Cosmology Dark Energy Dark Energy Eos

Equation of state

In cosmology, dark energy is the unknown agent driving the universe's accelerating expansion. Its essential property is the equation of state, a number written w that relates the energy density of a substance to its pressure. For a cosmological constant, the energy density is fixed in space and time, and the pressure is exactly the negative of the energy density, so w equals -1. This value makes the expansion accelerate rather than slow down. The leading measurements from supernovae and the cosmic microwave background are consistent with w = -1, though not yet precise enough to rule out small deviations.

Within the Recognition Science framework, the declaration dark_energy_eos establishes that the framework's model of dark energy has this same equation of state. The framework defines a quantity called equationOfState and sets it to -1. The theorem dark_energy_eos then proves, by direct computation, that this definition is correct: the equation of state equals -1. This is a formal statement in the framework's machine-checked library of formal theorems, not a new physical measurement. The framework models dark energy as emerging from what it calls ledger tension, a discrete record of events that must balance globally while the universe expands, creating new space for entries. The residual cost of maintaining that balance is the cosmological constant.

The framework's claim is that its model reproduces the standard cosmological constant value of w = -1. It does not claim to have measured this value, nor does it claim that the framework's derivation of dark energy itself is complete. The declaration is a definitional step: it states what the framework's model predicts, and that prediction matches the standard picture. The framework also defines a cosmological constant that scales as the square of the Hubble constant, and it asserts that dark energy dominates the universe's energy budget, but these are separate definitions and claims, not part of what dark_energy_eos itself establishes.

/-- **THEOREM**: Dark energy has w = -1 (cosmological constant). -/
theorem dark_energy_eos : equationOfState = -1 := rfl

/-- The dark energy equation of state: w = P/ρ. -/
noncomputable def equationOfState : ℝ := -1

What this page does not claim

The framework has measured w = -1 from astronomical data. The framework has a complete derivation of dark energy's origin. The framework's equation of state is a new prediction distinct from the standard cosmological constant model.

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

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