Morten Magnusson · Symbiose Research, Sandnes, Norway · ORCID: 0009-0002-4860-5095 · April 2026 · CC-BY-4.0
What is Energy-Flow Cosmology? A 60-second version.
The standard picture of the universe says 95% of it is made of two invisible ingredients — dark matter (the glue that holds galaxies together) and dark energy (the pressure that makes space expand faster and faster). Neither has ever been detected in a laboratory. The 5% we can actually measure is the only part nobody argues about.
EFC proposes a simpler idea: gravity adjusts itself where disorder (entropy) is still building up, and behaves like ordinary Einstein gravity everywhere else. One mechanism, two numbers, no invisible particles required.
The deepest difference is ontological. ΛCDM treats spacetime as a fixed stage and "dark matter" / "dark energy" as ingredients on that stage. EFC treats energy and entropy as primary — spacetime and the effective gravitational response emerge from energy flowing along entropy gradients through a discrete substrate. Time is secondary, an index over irreversible Grid transitions (Axiom 0). "Dark matter" is not a particle; it is a consequence of how a coarse-grained observer reads cross-regime gravity. Same observations, fewer primitives. See the Pitch for the full side-by-side comparison.
Result so far (121 registered tests; 103 active, 93 survived, 10 falsified, 18 in pipeline — from galaxy rotation curves to Planck 2018): EFC has survived 93 of 103 active probes. Ten probes have been falsified, demonstrating genuine testability. It does not yet outperform the standard model — the margins are too small to call a winner. The decisive experiments are pre-registered in the Roadmap.
Status: candidate theory under test. Non-rejectable. Not proven. Not falsified.
One sentence (technical): Energy-Flow Cosmology modifies gravity in the perturbation sector through an entropy-gradient coupling, contains ΛCDM as a limiting case, and predicts testable deviations — with a structured falsification protocol frozen before Stage-IV data release.
| Part | Title | Key Result | DOI |
|---|---|---|---|
| 1 | Recovery Conditions and the ΛCDM Limit | Three independent sufficient conditions establish EFC ⊃pert ΛCDM | 31970886 |
| 2 | Field Equations and Observable Mapping | μ(a) = 1 + βS(a); complete mapping to fσ8, S8, Σ, R(k,S) | 31970898 |
| 3 | Data, Validation Ledger, and Falsification Protocol | 121 tests (93 survived, 10 falsified); 2 sealed predictions; 5 kill criteria for Stage-IV | 31970904 |
| 4 | Regime Susceptibility and Cross-Scale Mapping | T(S) susceptibility; entropic continuum; w(a) = −β(S)·a | 31970907 |
Any viable extension of ΛCDM must recover standard cosmology in an appropriate limit. Part 1 proves three analytically independent sufficient conditions under which EFC reduces exactly to ΛCDM/GR:
| Condition | Limit | Domain | Status |
|---|---|---|---|
| I. Parameter | αL2 → 0 | Full perturbation sector | Analytic proof |
| II. Entropy | S < Sc ≈ 0.1 | L0/L1 (GR regime) | Analytic + KT1 |
| III. Density | ρ ≫ ρcrit | Solar system, stellar | Analytic + KT2/KT3 |
Corollary 1: EFC contains ΛCDM as a limiting case in the perturbation sector. LEVEL 2 ESTABLISHED
Open problem: Full background H(z) recovery (Level 3) remains unestablished. The background α-gate was found inconsistent with joint CMB+BAO constraints. This boundary is a feature: it precisely defines the domain of validity. The Background No-Go Theorem consolidates three independent proofs (sign lemma, CLASS verification, observational α-collapse) establishing this as a structural boundary.
Part 2 derives the field equations from the entropy-gradient principle and maps every equation to a testable observable.
| # | Element | Type |
|---|---|---|
| 1 | Entropy field S(a) ∈ [0, 1] | Fundamental |
| 2 | μ(a) = 1 + β S(a), β ≈ 0.16 from SPARC | Derived |
| 3 | Growth equation with μ(a) | Dynamical |
| 4 | fσ8, S8, Σ observables | Empirical |
| 5 | R(k,S) response surface | Unifying |
| Observable | Result | Status |
|---|---|---|
| αL2 (growth sector) | −1.00 ± 0.46 (2.20σ, ΔAIC = −2.91) | PASS |
| fσ8(z = 0.7) | EFC 0.430 vs ΛCDM 0.449 (2.0σ) | SEALED |
| fσ8 LOO robustness | 7/7 folds pass; |α|/σ ∈ [1.84, 2.42] | PASS |
| S8 (DES Y6, pre-registered) | 0.944 ± 0.018 vs 0.95 ± 0.03 (0.3σ) | PASS |
| Solar system (PPN) | EFC correction < 10−5 | PASS |
| αL2 (background) | Inconsistent with CMB+BAO | COLLAPSED |
The 2.20σ signal is a persistent directional hint, not a detection. Three simultaneous probes are needed to break the μ–Σ degeneracy (IG-1 gate).
A theoretical framework is evaluated by the sharpness of the boundary between “still viable” and “falsified”. Part 3 makes this boundary explicit, public, and permanent.
| Status | Count | Description |
|---|---|---|
| Pass | 67 | Tests passed at declared tier (incl. Kill-Test v6 Universality SPARC 175, 2026-04-11) |
| Partial | 5 | Marginal or partially resolved |
| Collapsed | 3 | Background gate, degeneracy, etc. |
| Failed | 17 | Did not pass (N-tests, etc.) |
| Falsified | 5 | Superseded by successor model version |
| Total | 103 | — |
Self-falsification history: EFC has already discarded two model versions (v1 scalar index, naïve GRAV→(μ,Σ) extrapolation) and formalised a third (B0 sign constraint). This is the strongest evidence for the seriousness of the framework.
| Prediction | Date | Parameters | Hash prefix |
|---|---|---|---|
| Freeze v1 | 2026-02-18 | αL2 = −0.689; fσ8 crossover z = 2.042 | 7a850cfa... |
| Freeze v2 | 2026-02-21 | αL2 = −0.702 | dbccda15... |
Thresholds frozen before data release. No post-hoc adjustment permissible.
| # | Criterion | Trigger | Consequence |
|---|---|---|---|
| KC1 | Growth suppression absent | |αL2| < 0.1 at 3σ | Growth sector falsified |
| KC2 | Wrong fσ8 trajectory | |zcross − 2.042| > 3σ | Crossover prediction falsified |
| KC3 | S8 converges to ΛCDM | S8 = S8,ΛCDM ± 0.005 | S8 channel falsified |
| KC4 | Gravitational slip absent | |η − 1| < 0.01 (Euclid) | Slip prediction falsified |
| KC5 | No dynamical dark energy | |w0 + 1| < 0.02 (Euclid) | Dynamical DE falsified |
| Level | Threshold | Channel | Survey | Timeline |
|---|---|---|---|---|
| Hint (current) | 2.20σ | fσ8 LOO | DESI+BOSS | 2026 |
| Suggestive | 3σ joint | fσ8 + S8 | +DES+KiDS | 2027 |
| Evidence | 3.5σ | μ–Σ + fσ8 | +Euclid Y1 | 2028 |
| Detection | 5σ | All channels locked | Euclid+Rubin | 2030+ |
Parts 1–3 established EFC as a perturbation-sector modification with correct limits and a persistent empirical signal. One structural gap remained: no connection between the galactic coupling (β from SPARC) and the cosmological amplitude. Part 4 addresses this with a single conceptual move.
Dark matter and dark energy are not substances — they are phases of a single entropic flow:
| Phase | ∇μJμ | Effect |
|---|---|---|
| Dark Matter regime | < 0 (convergent) | Excess gravity — structure formation |
| Matter-dominated | = 0 (equilibrium) | Standard expansion |
| Dark Energy regime | > 0 (divergent) | Accelerated expansion |
Physical interpretation: T(S) is the inverse dynamical capacity. Near the thermodynamic boundaries (S → 0 or S → 1), the system is “stiff” — small perturbations have large effects. At the midpoint S = 0.5, the system is maximally flexible. The observed ΩΛ/Ωm ≈ 2.5 at z = 0 is a snapshot of where the universe sits on this continuum, not a fundamental constant.
Kill criterion KC5: If Euclid measures w0 = −1 to within 2%, the dynamical dark energy prediction is falsified. AWAITING EUCLID
Euclid DR1 pipeline status (2026-04-12): (DOI 31990053) Custom efc_logistic gravity model implemented in hi_class Boltzmann solver.
Benchmark prediction frozen with SHA-256 hash at B0=0.02, M0=0.06:
σ8 +1.21%, P(kc) +2.09%, Cℓφφ −6.01%, EG −3.98%.
Planck ISW constrains M0 < 0.1. Stability requires M0 ≥ 3B0.
SEALED
| What EFC does | Modifies gravitational coupling in the perturbation sector via entropy gradients |
| Formal status | Contains ΛCDM as limiting case (perturbation sector); three independent recovery conditions proved |
| Current signal | αL2 = −1.00 ± 0.46 (2.20σ); ΔAIC = −2.91; 7/7 LOO folds pass |
| Validation | 121 tests (93 survived of 103 active, 10 falsified, 18 in pipeline); stage: non-rejectable model |
| Falsifiability | 5 kill criteria frozen before Stage-IV; 3 sealed blind predictions with cryptographic hashes (incl. Boltzmann-calibrated Euclid DR1 benchmark 2026-04-12) |
| New physics | T(S) susceptibility function; dynamical dark energy w(a) ≠ −1; cross-scale amplification βcosm/βgal ≈ 6.25; scale-localised EG bump at kc=0.05 h/Mpc (31985313) |
| What it does NOT claim | “Better than ΛCDM”, “no dark matter proven”, or “full cosmological validation” — all remain UNDER REVIEW |
| Open problem | Full background H(z) recovery (Level 3) — stated explicitly as a boundary, not a defect |
© 2026 Energy-Flow Cosmology Initiative · White Paper Series Elevator Pitch (v1.0 – April 2026)