Parameter Constraints
This page lists the marginalised constraints on every parameter of the three models for the Protocol 1b final run. Values are the median with the 16th–84th percentile offsets of 7,680,000 retained samples per model.
Key results
| Model | Parameter | Median | +1σ | −1σ | Unit |
|---|---|---|---|---|---|
| ΛCDM | H₀ | 73.861 | +0.144 | −0.145 | km/s/Mpc |
| ΛCDM | Ωₘ | 0.237 | +0.004 | −0.003 | — |
| CPL | H₀ | 73.880 | +0.324 | −0.314 | km/s/Mpc |
| CPL | Ωₘ | 0.272 | +0.007 | −0.008 | — |
| CPL | w₀ | −0.953 | +0.073 | −0.073 | — |
| CPL | wₐ | −1.183 | +0.454 | −0.457 | — |
| Ξosc | H₀ | 74.169 | +0.350 | −0.345 | km/s/Mpc |
| Ξosc | Ωₘ | 0.256 | +0.006 | −0.006 | — |
| Ξosc | w₀,mean | −1.142 | +0.044 | −0.046 | — |
| Ξosc | ε | 0.185 | +0.077 | −0.087 | — |
| Ξosc | T | 5.473 | +3.596 | −2.223 | Gyr |
| Ξosc | φ₀ | −0.090 | +2.460 | −2.382 | — |
Medians and offsets come from final_parameter_estimates.csv. The raw text summary of the same run differs slightly for ΛCDM and CPL (third decimal) because of a different post-processing; the CSV is used throughout the documentation.
Shared parameters: H₀ and Ωₘ
Result. H₀ lies near 73.9 km/s/Mpc in all three models, while Ωₘ moves from 0.237 (ΛCDM) to 0.272 (CPL) and 0.256 (Ξosc).
Interpretation. H₀ is pinned by the SH0ES-calibrated distance moduli (Pantheon+SH0ES); it is not an independent measurement. Ωₘ is shifted by the dark-energy freedom: it is anti-correlated with w₀,mean in the Ξosc corner plot (Corner Plots), so models that let w depart from −1 settle on a different matter fraction.
Caveat. This page does not compare with published Planck or DESI constraints: no external values are part of the verified fact set.
CPL: w₀ and wₐ
Result. w₀ = −0.953 (±0.073) and wₐ = −1.183 (+0.454, −0.457).
Interpretation. w₀ is close to −1, with an uncertainty that comfortably includes it; the weight of the CPL preference over ΛCDM sits in a negative wₐ, whose 16–84% interval stays below zero. In this parameterisation that suggests an equation of state that crosses −1 at very low redshift and grows increasingly negative towards higher z (see the w(z) figure on Ξosc Oscillation Diagnostic) — but wₐ is the least precisely constrained CPL parameter.
Ξosc: w₀,mean, ε, T, φ₀
Result. w₀,mean = −1.142 (+0.044, −0.046); ε, T and φ₀ are listed above.
Interpretation. The mean level sits below −1 (its 16–84% interval does not include −1), i.e. on average in the phantom regime, with the oscillation superposed. T and φ₀ have intervals spanning a large part of their prior (T: 1 to 10 Gyr; φ₀: −π to π): they are weakly constrained, and their medians should not be read as best-fit values. Discussion: Oscillation Diagnostic.