IndisputableMonolith.Cosmology.Predictions
This module derives the scalar spectral index n_s from an inflation potential inside the Recognition Science cosmology. Early-universe modelers cite it for RS-native predictions of observable parameters. The module organizes the work through the central ns_from_inflation definition together with its verification lemmas.
claim$n_s(V)$ computes the scalar spectral index from a given inflation potential $V$ in RS-native units, with auxiliary results confirming that the derived value satisfies the framework constraints.
background
Recognition Science builds cosmology on the core functional equation and the phi-ladder, with the fundamental time quantum τ₀ = 1 tick supplied by the Constants module. This Predictions module imports Mathlib for algebraic structures and Data.Import for handling numerical checks. It focuses on inflation, introducing the derivation of n_s together with verification that the result is consistent with RS scaling.
proof idea
This is a definition module. It introduces ns_from_inflation as the core derivation of the spectral index, followed by verify_ns and verify_ns_holds to establish that the computed value holds under the imported RS assumptions.
why it matters in Recognition Science
The module supplies the inflation-derived predictions that integrate into the broader Recognition Science cosmology, linking early-universe dynamics to the unified forcing chain and observable constants. It provides the concrete n_s result that downstream cosmology work would reference.
scope and limits
- Does not derive the tensor-to-scalar ratio.
- Does not compute the full primordial power spectrum.
- Does not address post-inflation reheating or late-time cosmology.