InflationPredictions
Recognition Science inflation packages its outputs in the record InflationPredictions holding the scalar spectral index, tensor-to-scalar ratio, and non-Gaussianity for sixty e-foldings. Cosmologists working inside the framework cite this record when tabulating model outputs against Planck constraints. The declaration is a bare structure definition that introduces three real fields with no computational content or proof obligations.
claimThe record type consists of three real numbers: the scalar spectral index $n_s$, the tensor-to-scalar ratio $r$, and the non-Gaussianity parameter $f_{NL}$, which together encode the predictions of Recognition Science inflation for $N=60$ e-foldings.
background
The Cosmology.Inflation module derives cosmic inflation from J-cost slow roll. The J-cost $J(x)=½(x+x^{-1})-1$ possesses a minimum at $x=1$; far from this point it grows linearly and supplies a nearly constant energy density that drives exponential expansion, solving the horizon, flatness, and monopole problems. The module documentation states that the inflaton is identified with the J-cost field itself and that inflation ends when the field reaches the minimum at $φ=1$.
proof idea
The declaration is a pure structure definition containing no proof body or tactics. It simply declares the three real-valued fields that are later instantiated by the downstream rsPredictions definition.
why it matters in Recognition Science
The structure supplies the concrete record type consumed by rsPredictions, which populates the fields with the explicit values $n_s=1-2/60$, $r=8/60^2$, and $f_{NL}=0$. It realizes the COS-001 target of obtaining inflation from J-cost slow roll inside the Recognition Science framework, where the eight-tick octave and phi-ladder set the scale of the dynamics. The listed predictions match the Planck value for $n_s$ and lie below current observational bounds for $r$.
scope and limits
- Does not derive the numerical values from the underlying J-cost potential.
- Does not include the running of the spectral index.
- Does not specify the explicit form of the inflaton potential.
- Does not address the power spectrum or quantum fluctuations.
formal statement (Lean)
195structure InflationPredictions where
196 n_s : ℝ -- Scalar spectral index
197 r : ℝ -- Tensor-to-scalar ratio
198 f_NL : ℝ -- Non-Gaussianity parameter
199
200/-- RS predictions for N = 60 e-foldings. -/