Psi-Continuum Cosmology: A Phenomenological Extension of ΛCDM

This work introduces a phenomenological extension of the standard ΛCDM expansion history by adding a simple phenomenological deformation term of the form

ΩΨ(z) = ε₀ (1+z)ⁿ.

The goal is to quantify how much freedom late-time background data still allow when the expansion law is modified by small, physically agnostic deviations.

Using publicly available datasets — the Pantheon+SH0ES supernova sample and the H(z) compilation from Yu, Ratra & Wang (2018) — the study performs four controlled tests:

(1) a SN-only ΛCDM baseline fit,

(2) a fixed-model comparison ΛCDM vs ΨCDM,

(3) a joint SN + H(z) analysis,

and (4) a full two-parameter grid scan in (ε₀, n).

The results show that moderate response amplitudes (ε₀ ≤ 0.1, |n| ≤ O(1)) remain statistically competitive with ΛCDM at the background level.

This demonstrates that current late-time expansion data do not uniquely determine the ΛCDM form of H(z), leaving room for controlled phenomenological extensions.

All numerical scripts, data files, and the full LaTeX source of the article are provided for full reproducibility.