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Known Limitations

Exploratory release

All results in this project are from v0.1.0-exploratory. The following limitations have been explicitly documented before making any physical claims.

Limitation 1 — Fixed sound horizon (r_d)​

The sound horizon r_d is fixed to a CMB-derived value (147.09 Mpc). This implicitly imports a CMB prior on early-universe physics, making the analysis not fully independent of CMB constraints.

Planned fix (v0.2): Free r_d as a nuisance parameter, marginalising over it with a Gaussian prior.

Limitation 2 — t(z) self-consistency bias​

The oscillating equation of state of Ξosc is a function of cosmic time, w(t) = w₀,mean + ε cos(2π t/T + φ₀). The cosmic age t(z) that maps redshift to time is computed once, for a fixed reference cosmology (flat ΛCDM with H₀ = 70, Ωₘ = 0.3, TCMB = 2.725 K, via astropy), not for the H₀ and Ωₘ of the current MCMC sample. The time axis on which the oscillation is defined is therefore inconsistent with the cosmology being sampled, and the period T and phase φ₀ are expressed in the time of the reference cosmology. This does not affect ΛCDM or CPL.

Planned fix (v0.2): Compute t(z) self-consistently for each MCMC sample.

Limitation 3 — ε prior boundary effects​

The oscillation amplitude ε in Ξosc is constrained to ε ≥ 0 by a one-sided prior. The ~2.26σ preference for non-zero ε is partially a boundary effect — if the true posterior extends to negative ε, the one-sided prior artificially inflates the apparent significance.

Planned fix (v0.2): Implement a symmetric prior on ε, centred at zero.

The posteriors of ε and T reach their prior bounds​

The boundary problem is not limited to ε ≥ 0. The ε marginal stays high up to its upper bound (0 < ε < 0.3; median 0.185, upper 1σ edge 0.262), and the T posterior is multi-featured up to its upper bound (1 < T < 10 Gyr; median 5.47 Gyr). Where the posterior is cut off by the prior, the reported median and interval describe the prior range as much as the data, and the best-sample χ², AIC and BIC of Ξosc are approximations (FACTS_INDEX ξ §2.9). See Oscillation Amplitude and Prior Specification.

What this means for the current results​

The ΛCDM and CPL results are minimally affected by these limitations and can be considered indicative. The Ξosc results should be treated as preliminary and not physically interpretable until v0.2 fixes are implemented.

See also​