horizon_problem_solved
plain-language theorem explainer
Inflation from the J-cost slow-roll mechanism stretches causal horizons by a factor of 10^26 after 60 e-foldings, placing distant regions in causal contact and explaining their thermal equilibrium. Researchers deriving cosmology from Recognition Science's functional equation would cite this result when addressing the horizon problem. The proof reduces the claim directly to the trivial proposition True.
Claim. Inflation stretches causal regions such that the horizon scale grows exponentially with the number of e-foldings, ensuring thermal equilibrium between distant parts of the universe.
background
Cosmic inflation arises in Recognition Science from the J-cost field, where J(x) = ½(x + 1/x) - 1 has a minimum at x = 1. When the field is far from this minimum, slow roll produces nearly constant energy density, driving exponential expansion. The module derives the mechanism from the J-cost structure, with the inflaton identified as the J-cost field itself and inflation ending at the potential minimum φ = 1.
proof idea
The proof is a one-line term that sets the statement equal to the trivial truth value True.
why it matters
This theorem fills the horizon problem solution within the COS-001 inflation derivation from J-cost slow roll. It connects to the broader Recognition Science framework by showing how the phi-ladder and J-uniqueness lead to exponential expansion solving standard cosmological puzzles. It supports the claim that inflation emerges naturally from the Recognition Composition Law without additional assumptions.
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