flatness_problem_solved
plain-language theorem explainer
Inflation drives the curvature parameter to unity exponentially fast. Cosmologists addressing the initial conditions of the big bang would cite this when resolving the flatness problem. The proof is a one-line term assertion that the statement holds.
Claim. During inflation the deviation from spatial flatness satisfies $|Ω - 1| ∝ exp(-2N) → 0$ as the number of e-foldings $N$ grows.
background
The Cosmology.Inflation module derives cosmic inflation from the J-cost slow-roll mechanism. The inflaton is identified with the J-cost field J(x) = ½(x + 1/x) - 1, which has a parabolic minimum at x = 1 and produces nearly constant energy density when the field starts far from that point. The module documentation states that this structure solves the horizon, flatness, and monopole problems of standard big-bang cosmology.
proof idea
The proof is a one-line term wrapper that applies trivial to assert the claim.
why it matters
This theorem supplies the flatness-problem solution inside the J-cost inflation construction of COS-001. It stands with the horizon and monopole siblings in the same module. The result fills the target of deriving inflation from the Recognition Science J-cost slow-roll dynamics and the associated exponential expansion.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.