Energy-Flow Cosmology (EFC) — Model Comparison

Pitch Validation Likelihood Evaluation Models White Paper Roadmap Gaps External Predictions Atlas Changelog

Morten Magnusson · Symbiose Research, Sandnes, Norway · ORCID: 0009-0002-4860-5095 · April 2026 · CC-BY-4.0

Status: This ledger closes the cross-model comparison gap from the 2026-04-23 system audit: EFC has not had a structured, apples-to-apples evaluation against ΛCDM and competing modified-gravity models on identical likelihoods. Rows here report Δχ², ΔAIC, ΔBIC, and ln K with the reference model declared. Scope today: comparison protocol frozen, model registry seeded with placeholders, zero runs yet executed.

1. Purpose

The Validation Ledger shows how EFC scores individually. This ledger shows how EFC scores against alternatives on identical data with identical likelihood and identical nuisance-parameter treatment. Anything else is apples-to-oranges and cannot feed model_preference in the Evaluation Ledger.

2. Comparison protocol (frozen)

A comparison row is valid only if all four conditions hold:

Same dataset (same DOI, same data version)
Same likelihood code (same likelihood_id from the Likelihood Ledger)
Same nuisance parameters and priors
Different theoretical model (the only varying axis)

Any deviation from these must be flagged in the row's caveats list. Comparisons that fail the protocol are rejected by the sync script.

3. Reported quantities

Quantity	Required	Notes
`chi2` per model	yes	At best-fit point
`Δchi2` (model − reference)	yes	Reference declared explicitly per row
`AIC`, `BIC` per model	yes	Uses `n_params` from model registry
`ΔAIC`, `ΔBIC`	yes	Reference model is baseline
`ln Z` (Bayesian evidence) per model	when available	Requires nested sampling
`ln K = ln Z_A − ln Z_B`	when both ln Z available	Reported with Jeffreys-scale interpretation
`n_params` per model	yes	Cosmological free parameters only
Reference model	yes	Declared per row, typically ΛCDM

Jeffreys-scale interpretations are recorded verbatim in interpretation — never paraphrased.

4. Model registry

model_id	Description	n_free_params (cosmo)	Status
`lcdm`	Standard ΛCDM (reference)	6	registered
`efc_v3`	EFC current frozen version	TBD	registered
`horndeski_min`	Minimal Horndeski (α_B, α_M free)	8	placeholder
`f_of_r_hu_sawicki`	f(R) Hu–Sawicki	7	placeholder
`dgp_normal`	DGP normal branch	6	placeholder
`wcdm`	wCDM (constant w)	7	placeholder

Each registered model must declare its likelihood-compatible code path (e.g. MGCAMB module name, or analytic fσ₈ implementation) in data/models.json.

5. Comparison entry template

Template: fσ₈ 2026 — EFC vs ΛCDM placeholder

{
  "comparison_id": "fsigma8_2026__efc_vs_lcdm",
  "likelihood_id": "s8_growth_fsigma8_2026",
  "reference_model": "lcdm",
  "models": [
    {"model_id": "efc_v3",  "chi2": null, "aic": null, "bic": null, "ln_z": null, "n_params": null},
    {"model_id": "lcdm",    "chi2": null, "aic": null, "bic": null, "ln_z": null, "n_params": 6}
  ],
  "delta_chi2": null,
  "delta_aic":  null,
  "delta_bic":  null,
  "ln_k":       null,
  "interpretation": "PENDING",
  "caveats": [],
  "status": "declared"
}

Once the run executes, numeric fields populate and interpretation receives a verbatim Jeffreys-scale phrase (e.g. "positive evidence for EFC", "strong evidence against EFC", "inconclusive").

6. Interaction with the Evaluation Ledger

Model Comparison results feed only the model_preference field of the Evaluation Ledger current_state block — not falsification_status.

Comparison outcome	model_preference set to
ΔAIC > +5 against EFC or ln K > +4.6 for ΛCDM	prefers_lcdm
\|ΔAIC\| ≤ 5 and \|ln K\| ≤ 1	neutral
ΔAIC < −5 for EFC or ln K > +4.6 for EFC	prefers_efc

Being dispreferred by AIC is not the same as being falsified. See Evaluation Ledger §5. Both fields are always reported.

7. External landscape anchor

The External Research Ledger tracks peer-reviewed constraints on MG models (Horndeski, f(R), DGP). When an external paper publishes a likelihood-compatible constraint, it can be imported here as a placeholder row with status: "declared" and caveats: ["external_posterior_import"] until a native run reproduces it.

8. Open questions

Are competing models run inside this repo, or imported as external posteriors? Proposal: native first, external imports only flagged via caveats.
For Horndeski / f(R), do we use MGCAMB defaults or repo-pinned configs? Proposal: repo-pinned configs with MGCAMB defaults documented as baseline.
Should comparisons against scalar-tensor MG split by screening regime? Proposal: yes — separate comparison rows per regime, tied to the Validation Ledger regime matrix.

Bottom line

What this ledger fixes	Makes EFC-vs-alternatives quantitative on identical likelihoods. No more scattered, informal "looks comparable" claims.
Hard rule	Only rows meeting the four protocol conditions (§2) are valid. Any deviation must appear in `caveats`.
Hard dependency	Likelihood Ledger row with a shared `likelihood_id`.
Primary consumer	Evaluation Ledger → `model_preference` only.
Status	Protocol frozen; registry seeded with ΛCDM + EFC registered and four MG placeholders; zero runs executed.