Evolving Dark Energy Calculator
Set w0 and wa and see what moves against flat ΛCDM at the same redshift
ΛCDM assumes the dark energy density never changes — that is what the Λ means. The usual way to relax it lets the equation of state run linearly with scale factor, w(a) = w0 + wa(1 − a), so that w0 is the value today and w0 + wa the value in the distant past. Set w0 = −1 and wa = 0 and the two columns below agree to the last digit, because the model has become ΛCDM again. Move either one and the gap opens.
Every point in the plane below is a different dark energy history. Fitting the DESI DR1 BAO distances at that point — with rd held at the Planck value of 147.1 Mpc — gives the Ωm and H₀ that go with it. Move the pointer to read them off — the calculator beside it follows your pointer, and a click pins it.
At ΛCDM the fit returns Ωm = 0.295, which is the value DESI publishes from these data, so the machinery is doing what it should. The H₀ beside it is worth reading carefully: BAO measures the product H₀rd, never H₀ alone, so every number here is conditional on the 147.1 Mpc. DESI quotes a lower H₀ from the same distances because it derives a slightly larger rd from big bang nucleosynthesis rather than fixing Planck's. The measured combination agrees; only the ruler differs.
At this redshift
| ΛCDM | w0waCDM | diff | |
|---|---|---|---|
| Ωm fitted | — | — | — |
| H₀ [km/s/Mpc] fitted | — | — | — |
| H(z) [km/s/Mpc] | — | — | — |
| age | — | — | — |
| lookback | — | — | — |
| DM/rd | — | — | — |
| DH/rd | — | — | — |
| θBAO [deg] | — | — | — |
| w(z) | — | — | — |
The diff column is the fractional change, (w0waCDM − ΛCDM) / ΛCDM, in percent. Ωm and H₀ are not typed in: each column carries the values that fit the DESI BAO distances for its own dark energy history, at the rd above.
Computing the grid…
What the two columns share, and what they don't
Both columns solve the same Friedmann equation. The dark energy term differs by construction, and Ωm and H₀ differ because the data make them: choosing w0 and wa already fixes what matter density and expansion rate the BAO distances will tolerate, so offering those as separate inputs would only let you build a universe the measurements reject. Where ΛCDM carries a constant ΩΛ, the evolving model carries ΩΛ × a−3(1+w0+wa) e−3wa(1−a), which is exactly 1 when w0 = −1 and wa = 0. At that setting the fit hands both columns the same Ωm and H₀ as well, so the diff column reads zero throughout — the same arithmetic, not a close approximation.
For parameters this close to ΛCDM the gaps are well under one percent, and they do not all move the same way. With the DESI BAO fit loaded, H(z) sits below ΛCDM at z = 1 and above it by z = 0.3: the evolving density crosses the constant one on the way, and the diff column changes sign as it does. Sweep z downward and watch it happen near z ≈ 0.5. That crossing is the whole content of an evolving equation of state, and it is why one measurement at one redshift cannot separate the two models. You need the shape, across a range — which is what a survey of millions of galaxies at many redshifts is for.
The preset labelled DESI BAO fit is a fit to the DESI BAO distance measurements on their own — not DESI's published constraint, which combines BAO with the CMB and with supernovae and lands further from ΛCDM. Use it as a starting point to move from, not as a result to quote. The ΛCDM page describes where the published preference for evolution stands.
The age integral, the comoving distance and θBAO are computed as on the cosmology calculator, by Simpson's rule under the substitution a = 1/(1+z). The linear w(a) form is an extrapolation far outside the range it was built to describe, so the redshift here is capped at 1100 rather than the 107 the ΛCDM calculator allows.