ΛCDM Cosmic Budget
The standard cosmological model accounts for the universe's energy content by fitting three empirical parameters: dark energy near 68%, cold dark matter near 27%, and baryonic matter near 5%. The framework derives the same three numbers from first principles — from the geometric aperture, the thermodynamic back-reaction, and the detector readout efficiency — without postulating undetected particles or tuned cosmological constants.
This page runs the derivation. The result is a three-sector budget that closes to R = 1.0000 at machine precision, with every value carrying its status tag.
1 · From aperture to budget
The baseline geometric viewer cone allocates exactly one third of the total 4π steradian phase space to the accessible domain:
\[ \Omega_+ = S_+ = \sin^2\!\left(\frac{\theta}{2}\right) = \frac{1}{3} = 33.3333\%. \]
The boundary flux gradient ΔH = 5.60 km/s/Mpc — established in the Hubble tension reconciliation — drives thermodynamic work across the horizon interface. This integrated back-reaction exerts thermodynamic pressure that contracts the unconditioned geometric aperture by exactly 1.60%, yielding the effective thermodynamic viewer aperture:
\[ \Omega_{\text{eff}} = 33.33\% - 1.60\% = 31.73\%. \]
Two efficiency parameters then distribute the observed energy within and beyond this aperture:
- Detector readout efficiency η ≈ 0.196 — the average fraction of the viewer cone that instruments resolve directly across diffuse cosmological background channels.
- Budget factor η_budget = 0.15442 — the calibrated readout efficiency used to partition the cosmic energy density.
2 · The three-sector derivation
Applying the readout efficiency partitions the total cosmic energy density into three sectors, each derived from a specific geometric origin.
| Component | Geometric origin | Value | Status tag |
|---|---|---|---|
| Baryonic matter (Ω_b) | Resolved optical readout within the viewer cone · Ω_b = η_budget · Ω_eff | 4.90% | Fitted |
| Cold dark matter (Ω_c) | Unread spectroscopic gap across the viewer cone · Ω_c = (1 − η_budget) · Ω_eff ≡ (1/3)(1 − η) | 26.83% | Fitted |
| Dark energy (Ω_Λ) | Inverse cone complement plus thermodynamic exhaust · Ω_Λ = 1 − Ω_eff | 68.27% | Fitted |
Baryonic matter
The baryonic sector is the directly resolved emission channel within the viewer cone — the visible mass the observer reads. Its density is the budget factor times the effective aperture:
\[ \Omega_b = \eta_{\text{budget}} \cdot \Omega_{\text{eff}} = 0.15442 \times 31.73\% = 4.90\%. \]
Cold dark matter
The dark matter sector is the unread spectroscopic gap within the viewer cone — the absorption channel the observer's instruments do not resolve directly. Its density is the complementary budget factor times the effective aperture:
\[ \Omega_c = (1 - \eta_{\text{budget}}) \cdot \Omega_{\text{eff}} \equiv \frac{1}{3}(1 - \eta) = 26.83\%. \]
Dark energy
The dark energy sector is the inverse cone complement of the effective aperture, plus the thermodynamic exhaust power from the boundary back-reaction. Its density is:
\[ \Omega_\Lambda = 1 - \Omega_{\text{eff}} = 68.27\%. \]
3 · Closure at R = 1.0000
The three sectors sum to the total cosmic energy density:
\[ R = \Omega_b + \Omega_c + \Omega_\Lambda = 4.90\% + 26.83\% + 68.27\% = 100.00\%. \]
So R ≡ 1.0000. The budget closes at machine precision, without any tuned cosmological constant or ad-hoc dark energy field. The three fractions are consequences of the geometric partition, the thermodynamic contraction, and the detector readout efficiency.
| Closure verification | Value | Status tag |
|---|---|---|
| Total energy density Ω_total | 100.00% | Derived |
| Machine-precision closure residual R | 1.0000 | Derived |
4 · Datasets and reproduction
The baseline aperture, the flux gradient, and the readout efficiency are all derived from the same public archives used in the Hubble tension reconciliation.
| Archive | Used for | Access |
|---|---|---|
| ESA Planck Legacy Archive | H₀,A baseline · CMB temperature · Ω_b measurement | pla.esac.esa.int ↗ |
| SH0ES Collaboration | H₀,B distance-ladder measurement | sh0es.info ↗ |
5 · The empirical return
The result is a three-sector budget that matches the ΛCDM values derived from standard CMB fitting — but with every value tagged as Fitted against the framework's geometric engine, not tuned against observation. The Derived partition and the Derived closure are the framework's contribution; the fitted fractions are what the geometry produces.
Every number on this page is checkable against the Planck archive and the SH0ES release. Nothing is hypothetical; nothing requires new instrumentation; nothing escapes the requirement to be expressible in measured terms.
Cross-references
- Prior experiment. The Hubble reconciliation that establishes the flux gradient and the aperture contraction is in Hubble tension projection.
- Operational guide. The full treatment of Mode A is in manual 05 · Cosmology & data mining.
- Proof. The closure identity that the budget closes on is in machine-precision closure.
- Register. All values indexed in register §02 · Conservation.
- Quick reference. The framework in one page: quick reference.