module module moderate

`IndisputableMonolith.Cosmology.Inflation`

This module identifies the inflaton potential with the J-cost function and defines associated slow-roll and e-folding quantities for Recognition Science cosmology. Cosmologists modeling early-universe dynamics would cite these definitions to link standard inflation observables to the recognition framework. The module consists of definitions and short lemmas built directly on the imported Cost and Constants modules.

claimThe inflaton potential is given by $V = J$, where $J$ denotes the J-cost. Slow-roll parameters are defined as slowRollEpsilon and slowRollEta, with eFoldings computed from the potential; the horizon, flatness, and monopole problems are addressed via sixty_efolds and related statements.

background

The module imports Constants, which fixes the RS time quantum as τ₀ = 1 tick, and Cost, which supplies the J-cost function. The supplied doc-comment states that the inflaton potential in RS is just the J-cost. Sibling declarations introduce inflatonPotential, potential_min_at_one, slowRollEpsilon, slowRollEta, eFoldings, and the three problem-solving statements.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the core objects used by the sibling declarations horizon_problem_solved, flatness_problem_solved, monopole_problem_solved, and powerSpectrum. It places the standard inflationary toolkit inside the Recognition Science setting that begins from the J-uniqueness and phi fixed-point steps of the forcing chain.

scope and limits

Does not derive the explicit functional form of J from an action principle.
Does not compute numerical values for slow-roll parameters or the spectral index.
Does not treat reheating or the transition to radiation domination.
Does not address quantum fluctuations or the power spectrum normalization.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (24)

def inflatonPotential L48
theorem potential_min_at_one L51
theorem potential_positive L59
def slowRollEpsilon L68
def slowRollEta L77
theorem slow_roll_at_large_phi L85
def eFoldings L94
theorem sixty_efolds L100
theorem horizon_problem_solved L109
theorem flatness_problem_solved L116
theorem monopole_problem_solved L122
def powerSpectrum L130
def spectralIndex L137
theorem nearly_scale_invariant L142
def tensorScalarRatio L148
theorem small_tensor_modes L153
structure Reheating L161
theorem efficient_reheating L169
theorem inflation_is_cost_relaxation L184
structure InflationPredictions L195
def rsPredictions L201
def planckMeasurements L208
structure InflationFalsifier L218
def experimentalStatus L225