MTP Cosmology — Windowed Interacting Dark Energy Toy Model

A GR-consistent windowed interacting dark energy (IDE) model. A late-time activation window (centered near the dark-matter/dark-energy coincidence epoch, z* ≈ 0.3–0.5) drives an effective phantom crossing (w < −1) and produces a w₀–wₐ time-variation signal consistent in direction with DESI DR1.

Honest scope. The hierarchy term F_hier(z) is nearly constant over the observable range (z ≲ 2), so the model is, operationally, a windowed IDE model. The "MTP / hierarchy" naming is kept for historical/philosophical context. See ARCHITECTURE.md §1.

Quick start

pip install -r requirements.txt
python scripts/run_v03.py          # reproduces figures/mtp_v03.png + the §3 table

The core model is an importable, side-effect-free package:

import sys; sys.path.insert(0, "src")
from mtp_cosmology import Params, Hz, w_eff
import numpy as np

z = np.linspace(0.001, 2.5, 500)
p = Params(beta0=0.10, z_star=0.5, sigma=0.4)
H, rho_c, rho_de = Hz(z, p)
print("w_eff(0) =", w_eff(z, rho_de)[0])

Repository layout

src/mtp_cosmology/      Importable core (model.py: kernel, ODE, observables)
scripts/                Drivers: run_v03.py (figures+table), run_mcmc.py (P1)
legacy/                 v0.1/v0.2 prototypes + flat v0.3 + toy-w MCMC (history)
figures/  results/      Generated artifacts
paper/                  Paper draft (P3)
docs/                   Notes
MTP_consolidated_report.md   Original consolidated dev report (v0.1→v0.3)
ARCHITECTURE.md         Physics derivation + code architecture + decisions
worklog.md              Dated work log

Status & roadmap

Phase	Scope	State
P0	Reproducible landing: importable core, fixed paths, docs	✅ done
P1	Observable-based likelihood (H/D_M/fσ8) + emcee MCMC	✅ done
P2	Real DESI DR1 BAO fit + Bayesian evidence vs ΛCDM	✅ done
P3	Scalar-tensor screening micro-model + paper draft	✅ done

Headline results (all honest, reproducible):

• The coupling at β₀≈0.1 is a sub-percent effect on H/D_M/fσ8 — below current precision. Pipeline recovers injected β₀ within 1σ at forecast precision; β₀–σ is degenerate from background+growth data (only β₀ amplitude is constrained).
• DESI DR1 BAO: β₀ < 0.27 (95%), Δln Z = −1.9 (1-param) / −1.2 (3-param) → weak preference for ΛCDM. The coupling is too weak to relieve the LRG1 D_H feature.
• Screening: a chameleon with Solar field excursion < 4.3×10⁻⁸ M_Pl satisfies the Cassini bound.

Run: python scripts/run_v03.py, python scripts/run_mcmc.py --fit beta0, python scripts/run_realfit.py --fit beta0. See paper/paper.md.

Model comparison (primary objective)

The point of the project is fair model comparison: does windowed IDE explain late-time phantom-like dynamics and growth with comparable or fewer effective degrees of freedom than ΛCDM, CPL, and existing IDE variants? The methodology (model set, datasets, priors, metrics, success/failure thresholds, run matrix) is specified in docs/comparison_methodology.yaml.

python scripts/run_compare.py --stage phase_0   # mock pipeline validation
python scripts/run_compare.py --stage phase_1   # real DESI DR1 BAO (geometry)
python scripts/run_compare.py --stage phase_3   # + Gold-2018 RSD (growth)
python scripts/run_compare.py --stage phase_4   # + Planck18 compressed CMB

Outputs an AIC/BIC/Δln Z table over {ΛCDM, CPL, constant IDE, sign-switching IDE, MTP-3p, MTP-4p}, all under identical priors/likelihood/sampler.

Verdict across geometry → growth → CMB (real data): CPL is the only model that beats ΛCDM on both AIC and BIC, capturing the DESI evolving-DE signal (w₀≈−0.7, wₐ≈−1). The windowed IDE never beats ΛCDM; adding Planck's (R, l_A) drives the IDE coupling to zero (D_M(z*) pins the late-time expansion), so β₀ ends up consistent with 0. As a GR-perturbative late-time coupling the model is not economical vs CPL — see worklog.md, paper/paper.md, and docs/phase4_cmb.md.

See worklog.md for the running log and ARCHITECTURE.md for the model.