Energy-Flow Cosmology (EFC) — Predictions

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

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

RCMP framing. EFC is read by regime (L0–L3), not by the background: ΛCDM is the special-case limit of EFC in L0/L1, derived from the variational action (K(ρ)→∞ ⇒ μ,Σ,η→1), so recovering ΛCDM there is a designed feature, not a contest. EFC-distinctive physics lives in L2 (perturbation/growth) and L3 (galactic). falsification_status ≠ model_preference.

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.

April 2026 update (v2.0). Two structural predictions added: P7 — H0 three-window decomposition (32113399, 2026-04-28) reframes the Hubble tension as a regime-mismatch artefact (Planck L0, DESI L1, SH0ES L2); P8 — falsified bar-instability criterion (32101111, 2026-04-25) shows EFC's Π bar-criterion is falsified on N=43 SPARC (AUC=0.217, 0/12 bars), with Π_min retained as an independent disk-state parameter. P2–P4 are constrained by the proven coupling-structure closure of the growth-sector (32084670): fσ₈=0.43 and S₈≈0.82 (robust, down) are fixed by the proven coupling-structure closure (no free-parameter escape route). The α-parameter is independently constrained to α ∈ [−0.72, −0.68] via non-MCMC analysis (32101213), consistent with both blind freezes (−0.689, −0.702). Latest validation-ledger audit: VAL-2026-006.

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

Grouped by status, not just test-class: predictions already confronted with real data (a verdict exists) are separated from those sealed and awaiting their decisive Stage-IV dataset. Awaiting predictions show only their test class — no verdict badge — to avoid implying a result before the data arrives.

2a — Tested against real data (verdict exists)

ID	Observable	EFC	ΛCDM	Data used	Verdict	Seal
P4	Cosmic shear S₈	≈0.82 (robust, shifted downward; Σ=μ(1+η)/2 with η→1 ⇒ Σ≈0.99<1). The 0.847 ± 0.015 value required Σ∈[1.03,1.07] (the η∈[1.05,1.15] boost = 0% robust)	0.811 ± 0.006 (Planck)	DES Y6 (0.789), KiDS-Legacy (0.815)	PASS/mild	32013738
P5	Horndeski no-go	EFC reaches (μ < 1 ∧ Σ > 1) only via the fragile η-boost (η-dependent, 0% robust per 32037990). Robust EFC has Σ≈μ<1, outside the forbidden quadrant — does not exclude Horndeski	Allowed	Parameter scan (done)	FRAGILE	32037990
P6	Background sign lemma	ΔE²(z) ≤ 0 ∀ z > 0	Neutral	`reproduce_efc.py`	PROVEN	31333414
P8	Bar-instability Π criterion	Π_min falsified as a bar predictor (AUC=0.217, captures 0/12 bars, N=43 SPARC); retained as independent disk-state parameter	ELN: ε = V_max/√(GM_d/R_d) > 1.1	SPARC + S4G + Galaxy Zoo	FALSIFIED	32101111

2b — Sealed, awaiting data (no verdict yet — test class only)

ID	Observable	EFC	ΛCDM	Awaiting	Status	Seal
P1	Σ_eff(z) lensing crossover	≈ flat in z (robust; η→1 ⇒ Σ≈μ≈0.99, near-GR, monotonic). Sign change at z ≈ 0.44 is fragile (η-dependent, 0% robust per 32037990)	Monotonic	Euclid DR1 tomography (Oct 2026)	SEALED — awaiting; kill-test class (fragile)	32037990
P2	fσ₈(z = 0.7)	0.430 (partial existing data: DESI DR1 z=0.706 = 0.413 ± 0.029, mildly favours EFC)	0.449	DESI DR2 full-shape RSD	SEALED — awaiting; damage-test class	32013156
P3	E_G^EFC/E_G^GR	≈1 (robust; η→1 ⇒ no enhancement). 1.086 ± 0.012 at k_c ≈ 0.05 h/Mpc is fragile (η-dependent, 0% robust per 32037990)	1.000 ± 0.01	SO × Euclid DR2 (~2027)	SEALED — awaiting; kill-test class (fragile)	32023788
P7	H₀ three-window decomposition	Triple-null test: EFC predicts non-null in all three windows. H₀^L0≈67.5, H₀^L1≈69.5, H₀^L2≈73.5 is an interpretive mapping, not the paper's decomposition	Single H₀; tension persists	Disaggregated Planck + DESI + SH0ES test	SEALED — awaiting; structural	32113399

3. Prediction details

P1 — Lensing crossover: robust EFC ≈ flat (near-GR) FRAGILE

Claim. The non-monotonic Σ_eff(z) crossover at z ≈ 0.44 (enhancement at z < 0.4, suppression at z > 0.5) requires Σ > 1 at low z — which comes from the gravitational-slip boost η ∈ [1.05, 1.15], classified 0% robust (fragile) by EFC's own perturbation-sector analysis (32037990). The crossover values below are therefore tagged fragile (η-dependent, 0% robust per 32037990). The robust EFC (η→1; slip terms ε_λ, ε_K cancel under screening) gives Σ ≈ μ ≈ 0.99 flat in z ⇒ no crossover (near-GR, monotonic). 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, fragile branch only). A monotonic Σ_eff(z) across all bins with no sign change inside z ∈ [0.3, 0.6] kills only the fragile (η-boosted) crossover branch — a monotonic result is consistent with the robust EFC prediction (Σ ≈ μ ≈ 0.99 flat, near-GR). Source: evidence/05_results.md R8 · DOI 32037990, Result 3, Fig. 1; robustness per same DOI.

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. Growth model anchored to the DOI-verified existing fσ8 compilation: 6dFGS (10.1111/j.1365-2966.2012.21136.x), SDSS-MGS (10.1093/mnras/stu2693), BOSS DR12 (10.1093/mnras/stx721), VIPERS (10.1051/0004-6361/201526553), FastSound (10.1093/pasj/psw029) — EFC fits it at χ²_r=0.340 (α=−0.68) vs ΛCDM 0.554; the DESI DR2 test above remains the decisive blind test.

P3 — E_G: robust EFC ≈ 1 (no enhancement) FRAGILE

Claim. Galaxy–CMB-lensing cross-correlation combined with RSD produces the gravitational slip estimator E_G. The E_G enhancement E_G^EFC/E_G^GR = 1.086 ± 0.012 at k_c ≈ 0.05 h/Mpc and z_eff ≈ 0.5 rests on the gravitational-slip boost η ∈ [1.05, 1.15], which EFC's own perturbation-sector robustness analysis (32037990) classifies as 0% robust (fragile). The 1.086 value is therefore tagged fragile (η-dependent, 0% robust per 32037990). The robust EFC prediction (η→1; slip terms ε_λ, ε_K cancel under cosmological screening) gives Σ = μ ≈ 0.99 < 1 ⇒ E_G ≈ 1 (no enhancement). The robust prediction does not require E_G > 1.

Fragile pass window (η-dependent): [1.03, 1.14]. Test. Simons Observatory CMB lensing × Euclid DR2 galaxy catalogue (~2027–2028). Source: DOI 32023788, sealed 15 Apr 2026 with SHA-256 falsifier; robustness per DOI 32037990.

P4 — Cosmic shear S₈ ≈ 0.82 (robust, shifted downward) PASS/mild

Claim (derivation result, not data-fit). The robust EFC growth sector gives Σ = μ(1+η)/2 with η→1 ⇒ Σ ≈ 0.99 < 1, so S₈ shifts slightly downward to S₈ ≈ 0.82 (DOI 31188193: “S₈ shift downward… consistent with the S₈ tension”). The earlier S₈ = 0.847 ± 0.015 value (cosmic shear ξ₊ enhancement of ~8%, requiring Σ ∈ [1.03, 1.07]) depended on the η ∈ [1.05, 1.15] boost, which is 0% robust / fragile. New canonical: S₈ ≈ 0.82 (robust, down).

Test. Rubin LSST DP2 (Jul–Sep 2026); DES Y6 + KiDS Legacy via RCMP. Comparison. S₈ ≈ 0.82 vs DES Y6 0.789 (~1–1.5σ) and KiDS-Legacy 0.815 (< 0.5σ) — PASS/mild. Falsifier (F4). DP2 + Euclid DR1 combined return S₈ consistent with Planck ΛCDM (0.811 ± 0.006) at < 1σ — EFC loses motivation. Source: DOI 32013738, sealed with SHA-256 falsifier; S₈-direction per DOI 31188193.

P5 — Horndeski no-go: robust EFC does not exclude Horndeski FRAGILE

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 was claimed to break this only by reaching the forbidden (μ < 1, Σ > 1) quadrant, which requires the gravitational-slip boost η > 1 (the Σ > 1 piece) — classified 0% robust (fragile) per 32037990. The robust EFC has Σ ≈ μ < 1 (both suppressed, η→1), so it does not occupy the forbidden quadrant and does not exclude Horndeski.

Test. Full numerical scan of (α_B, α_M) parameter space (done, 135,000 points; 0 Horndeski solutions vs 15 EFC solutions — the 15 EFC solutions all sit in the fragile η-boosted region). Implication (doubly-conditional). EFC distinguishes itself from Horndeski only via the fragile η-boost. The earlier “if P1+P3 are confirmed ⇒ standard Horndeski is excluded” wording is now doubly-conditional: both P1 and P3 are fragile / η-dependent, so the exclusion holds only if both fragile branches survive Stage-IV. Source: evidence/05_results.md R9 · DOI 32037990, Result 1; robustness per same DOI.

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.

P7 — H₀ three-window decomposition STRUCTURAL

Claim. The Hubble tension is not a free-parameter degeneracy but a regime-mismatch artefact. EFC predicts that Planck (L0 background), DESI BAO (L1 transition), and SH0ES (L2 perturbation) measure H₀ in distinct regime windows that do not need to coincide. The three-window decomposition (thermal / geometric / structural redshift) is a synthesis of existing EFC results, not a new derivation — the projection P_ξ is specified to first order only. The triplet H₀^L0≈67.5, H₀^L1≈69.5, H₀^L2≈73.5 km/s/Mpc is an interpretive mapping, not the paper's decomposition. The atlas role for H0_tension was upgraded 2026-04-29 from addresses_open to proposes_resolution.

Test. Joint regime-disaggregated chain on Planck + DESI DR2 BAO + SH0ES + Euclid DR1 shear (three-window decomposition per DOI 32113399). Falsifier (triple-null test). EFC predicts a non-null signal in all three windows; a triple-null result consistent with ΛCDM in every window is a clean falsification. Source: DOI 32113399 (2026-04-28); validation candidate vc_e36e011d1270.

P8 — A falsified bar-instability criterion reveals an independent disk-state parameter FALSIFIED

Result. EFC's Π bar-criterion Π_EFC = σ_R·κ_eff/(3.36·G·Σ) < 1 (with κ_eff incorporating the entropy-gradient correction κ²_eff = κ²_GR + κ²_S-flow) was tested on N = 43 SPARC galaxies and is falsified as a bar predictor: AUC = 0.217 (anti-correlated), capturing 0/12 bars. Π_min is retained not as a bar predictor but as an independent disk-state parameter (ρ[Π, logΣ] = −0.71, ρ[Π, f_gas] = +0.65, n = 112).

Test. Cross-population test against SPARC (N = 43 with the bar label; 175 in the rotation-curve sample), S4G (~2300), Galaxy Zoo bar-fractions; protocol pre-registered as vc_140e79363cbe. Source: DOI 32101111 (2026-04-25), “A Falsified Bar-Instability Criterion Reveals an Independent Disk-State Parameter”.

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 (fragile η-branch)	15 solutions found (all η-boosted)
F9	KILL	Σ_eff(z) profile	Monotonic, no crossover	P1 (fragile η-branch; monotonic is consistent with robust EFC)	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)
Joint Planck + DESI DR2 + SH0ES + Euclid DR1	2026–2027	Regime-disaggregated H₀ chain	P7
SPARC + S4G + Galaxy Zoo cross-population	Available now	Bar fraction f_bar(M_*, σ_R, κ_eff)	P8
DES Y6 + KiDS Legacy (RCMP)	2026	L2 weak lensing via RCMP protocol	P3, P4

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

Most distinctive (fragile) prediction	P1 — lensing crossover at z ≈ 0.44. Structurally distinctive but fragile: the crossover is the η-boost signature (η-dependent, 0% robust per 32037990). Robust EFC predicts a near-flat (monotonic, ≈GR) Σ_eff(z). 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, the fragile (η-boosted) P1 branch is dead — but a monotonic result is consistent with the robust EFC (≈GR) prediction.
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”.
Falsified criterion	P8 (bar-instability). EFC's Π bar-criterion is falsified on N=43 SPARC (AUC=0.217, 0/12 bars). Π_min survives only as an independent disk-state parameter (ρ[Π, logΣ]=−0.71, ρ[Π, f_gas]=+0.65, n=112) — not as a bar predictor.
Strongest reframing	P7 (H₀ three-window). The Hubble tension is restructured rather than resolved: SH0ES, Planck and DESI never measured the same quantity. Atlas role upgraded from `addresses_open` to `proposes_resolution`.
Structural lock	Growth-sector coupling-structure closure (DOI 32084670): fσ₈=0.43 and S₈≈0.82 (robust, down) are constrained by the proven coupling-structure closure (unique μ/Σ under EBE) — no free-parameter escape route remains.