pith. sign in
def

criticalDensity

definition
show as:
module
IndisputableMonolith.Cosmology.DarkEnergy
domain
Cosmology
line
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plain-language theorem explainer

Critical density is defined as 3 H_0² over 8π in natural units, with H_0 the present Hubble parameter. Cosmologists working inside the Recognition Science ledger-tension model cite this when normalizing the dark energy density. The implementation is a one-line definition that transcribes the standard Friedmann critical-density expression.

Claim. $ρ_c = 3 H_0^2 / (8 π)$ where $H_0$ is the Hubble parameter today.

background

The Cosmology.DarkEnergy module derives the cosmological constant from ledger tension: global J-cost balance must hold while expansion continually creates new spacetime volume. H0 is the present expansion rate, fixed at 2.2 × 10^{-18} s^{-1} in natural units. The upstream density definition supplies the phi-ladder scaling used for mass and energy densities elsewhere in the framework.

proof idea

One-line definition that directly encodes the Friedmann critical-density formula using the imported H0 value.

why it matters

This supplies the reference scale for the downstream darkEnergyDensity declaration, which asserts that dark energy dominates the universe today. It completes the COS-006 step in which Λ emerges as the J-cost per unit volume required to maintain ledger coherence during expansion, reproducing the observed (H0)² scaling mediated by the golden-ratio structure.

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