wCDM, constant equation of state

1997Michael Turner, Martin White, DESI CollaborationConsensus4 primary sources, 4 established Reviewed May 17, 2026

The simplest extension of plain ΛCDM. Lets the dark energy equation of state w be a measurable constant, instead of fixing it at -1.

Visualisation · Standard Cosmological Model

dark energy: The unknown component driving the accelerating expansion of the universe, making up about 68 percent of its energy.
dark matter: A form of matter that interacts gravitationally but emits no light, making up about 27 percent of the universe.
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.
singularity: A point in a theory where quantities like density become infinite, signaling the theory has broken down.

§1 · The claim, in one sentence

The simplest extension of plain ΛCDM, treats dark energy's equation of state as one free constant instead of fixing it at exactly -1. Current data say the answer is consistent with a constant.

§2 · Why it might be true

wCDM is the minimal one-parameter step beyond plain ΛCDM. Where ΛCDM fixes the dark energy equation of state w at exactly -1, wCDM treats w as a single free parameter constant in time. ΛCDM is the special case w = -1.

Turner and White introduced this framework in 1997 under the name 'CDM with a smooth component', the general dark sector with one fluid characterized by its equation of state. The choice of name matters: a smooth component to distinguish from dark matter, which clusters, and 'CDM' to flag that everything else, structure formation, the cold dark matter component, and the standard cosmological parameters, is held fixed.

Conceptually, wCDM is the stepping stone between ΛCDM and w0waCDM. The hierarchy is ΛCDM ⊂ wCDM ⊂ w0waCDM. If dark energy is just slightly different from a cosmological constant but not evolving, wCDM is enough. If it's evolving, wCDM is not enough and you need w0waCDM. DESI 2024 BAO alone gives w = -0.99 +0.15/-0.13, consistent with -1, so the case for constant-w dark energy is weak. The interesting tension lives in the evolution.

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 BAO alone: w = -0.99 +0.15/-0.13
Planck 2018 + BAO + SN combinations also find w consistent with -1 within ~5%
Provides a clean one-parameter null test of plain ΛCDM

§3 · What you'd need to test it

If w is not exactly -1, dark energy density changes over cosmic time rather than staying constant, growing denser in the past if w is more negative than -1 and thinning out if w is less negative (formally ρ_de ∝ a^{-3(1+w)})
If w < -1 (phantom dark energy), dark energy density grows with cosmic expansion and the universe ends in a finite-time 'big rip'
Distance moduli to high-z supernovae differ from ΛCDM by a few hundredths of a magnitude, within reach of LSST and Roman

§4 · Where it breaks

Current data don't show meaningful preference for wCDM over plain ΛCDM. The interesting signal is in the evolution (w0waCDM), not in a constant offset
wCDM is a parameterization, not a model. No fundamental physics predicts a fluid with constant w ≠ -1
Phantom dark energy (w < -1) violates the dominant energy condition, theoretically awkward but not ruled out by data alone

Go deeper

Energy density evolution: a perfect fluid with constant w satisfies ρ_de(a) ∝ a^{-3(1+w)}. ΛCDM (w = -1) gives ρ constant. For w = -0.9, dark energy was about 26% denser at z = 1 than today; for w = -1.1 (phantom), it was about 26% less dense. These are small effects but accessible to BAO and SN at z ~ 0.5 to 2.

Quintessence connection: any minimally coupled scalar field with a flat-enough potential approximates wCDM with w slightly greater than -1. Realistic quintessence almost always shows some evolution in w, which is why w0waCDM gets more attention.

Phantom regime: models with w < -1 require either a non-canonical kinetic term (ghost field) or modified gravity. The dominant energy condition (ρ + p ≥ 0) is violated. Future-eternal phantom dark energy with w < -1 leads to a 'big rip' singularity where the scale factor diverges in finite time.

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

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