Energy-Flow Cosmology (EFC) — Predictions

Pitch Ledger 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: Background-only tests at current precision show no statistically significant deviation from ΛCDM: the fsσ₈ signal collapsed from 2.20σ (pre-DESI DR2) to 0.68σ after DESI DR2, and the Variant H MCMC returns ΔAIC = +4.05 (ΛCDM preferred). The perturbation-sector discriminants (P1, P3) remain untested; decisive outcomes require Stage-IV lensing (Euclid DR1, Rubin LSST, SO × Euclid). EFC therefore remains a candidate extension of ΛCDM pending both CMB likelihood validation and Stage-IV tomography. Predictions below are pre-registered: each has an observable, a quantitative threshold, a reproducible test script or DOI-sealed artefact, and a falsification criterion. A testable model must define where it fails — the dedicated falsification section below lists F7–F9 that kill the perturbation sector cleanly.

1. Why a Predictions page?

The Gap Analysis says what we do not yet know. The Validation Ledger says what has already been tested. This page says what we claim will happen — in Stage-IV data — so that external reviewers can test EFC without reading the full theory stack. Each prediction is structured as:

Observable — what is measured (numerical, in a specific survey).
EFC value — what EFC predicts, with uncertainty.
ΛCDM value — the null baseline.
Test — how to compare, in which data release.
Falsifier — the quantitative outcome that kills the prediction.
Seal / DOI — SHA-256 locked artefact on figshare.

Grounded in evidence/ (GitHub): 01_hypothesis, 05_results, 06_falsification, benchmark_table.json.

2. Headline predictions

ID	Observable	EFC	ΛCDM	Arbiter	Type	Seal
P1	Σ_eff(z) lensing crossover	Sign change at z ≈ 0.44	Monotonic	Euclid DR1 tomography	KILL	32037990
P2	fσ₈(z = 0.7)	0.430	0.449	DESI DR2 full-shape RSD	DAMAGE	32013156
P3	E_G^EFC/E_G^GR	1.086 ± 0.012 at k_c ≈ 0.05 h/Mpc	1.000 ± 0.01	SO × Euclid DR2	KILL	32023788
P4	Cosmic shear S₈ (DP2)	0.847 ± 0.015	0.811 ± 0.006 (Planck)	Rubin LSST DP2	DAMAGE	32013738
P5	Horndeski no-go	μ < 1 ∧ Σ > 1 forbidden with α_T=0	Allowed	Parameter scan (done)	STRUCTURAL	32037990
P6	Background sign lemma	ΔE²(z) ≤ 0 ∀ z > 0	Neutral	`reproduce_efc.py`	PROVEN	31333414

3. Prediction details

P1 — Lensing crossover at z ≈ 0.44 KILL

Claim. The effective lensing amplitude Σ_eff(z) is non-monotonic with a sign change at z ≈ 0.44. EFC predicts enhanced lensing at z < 0.4 and suppressed lensing at z > 0.5. This profile is absent in ΛCDM and in standard QS Horndeski models with α_T=0.

z	Σ_eff	Deviation
0.10	1.026	+2.6%
0.29	1.008	+0.8%
0.44	1.000	crossover
0.58	0.994	−0.6%
0.87	0.988	−1.2%
1.21	0.985	−1.5%

Test. Euclid DR1 tomographic cosmic shear (4+ z-bins, Oct 21, 2026). Falsifier (F9). A monotonic Σ_eff(z) across all bins with no sign change inside z ∈ [0.3, 0.6] falsifies the prediction. Source: evidence/05_results.md R8 · DOI 32037990, Result 3, Fig. 1.

P2 — fσ₈(z = 0.7) = 0.430 DAMAGE

Claim. The regime-transition growth model predicts fσ₈(z=0.7) = 0.430 vs ΛCDM 0.449. Joint BAO distance prediction: D_H/r_d(z=0.7) = 19.797 vs 20.719; D_H/r_d(z=1.0) = 16.527 vs 17.466.

Test. DESI DR2 full-shape RSD at z ∼ 0.5–0.7 (release pending 2026). Falsifier. Measured fσ₈(z=0.7) > 0.449 at > 3σ — i.e. consistent with ΛCDM at high significance — damages but does not kill EFC (point prediction, not structural). Source: evidence/05_results.md R5, R8 · DOI 32013156.

P3 — E_G enhancement: E_G^EFC/E_G^GR = 1.086 ± 0.012 KILL

Claim. Galaxy–CMB-lensing cross-correlation combined with RSD produces the gravitational slip estimator E_G. EFC predicts E_G^EFC/E_G^GR = 1.086 ± 0.012 at k_c ≈ 0.05 h/Mpc and z_eff ≈ 0.5, driven by the combination μ < 1 with Σ > 1.

Pass window: [1.03, 1.14]. Kill condition: measurement = 1.00 ± 0.01 at > 3σ (GR recovery). Test. Simons Observatory CMB lensing × Euclid DR2 galaxy catalogue (~2027–2028). Source: DOI 32023788, sealed 15 Apr 2026 with SHA-256 falsifier.

P4 — Rubin DP2 cosmic shear S₈ = 0.847 ± 0.015 DAMAGE

Claim. Large-scale cosmic shear ξ₊ enhancement of ~8% at angular scales 20′–300′, producing S₈ = 0.847 ± 0.015. Discriminates EFC from f(R) (which predicts μ > 1) and from background-only entropic gravity models.

Test. Rubin LSST DP2 (Jul–Sep 2026). Falsifier (F4). DP2 + Euclid DR1 combined return S₈ consistent with Planck ΛCDM (0.811 ± 0.006) at < 1σ — the S₈ tension dissolves and EFC loses its primary motivation. Source: DOI 32013738, sealed with SHA-256 falsifier.

P5 — Horndeski no-go (structural) STRUCTURAL

Claim. Standard quasi-static Horndeski with α_T=0 and c_s² > 0 cannot produce μ < 1 and Σ > 1 simultaneously — the action forces Σ ≤ μ universally. EFC breaks this via the Lagrange-multiplier flow constraint.

Test. Full numerical scan of (α_B, α_M) parameter space (done, 135,000 points; 0 Horndeski solutions vs 15 EFC solutions). Implication. If P1+P3 (lensing enhancement with growth suppression) is confirmed, standard Horndeski is excluded as the mechanism; EFC or an equivalent slip-extension is required. Source: evidence/05_results.md R9 · DOI 32037990, Result 1.

P6 — Background sign lemma PROVEN

Claim. ΔE²(z) ≤ 0 for all z > 0, i.e. H_EFC(z) ≤ H_ΛCDM(z). Reduced Hubble friction enhances growth; analytically proven (Lemma 1) and numerically verified at A ∈ {0.01, 0.1, 1.0, 5.0}.

Reproducibility. python reproduce_efc.py — test sign_lemma_A=*. Source: DOI 31333414, Lemma 1.

4. Known negative result (Variant H)

Included here explicitly for honesty: the Variant H entropy-gradient MCMC against DESI DR2 BAO + fσ₈ + H(z) + SNIa (40 bins) returns ΔAIC = +4.05, ΔBIC = +3.94. ΛCDM is preferred by current background data. S₀ = 0.210 ± 0.141 is consistent with zero at 1.5σ. The σ₈ shift is only −1.2%. This does not falsify EFC (the signal may sit below present sensitivity, and the perturbation-sector discriminants P1/P3 remain untested), but it sets a quantitative baseline: background-only tests at current precision do not favour EFC. Source: evidence/05_results.md R7 · DOI 32037990, Result 4.

5. Falsification criteria for these predictions

Each prediction is tied to an explicit falsifier. The KILL-level entries (F1, F7–F9) would invalidate the perturbation-sector mechanism; DAMAGE-level entries (F4–F6) would reduce scope without disproving the framework. Full definitions live in evidence/06_falsification.md.

ID	Type	Observable	Threshold	Kills which prediction	Status
F1	KILL	CMB C_ℓ	\|ΔC_ℓ/C_ℓ\| > 0.1%	Framework (L0 limit)	Sanity pass, likelihood pending
F2	KILL	μ₀	μ₀ > 1 at 3σ	Entropy mechanism	Excluded by existing data
F3	KILL	Void ISW / lensing	>5% deviation	Regime boundary (L0/L1)	Planned
F4	DAMAGE	S₈ tension	< 1σ across Stage-IV	P4 motivation	Monitoring (2–3σ now)
F5	DAMAGE	Unified χ²	Δχ² > +5	Global fit	Current +1.72
F6	DAMAGE	SPARC win rate	< 40%	Galactic sector	Current 60.2%
F7	KILL	Gravitational slip η	η = 1 at 3σ across Stage-IV	P1, P3 (slip sector)	Untested
F8	KILL	(μ, Σ) region	Zero solutions in scan	P3, P5 (mechanism)	15 solutions found
F9	KILL	Σ_eff(z) profile	Monotonic, no crossover	P1 (distinctive signature)	Pre-registered, awaiting Euclid DR1

6. Stage-IV test schedule

Survey / Release	Date	Tests	Prediction at stake
DESI DR2 full-shape RSD	2026	fσ₈(z=0.5–0.7), D_H/r_d	P2
Rubin LSST DP2	Jul–Sep 2026	Early shear, S₈, ξ₊	P4
Euclid DR1	Oct 21, 2026	Tomographic Σ_eff(z), η, E_G	P1, P3, F7
SO × Euclid	~2027–2028	E_G at k_c ≈ 0.05 h/Mpc	P3
DESI DR3	~2027–2028	Full RSD, Lyα BAO, high-z growth	P2 (extended)
Planck plik_lite TTTEEE	Ongoing	Full CMB likelihood	F1 (framework-level)

7. Reproducibility

Every prediction above either reproduces deterministically from the repository (reproduce_efc.py, reproduce_bao.py, reproduce_sparc.py, reproduce_cmb_sanity.py) or is SHA-256 sealed on figshare with the falsifier locked pre-data. Full binding: evidence/benchmark_table.json.

Coverage today: 88/88 reproducibility checks across four scripts (fsσ₈ 31/31, BAO 11/11 diagonal, SPARC 12/12, CMB sanity 24/24, plus the minimal simple/run.py 10/10). Full Boltzmann-solver CMB likelihood remains the single outstanding KILL-level gap — see Gap Analysis §2 KC.

Bottom line

Strongest prediction	P1 — lensing crossover at z ≈ 0.44. Structurally distinctive, absent in ΛCDM and in QS Horndeski with α_T=0. Directly testable in Euclid DR1 (Oct 2026).
Soonest test	P2 (DESI DR2 RSD, 2026). First opportunity to check a sealed EFC point prediction against fresh data.
Cleanest falsifier	F9 — monotonic Σ_eff(z). If Euclid DR1 sees no sign change, P1 is dead.
Known weakness	Variant H MCMC (R7): ΔAIC = +4.05 against DESI DR2 background data. ΛCDM is preferred on current background-only tests.
Single outstanding gate	Full CMB likelihood (F1). Sanity checks pass, but plik_lite TTTEEE with hi_class/CLASS patch is required before any of P1–P4 can be considered “accepted”.