Cosmology Early Universe

Early universe and dark energy

Cosmology studies the origin, evolution, and large-scale structure of the universe. The standard model describes a hot, dense beginning about 13.8 billion years ago, followed by expansion, cooling, and the formation of galaxies. Two puzzles dominate the field: what exactly happened at the initial instant, and why the universe's expansion is accelerating, attributed to a mysterious dark energy. The framework called Recognition Science (RS) offers a different account of both, built from a single mathematical object: a discrete record of events, or ledger.

In RS, the universe begins in the unique zero-defect configuration. A defect is a mismatch in the ledger, an entry that is not equal to one. The initial state has all entries equal to one, so its total defect is zero, the global minimum. This is not a singularity, not a point of infinite density, but the ledger's minimal-cost state. The Big Bang is the first tick, the moment the first nonzero defect appears. This is a proved theorem in the framework's machine-checked library: the initial configuration has zero defect and is the global minimum among all configurations.

Dark energy, in RS, is not a new field or a cosmological constant in the usual sense. It is the fraction of ledger modes that are in the vacuum, or unexcited, state within the eight-tick recognition cycle. The framework derives the density parameter ΩΛ = 11/16 − α/π, where α is the measured fine-structure constant. The number 11/16 = 0.6875 is the vacuum-mode fraction; the small correction subtracts the tiny influence of matter-coupled modes. The framework proves this value lies between 0.6851 and 0.6852, which is close to the Planck satellite's measured 0.6889 ± 0.0056, though the difference is about 0.7 standard deviations, not a precise match. The framework also proves ΩΛ is positive and less than one, so dark energy exists and does not overwhelm the universe.

This account dissolves the cosmological constant problem, the famous discrepancy of 10^120 between quantum field theory's predicted vacuum energy and the observed value. In RS, the quantum field theory vacuum energy is a misidentification, not a physical observable. The actual ΩΛ is a number from counting ledger modes, not an energy density needing renormalization. There is no fine-tuning because there is no parameter to tune. The framework's library states this as a theorem: the cosmological constant is resolved by identifying it as the vacuum-mode fraction.

/-- **EU-001 Resolution**: There is no Big Bang singularity.

    1. The initial state is the zero-defect configuration (all entries = 1)
    2. This state has ZERO total defect (minimum energy)
    3. Defect = 0 means "nothing to recognize" — the null ledger
    4. The "Big Bang" is the first tick: when the first nonzero defect appears
    5. There is no infinite density, no singularity, no breakdown of physics

    The initial state is not "the universe compressed to a point" but
    "the ledger in its unique consistent initial configuration." -/
theorem no_singularity (N : ℕ) (hN : 0 < N) :
    Foundation.InitialCondition.total_defect
      (Foundation.InitialCondition.unity_config N hN) = 0 ∧
    (∀ c : Foundation.InitialCondition.Configuration N,
      Foundation.InitialCondition.total_defect
        (Foundation.InitialCondition.unity_config N hN) ≤
      Foundation.InitialCondition.total_defect c) :=
  ⟨Foundation.InitialCondition.unity_defect_zero hN,
   Foundation.InitialCondition.unity_is_global_minimum hN⟩

/-- Ω_Λ = 11/16 − α/π, with α the measured fine-structure constant.

    The value 11/16 = 0.6875 comes from the fraction of ledger modes that are in the
    vacuum (unexcited) state in the 8-tick cycle. That mode count is where the content
    of this prediction lives. The correction −α/π accounts for the small perturbation
    from matter-coupled modes.

    α enters as a measurement and not as a construction. Its value is a free boundary
    datum in RS, and the first-order constructed value is excluded by measurement, so
    the canonical reading is `ExternalAnchors.alpha_CODATA`.
    `Cosmology.OmegaLambdaDerivation` takes the same input and says so explicitly.

    Corrected 2026-07-27. This read `11/16 - alphaLock / π` until then.
    `alphaLock = (1 − 1/φ)/2 ≈ 0.191` is the information-limited-gravity kernel
    exponent, not the fine-structure constant ≈ 0.0073, and its own module header has
    said so since 2026-07-06. The substitution put this observable at 0.6267 against
    Planck's 0.6889 ± 0.0056, more than ten standard deviations out. It was never a
    competing derivation of dark energy; it was the wrong constant in the α slot. The
    excluded expression survives under its own name as
    `Cosmology.PrecisionExposure.omega_lambda_alphaLock`, so the defect cannot return
    silently. -/
noncomputable def omega_lambda : ℝ :=
  11/16 - Constants.ExternalAnchors.alpha_CODATA / Real.pi

/-- A certified numeric bracket on Ω_Λ.

    This module carried no numeric bound at all before 2026-07-27, only positivity and
    subunitarity, and that absence is precisely why the `alphaLock` substitution
    survived: nothing here could be placed against a measurement, so a value 0.06 away
    from Planck violated nothing that was stated. -/
theorem omega_lambda_bracket :
    (0.6851 : ℝ) < omega_lambda ∧ omega_lambda < 0.6852 := by
  unfold omega_lambda
  have h1 := alpha_over_pi_lt
  have h2 := alpha_over_pi_gt
  constructor <;> linarith

/-- **D-003 Resolution**: The cosmological constant is NOT the vacuum energy
    of QFT. It is the fraction of vacuum modes in the ledger.

    The "10^120 discrepancy" dissolves because:
    1. QFT vacuum energy is a misidentification (not a physical observable)
    2. The actual Ω_Λ comes from ledger mode counting: 11/16 − α/π
    3. This is a NUMBER, not an energy density requiring renormalization

    There is no fine-tuning because there is no parameter to tune. -/
theorem cosmological_constant_resolution :
    0 < omega_lambda ∧ omega_lambda < 1 :=
  ⟨omega_lambda_pos, omega_lambda_lt_one⟩

What this page does not claim

The framework does not derive the fine-structure constant α; it uses the measured CODATA value as an input. The framework does not prove that its ΩΛ value exactly matches the Planck measurement; the difference is about 0.7 standard deviations. The framework does not claim that the Big Bang was an explosion; it models it as the first tick in the ledger. The framework does not prove that quantum field theory vacuum energy is unobservable; it states this as a resolution within its 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/EarlyUniverse.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

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