Morten Magnusson · Symbiose Research, Sandnes, Norway · ORCID: 0009-0002-4860-5095 · June 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 (142 registered tests; 116 active, 106 survived, 10 falsified, 26 in pipeline — from galaxy rotation curves to Planck 2018): EFC has survived 106 of 116 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 | 142 tests (106 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 — and it collapsed to 0.68σ after DESI DR2, where the joint background fit prefers ΛCDM (ΔAIC=+1.59 — graph-verified; the Variant-H growth-extension gives +4.05). 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 |
|---|---|---|
| Survived | 105 | Passed at declared tier (of 116 active probes) |
| Falsified | 10 | Failed / superseded by successor model version |
| In pipeline | 26 | Planned / awaiting Stage-IV data |
| Total public | 142 | 116 active + 26 pipeline |
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) | Falsifies only the fragile η-boost branch — robust EFC has η → 1, so η = 1 is not a clean kill (the η ≈ 1.10 value is 0% robust per 32037990) |
| 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 — fσ8 + H(z) data now DOI-anchored to primary sources (6dFGS 10.1111/j.1365-2966.2012.21136.x, SDSS-MGS 10.1093/mnras/stu2693, VIPERS 10.1051/0004-6361/201526553, FastSound 10.1093/pasj/psw029, BOSS DR12 10.1093/mnras/stx721, cosmic chronometers Moresco+2022 10.1007/s41114-022-00040-z); both prefer EFC α<0 in isolation (χ²r 0.340/0.941 vs ΛCDM 0.554/1.549), though the joint fit including DESI DR2 BAO still prefers ΛCDM (ΔAIC=+1.59; the Variant-H growth-extension gives +4.05) |
| Validation | 142 tests (106 survived of 116 active, 10 falsified, 26 in pipeline); stage: non-rejectable model |
| Falsifiability | 5 kill criteria frozen before Stage-IV; 2 sealed blind predictions (cryptographic freezes) plus a 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)