InflationModel
plain-language theorem explainer
This inductive definition enumerates five canonical inflationary potentials for config dimension 5: chaotic quadratic, new inflation plateau, hybrid, natural axion-like, and alpha-attractor. Cosmologists working in the Recognition Science framework cite it when fixing the model count for slow-roll predictions of n_s and r. The declaration is a direct inductive type with five constructors that derives Fintype to support immediate cardinality theorems.
Claim. The inductive type of inflation models consists of five constructors: chaotic quadratic potential, new inflation plateau, hybrid inflation, natural axion-like, and alpha-attractor, each tied to a distinct inflaton family at config dimension 5.
background
The InflationModelsFromConfigDim module fixes configDim at 5 to select five standard inflaton-potential families: chaotic (m²φ²), new inflation (plateau), hybrid, natural (axion-like), and alpha-attractor (conformal). Each family produces distinct slow-roll predictions for the spectral index n_s and tensor-to-scalar ratio r. The module imports Constants and aligns with upstream inductive enumerations in CosmicInflationFromJCost and InflationaryCosmologyFromRS that also fix five models but use different constructor names.
proof idea
The declaration is the inductive definition itself, introducing the five constructors and deriving DecidableEq, Repr, BEq, and Fintype instances in one step to enable downstream cardinality proofs.
why it matters
This definition supplies the model enumeration required by downstream structures CosmicInflationCert and InflationModelsCert, both of which assert Fintype.card InflationModel = 5, and by InflationaryCosm which adds the Nefolds = 44 constraint. It occupies the configDim = 5 slot in the Recognition Science cosmology chain, linking directly to J-cost thresholds and the five-model count used across the framework.
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