Cosmology Cosmological Constant Observational Status

The observational record

The cosmological constant, written Λ, is the energy density of empty space itself in general relativity. It acts as a repulsive force that accelerates the expansion of the universe. The measured value is about Λ = (1.1 ± 0.01) × 10⁻⁵² m⁻², which in natural units corresponds to an energy scale of roughly 10⁻³ eV. This number is famously tiny compared with naive quantum field theory estimates, which overshoot by some 120 orders of magnitude, a discrepancy known as the cosmological constant problem.

The equation of state parameter w relates pressure to energy density for dark energy. For a pure cosmological constant, w equals exactly −1, meaning the energy density does not change as the universe expands. Current measurements give w = −1.03 ± 0.03, consistent with −1 within errors. There is no evidence that w has changed over cosmic time, and future surveys aim to pin it down to 0.3% precision. These numbers come from standard cosmological observations, not from any theory of quantum gravity.

In Recognition Science, the library's declaration observationalStatus (a machine-checked list of strings) simply records these measured facts: the central value and uncertainty for Λ, the value and uncertainty for w, the null result on evolution, and the future precision target. It is a definition, not a theorem. The declaration does not derive Λ from first principles, does not explain why the value is so small, and does not prove that w equals −1. It is a catalog of what telescopes and surveys have found.

What the declaration does not claim is just as important. It does not assert that the Recognition Science framework has solved the cosmological constant problem. The framework's own documents mark the derivation of Λ as a target, not an achievement. The declaration does not claim that dark energy is fundamental or emergent; those statements live in a separate implications list, which is a list of aspirations, not proofs. It does not claim that the measured value matches any prediction from the framework's golden-ratio scaling. The status entry is a snapshot of the observational record, nothing more.

The practical consequence for a reader is a clean separation: the numbers are measurements with error bars, and the framework's ambitions are hypotheses with named falsifiers. The declaration's four lines give you the current state of cosmology, and the framework's own documentation tells you what would have to be true for its account to fail, such as w differing from −1 or Λ varying over time. That separation is the whole point of the status entry.

/-- The observed cosmological constant Λ ≈ 1.1 × 10⁻⁵² m⁻². -/
noncomputable def lambda_observed : ℝ := 1.1e-52

/-- Current observations constrain:

    1. Λ value: Known to ~1%
    2. w = -1.03 ± 0.03 (consistent with -1)
    3. No time evolution detected (w₀ - wₐ constraints)

    Future tests:
    - DESI, Euclid, LSST will measure w to 0.3%
    - Any deviation from w = -1 would be significant -/
def observationalStatus : List String := [
  "Λ = (1.1 ± 0.01) × 10⁻⁵² m⁻²",
  "w = -1.03 ± 0.03",
  "No evidence for w evolution",
  "Future: 0.3% precision on w"
]

/-- Current observations constrain:

    1. Λ value: Known to ~1%
    2. w = -1.03 ± 0.03 (consistent with -1)
    3. No time evolution detected (w₀ - wₐ constraints)

    Future tests:
    - DESI, Euclid, LSST will measure w to 0.3%
    - Any deviation from w = -1 would be significant -/
def observationalStatus : List String := [
  "Λ = (1.1 ± 0.01) × 10⁻⁵² m⁻²",
  "w = -1.03 ± 0.03",
  "No evidence for w evolution",
  "Future: 0.3% precision on w"
]

What this page does not claim

The declaration does not claim the framework has derived Λ from its J-cost ground state. The declaration does not claim the measured value matches any framework prediction. The declaration does not claim dark energy is fundamental or emergent.

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

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: