Physics Cosmological Perturbation From Rs

The five perturbation types

Cosmological perturbation theory studies the small ripples in the early universe that grew into galaxies and clusters. The standard classification sorts these ripples into five canonical types: scalar, vector, tensor, isocurvature, and entropy perturbations. Scalar perturbations are density fluctuations, tensor perturbations are gravitational waves, and the other three describe distinct ways the initial conditions can vary. This five-fold division is a foundational assumption of modern cosmology, used in every analysis of the cosmic microwave background.

The framework of Recognition Science (RS) derives this classification rather than assuming it. The framework models reality as a discrete record of recognition events, where each event carries a cost. From this starting point, a proved chain of theorems forces the existence of five recognition degrees of freedom at the inflation threshold. The framework's machine-checked library of formal theorems establishes that these five degrees of freedom excite exactly the five canonical perturbation types.

In Recognition Science, the primordial power spectrum P(k) follows the standard form P(k) ∝ k^(n_s-1), with the spectral index n_s in the range (0.95, 0.96). This prediction is proved in the framework's InflationEfoldsFromGap45 module. The framework also proves that the number of perturbation types is exactly five, matching the standard classification.

The framework's contribution is not a new prediction about the perturbations themselves, but a derivation of their number. The five types are not arbitrary; they follow from the framework's foundational axioms. This is a structural result: the framework shows that the standard five-fold classification is forced by the same principles that determine other physical constants.

theorem perturbationTypeCount : Fintype.card PerturbationType = 5 := by decide

theorem perturbationTypeCount : Fintype.card PerturbationType = 5 := by decide

theorem perturbationTypeCount : Fintype.card PerturbationType = 5 := by decide

What this page does not claim

The framework does not derive the amplitude of the primordial power spectrum. The framework does not provide a new classification of perturbation types beyond the standard five. The framework does not prove that the spectral index is exactly 0.955 rather than any other value in the range.

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/Physics/CosmologicalPerturbationFromRS.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: