Theory Overview

Psi-Continuum v2

Psi-Continuum v2 (ΨCDM) is a minimal one-parameter phenomenological extension of the standard ΛCDM cosmological model at the background expansion level.

It introduces a single smooth late-time deformation of the Hubble expansion, governed by the dimensionless parameter ε₀, while leaving early-Universe physics unchanged and not introducing any modifications to standard perturbation dynamics.

Background Expansion

The modified Hubble expansion rate is defined as:

H_Ψ(z) = H_Λ(z) · (1 + ε₀ / (1 + z))

A visual comparison between ΛCDM and ΨCDM is shown below:

Psi-Continuum Hubble function

This parametrisation:

reduces exactly to ΛCDM when ε₀ = 0,
produces percent-level deviations only at low redshift,
suppresses all deviations as z → ∞,
leaves early-Universe observables (CMB, primordial BAO) unchanged.

Scope of the Model

Psi-Continuum v2 is intentionally restricted to the late-time background expansion.

It does not introduce:

modifications of gravity,
additional dynamical fields,
changes to perturbation equations,
or alterations of early-Universe physics.

Included Functionality

This package provides a fully reproducible late-time cosmology pipeline, including:

ΛCDM and ΨCDM background expansion models
Distance measures: H(z), E(z), d_L(z), D_M/r_d, D_H/r_d, D_V/r_d
Pantheon+ High-Fidelity SNe Ia likelihood (full covariance)
32 cosmic-chronometer H(z) measurements
SDSS DR12 and DESI DR2 Gaussian BAO likelihoods
Full joint χ² framework (SN + CC + BAO)
ε₀ scans, Δχ² profiling, and ΛCDM comparison
Publication-grade figure generator
Command-line interface (psi-cli) for running the complete pipeline

All numerical results reported in the accompanying paper are fully reproducible using this software.

Associated Publications

Psi-Continuum v2 preprint https://doi.org/10.5281/zenodo.17879744
Psi-Continuum v2 software archive https://doi.org/10.5281/zenodo.17928837

Project Status

Psi-Continuum v2 is a final archived research release.

The code and documentation are frozen for long-term reproducibility and citation. Further theoretical developments will be released separately as Psi-Continuum v3.