Institute for Theoretical Physics, Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
    • 2Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, England, United Kingdom

    • *Contact author: montefalcone@utexas.edu
    • †Contact author: richard.stiskalek@physics.ox.ac.uk

    Phys. Rev. D 114, 043538 – Published 20 August, 2026

    DOI: https://doi.org/10.1103/xx41-1ndv

    Abstract

    We introduce a minimal two-parameter formulation of the dark energy (DE) density evolution normalized to its present-day value, fDE(z)≡ρDE(z)/ρDE,0, in terms of fp≡fDE(zp) and the DE equation of state wp≡w(zp), at a pivot redshift zp. This provides an alternative framework for assessing the evidence for evolving DE, complementary to the established Chevallier-Polarski-Linder (CPL) parametrization of the DE equation of state in terms of w0 and wa. By parametrizing the DE density directly, the (wp,fp) formulation avoids the approximate degeneracies intrinsic to the (w0,wa) basis—in particular the weak sensitivity of the expansion history to wa—while reproducing the background evolution of representative thawing quintessence models with equivalent accuracy. Confronting it with the latest baryon acoustic oscillation (BAO) measurements from DESI, a prior on early-Universe parameters from Planck cosmic microwave background (CMB) observations, and Type Ia supernovae (SNe) data, we find that the wp and fp parameters are both tightly constrained and sensitive to distinct subsets of the data. Specifically, wp is measured to percent-level precision by BAO and CMB alone, while fp is pinned down by the independent matter density constraint that only SNe provide. Including the Pantheon+ SNe sample, we obtain wp=−1.04±0.04 and fp=1.07±0.04, with similar results when using the DESY5 SNe sample. The frequentist preference for evolving DE over ΛCDM remains below 3σ across all dataset combinations, comparable to that obtained with CPL. Notably, the proximity of both wp and fp to their cosmological constant values of (−1,1)—precisely at the epoch where the data are most sensitive—deepens the coincidence previously identified in the CPL framework, reinforcing the case for caution in interpreting the current evidence for dynamical DE.

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