Cosmology Dark Energy Equation Of State W Lambda

A baseline and its bound

In cosmology, the equation of state parameter w for dark energy is the ratio of its pressure to its energy density. A value of w = -1 corresponds to the cosmological constant, the simplest model where dark energy has a fixed density in space. This baseline is what the Recognition Science declaration wLambda establishes: it defines the baseline value as exactly -1.

The framework's library also defines a correction bound, bitCorrectionBound, equal to phi - 3/2, where phi is the golden ratio. This evaluates to approximately 0.118. The library states that the absolute deviation of w from -1, written |w - (-1)|, is bounded by this value. This bound is presented as an exact closed form, not an approximation, because of the identity 1/phi = phi - 1.

In Recognition Science, the framework models dark energy through its own internal structure. Its prediction is that the present-day value w_0 lies in the interval (-1 - J(phi), -1), approximately (-1.13, -1), where J(phi) is the same golden-ratio-based constant. This means the framework predicts a phantom-like dark energy, with w_0 less than -1, but bounded away from the baseline by no more than about 0.118.

The declaration itself is a definition, not a measurement. It sets the baseline for the framework's own cosmological model. The bound is a separate definition, and the prediction is a hypothesis stated in the documentation, not a proved theorem in the library. The library contains no proof that the actual observed value of w satisfies this bound; it only defines the bound and the baseline.

/-- Dark energy EoS w_0 = -1 (cosmological constant baseline). -/
def wLambda : ℝ := -1

/-- BIT correction bound: `|δw| ≤ J(φ)`. This is the exact phantom-Carnot ceiling
`J(φ) = φ − 3/2 ≈ 0.118` in closed form (not an approximation): since `1/φ = φ − 1`,
the earlier obfuscated form `1/φ − 3/2 + 1` equals `φ − 3/2` exactly. -/
noncomputable def bitCorrectionBound : ℝ := phi - 3 / 2

/-- BIT correction bound: `|δw| ≤ J(φ)`. This is the exact phantom-Carnot ceiling
`J(φ) = φ − 3/2 ≈ 0.118` in closed form (not an approximation): since `1/φ = φ − 1`,
the earlier obfuscated form `1/φ − 3/2 + 1` equals `φ − 3/2` exactly. -/
noncomputable def bitCorrectionBound : ℝ := phi - 3 / 2

What this page does not claim

The declaration does not prove any observed value of w satisfies the bound. The framework does not claim to derive the cosmological constant from first principles. The prediction of w_0 in the interval (-1.13, -1) is a hypothesis, not a proved theorem.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Cosmology/DarkEnergyEquationOfState.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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