IndisputableMonolith.Cosmology.InflatonPotentialFromJCost
This module defines the inflaton potential on the recognition manifold as V(φ_inf) = J(1 + φ_inf), with φ_inf the dimensionless displacement from the canonical reference rung. Cosmologists modeling inflation inside Recognition Science would cite it to link the J-cost function to early-universe dynamics. The module consists entirely of definitions and immediate corollaries with no proof obligations.
claim$V(\phi_{\rm inf}) = J(1 + \phi_{\rm inf})$, where $\phi_{\rm inf}$ measures dimensionless displacement from the reference rung and $J$ is the J-cost function.
background
The module imports Constants, which fixes the RS time quantum as τ₀ = 1 tick, and Cost, which supplies the J-cost. Recognition Science places the inflaton potential on the recognition manifold, where the argument φ_inf is the displacement from the canonical reference rung on the phi-ladder. The J function itself originates in the T5 uniqueness step of the unified forcing chain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the explicit inflaton potential used by downstream cosmology constructions inside the Recognition framework. It directly implements the J-cost expression for inflation and thereby connects the forcing chain (T5 J-uniqueness, T7 eight-tick octave) to cosmological dynamics. No parent theorems are listed among the used-by edges.
scope and limits
- Does not derive the form of V from the Recognition Composition Law.
- Does not compute slow-roll parameters or spectral indices.
- Does not address reheating or post-inflationary evolution.
- Does not relate φ_inf to specific particle masses on the phi-ladder.