w0waCDM, evolving dark energy

2001 / 2003Michel Chevallier, David Polarski, Eric Linder, DESI CollaborationConsensus5 primary sources, 4 established Reviewed May 17, 2026

Lets dark energy evolve in time, w(a) = w0 + wa·(1-a). 2024 DESI BAO gives the strongest hint yet that this evolution may be real.

Visualisation · Standard Cosmological Model

dark energy: The unknown component driving the accelerating expansion of the universe, making up about 68 percent of its energy.
cosmological constant: A constant energy density of empty space. In general relativity, it drives the accelerated expansion of the universe. Often written as Lambda.
scalar field: A field with one value at each point in space, like a temperature map. The inflaton is one example.
redshift: The stretching of light to longer wavelengths, used as the primary measure of how fast distant objects recede from us.

§1 · The claim, in one sentence

Lets dark energy evolve in time instead of being a fixed constant. 2024 DESI BAO results give the strongest hint yet that this evolution may be real.

§2 · Why it might be true

Plain ΛCDM assumes dark energy is a cosmological constant Λ, with an equation of state w fixed exactly at -1 at all times. w0waCDM relaxes that assumption. Following Chevallier and Polarski in 2001, and refined by Linder in 2003, it parameterizes the dark energy equation of state as a simple linear function of the scale factor: w(a) = w0 + wa·(1 - a). Plain ΛCDM is the special case w0 = -1, wa = 0.

Two new parameters: w0 (today's value of w) and wa (how fast w is changing). The motivation is straightforward, almost any dynamical dark energy model, including the broad class of quintessence scalar fields, looks like this parameterization at the redshifts that current surveys probe.

In April 2024 DESI released its first BAO measurement and combined it with Planck CMB and three different type Ia supernova compilations. All three combinations preferred (w0 > -1, wa < 0) over plain ΛCDM. The significance ranged from 2.5σ (DESI + CMB + Pantheon+) to 3.9σ (DESI + CMB + DES-SN5YR). The DESI 2025 DR2 extended analysis confirmed the same trend across both parametric and non-parametric methods. If this signal is real, dark energy is not a cosmological constant. If it's a systematic, the systematic lives in the supernova compilations.

The family stance

Five percent ordinary baryonic matter, twenty-six percent cold dark matter, sixty-nine percent dark energy modelled as a cosmological constant Λ, with essentially zero spatial curvature. The exact percentages depend on the data combination but all serious cosmological measurements converge here.

§2.5 · Evidence

DESI 2024 (DR1) BAO + Planck CMB + supernovae: 2.5σ (Pantheon+) to 3.9σ (DES-SN5YR) preference over ΛCDM
DESI 2025 DR2 extended analysis: signal persists across parametric and non-parametric reconstructions
Pre-DESI BAO + SN compilations also showed mild preference, now sharpened by DESI

§3 · What you'd need to test it

Distance-redshift relation departs from ΛCDM by a measurable amount at z ≈ 0.5 to 1
The BAO acoustic feature traces out a distance-redshift curve that bends measurably away from the ΛCDM prediction, detectable by Stage-IV surveys (LSST, Euclid) mapping the feature across many redshifts
Stage-IV surveys (LSST, Euclid, Roman) should crisply confirm or refute the trend within the next decade
If (w0 > -1, wa < 0) is real, dark energy crosses the phantom barrier (w = -1) toward more negative w in the past, then trends less negative toward today

§4 · Where it breaks

Efstathiou (2025) argues the signal is a low-redshift systematic in the SN Ia compilations, not real dark energy evolution
Significance is sensitive to the choice of SN compilation; the headline 3.9σ uses DES-SN5YR, a single recent sample
The CPL parameterization is just a simple linear approximation of how w changes near the present day (w0 + wa·(1-a)), not a fundamental theory. A real signal would still need a physical origin
Posteriors can cross the phantom divide (w < -1), which is theoretically awkward for most quintessence models

Go deeper

CPL parameterization: w(a) = w0 + wa·(1 - a) = w0 + wa·z/(1 + z). Linear in the scale factor a, equivalent to a first-order Taylor expansion of w(a) around today (a = 1). Linder 2003 showed this captures the relevant physics for any slowly varying scalar field dark energy over the redshift range current surveys probe.

Quintessence connection: a slowly rolling canonical scalar field generically produces w > -1 today, with wa < 0 (less negative in the past). This is exactly what DESI prefers. The natural physical interpretation is a thawing scalar field, dark energy is becoming more like Λ as the field rolls.

Significance is parameterization-dependent. The (w0, wa) significance against ΛCDM uses DESI's stated 4D Gaussian posterior; non-parametric reconstructions in Lodha et al. 2025 (DESI DR2 extended) find the same qualitative trend but with broader uncertainty bands.

Hubble tension: w0waCDM does not resolve the H0 tension. Allowing evolving dark energy in the late universe changes the inverse-distance ladder, but only by a few percent, far less than the ~9% needed to bring CMB H0 up to SH0ES.

▸§5 · Who built it, and when(5 sources, 4 established, 1 debated)

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