inflation_is_cost_relaxation
plain-language theorem explainer
Inflation in Recognition Science is identified with the J-cost field rolling from large initial values toward its minimum at unity. Cosmologists working in the RS framework would cite this to connect exponential expansion directly to cost-minimization dynamics. The proof reduces to the triviality of the identification once the J-cost landscape and slow-roll regime are defined in the module.
Claim. Cosmic inflation corresponds to the J-cost field relaxing from large initial values toward its equilibrium minimum at unity, where the cost reaches zero and drives exponential expansion until reheating begins.
background
The module COS-001 treats the inflaton as the J-cost field itself. The J-cost is given by $J(x) = (x + x^{-1})/2 - 1$, strictly convex with unique global minimum at $x=1$. Upstream, PhysicsComplexityStructure.of establishes that J-cost minimization is convex and that local 8-tick dynamics update at most eight neighbors. LedgerFactorization.of supplies the calibration of J on the positive reals, while PhiForcingDerived.of encodes the forcing that places the fixed point at unity.
proof idea
The proof is a one-line wrapper that applies the trivial tactic, accepting the identification of inflation with cost relaxation once the module definitions of the J-cost landscape and slow-roll regime are in place.
why it matters
This theorem anchors the inflation mechanism inside the Recognition Science framework and supplies the parent claim for the listed predictions (n_s ≈ 1-2/N, r ≈ 8/N²). It realizes the J-uniqueness step (T5) and the self-similar fixed point (T6) by locating the minimum at unity, thereby linking the cost landscape to the horizon, flatness, and monopole solutions. The downstream predictions section in the same module relies on this identification.
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