# Proof: Dark energy constitutes more than 68% of the universe's total energy density according to the Planck 2018 legacy release

- **Generated:** 2026-03-28
- **Verdict:** PROVED (with unverified citations)
- **Audit trail:** [proof_audit.md](proof_audit.md) | [proof.py](proof.py)

## Key Findings

- The Planck 2018 legacy release reports a dark energy density parameter of **ΩΛ = 0.6853 ± 0.0074** in the base-ΛCDM model, corresponding to **68.53%** of the universe's total energy density.
- This value exceeds the 68% threshold stated in the claim: **0.6853 > 0.68**.
- An independent derivation from the matter density parameter (Ωm = 0.315 ± 0.007) yields ΩΛ = 1 − Ωm = 0.685, consistent with the directly reported value (relative difference < 0.05%).
- No revisions, errata, or retractions affecting this value have been issued.

## Claim Interpretation

**Natural language:** "Dark energy constitutes more than 68% of the universe's total energy density according to the Planck 2018 legacy release."

**Formal interpretation:** The dark energy density parameter ΩΛ (Omega Lambda), as reported in the Planck 2018 legacy release (Planck Collaboration VI, A&A 641, A6, 2020), must be strictly greater than 0.68. "More than 68%" is interpreted as ΩΛ > 0.68. In the base-ΛCDM model with spatial flatness (Ωtotal = 1), ΩΛ = 1 − Ωm. The claim is evaluated against the best-fit central value, not the confidence interval.

*Source: proof.py JSON summary*

## Evidence Summary

| ID | Fact | Verified |
|----|------|----------|
| B1 | Planck 2018 paper: matter density Ωm = 0.315 ± 0.007 | Partial (aggressive normalization on ar5iv HTML rendering) |
| B2 | UNLV cosmic parameters reference: ΩΛ = 0.6853(74) from Planck 2018 | Yes |
| A1 | Derived ΩΛ from Ωm via flat-ΛCDM relation | Computed: 0.685 (= 1 − 0.315) |
| A2 | Cross-check: derived ΩΛ vs directly reported ΩΛ | Computed: True (values agree within 0.05% relative tolerance) |

*Source: proof.py JSON summary*

## Proof Logic

The proof proceeds in two independent paths that converge:

**Path 1 — Direct report (B2):** The UNLV Cosmic Parameters reference page directly reports the Planck 2018 value as "Omega_Lambda 0.6853(74) Assuming Omega = 1 (Planck 2018 p. 14)." This gives ΩΛ = 0.6853, sourced from page 14 of the Planck 2018 paper.

**Path 2 — Derivation from Ωm (B1 → A1):** The Planck 2018 paper abstract states "matter density parameter Ωm = 0.315 ± 0.007." In the base-ΛCDM model (spatially flat), ΩΛ = 1 − Ωm = 1 − 0.315 = 0.685 (A1).

**Cross-check (A2):** The derived value (0.685) and the directly reported value (0.6853) agree within 0.05% relative difference. The small discrepancy arises because Ωm = 0.315 is rounded from the full-precision value (Ωm = 0.3147 yields ΩΛ = 0.6853 exactly).

**Claim evaluation:** ΩΛ = 0.6853 > 0.68 = True. The claim holds.

*Source: author analysis*

## Counter-Evidence Search

1. **Has the Planck 2018 value been revised or retracted?** Searched for errata and corrections. The Planck 2018 paper was published as the final legacy release in A&A 641 (2020). No revisions to cosmological parameters have been issued.

2. **Could alternative models give ΩΛ < 0.68?** Extended models (w0waCDM, non-flat) can shift ΩDE slightly, but the claim specifically references base-ΛCDM results. In this model, ΩΛ = 0.6853 ± 0.0074 — even at the lower 1σ bound (0.6779), the central value remains clearly above 0.68.

3. **Is the 68% threshold ambiguous?** In standard cosmology, "dark energy fraction of total energy density" unambiguously refers to ΩΛ = ρΛ/ρcritical, which equals the fraction of total energy in a flat universe.

*Source: proof.py JSON summary*

## Conclusion

**PROVED (with unverified citations).** The Planck 2018 legacy release reports ΩΛ = 0.6853 ± 0.0074, which is strictly greater than 0.68. The claim holds.

One citation (B1, Planck paper via ar5iv) was verified only via aggressive normalization (partial match due to LaTeX-to-HTML rendering artifacts on the ar5iv page). However, the conclusion does not depend solely on B1 — the directly reported ΩΛ value from B2 (UNLV reference, fully verified) independently establishes the claim. B1 serves as a cross-check via the matter density derivation and is consistent with B2.

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Generated by [proof-engine](https://github.com/yaniv-golan/proof-engine) v0.10.0 on 2026-03-28.