Bayesian reconstruction and exhaustive symbolic regression on CMB, BAO, and supernova data yield the one-parameter dark energy parametrization w(a) = w0 / sqrt(a) that fits observations comparably to CPL and better than LambdaCDM.
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One-parameter dynamical dark energy: Hints for oscillations
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abstract
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.
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Bin-wise uncorrelated reconstruction from DESI/SDSS BAO and Pantheon+/Union3.1/DES-Dovekie supernovae yields dark energy density peaking then declining and equation of state oscillating with phantom crossing near z~0.7, consistent across datasets at moderate significance.
A sign-switching dark energy model (Λ_s CDM) recovers positive effective neutrino masses (0.055 ± 0.050 eV) consistent with oscillation data, unlike ΛCDM which prefers negative values (-0.075 eV), for DESI DR2 + CMB + supernova fits with z_† > 2.4.
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This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.
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DESI data hint that dark energy evolves (w0>−1, wa<0, phantom crossing) at 2.5–4.2σ, but the same expansion history can also be produced by interacting dark sectors, modified gravity, or non-cold dark matter.
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The Quintom theory of dark energy after DESI DR2
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