Chapter 44: Inflation-as-Regime: No Inflaton Sector

Inflation — the hypothesis that the early universe underwent a brief epoch of exponential expansion — is the cornerstone of modern observational cosmology. It solves the flatness problem (why is the spatial curvature so close to zero?), the horizon problem (why is the CMB uniform across causally disconnected regions?), and the monopole problem (why have magnetic monopoles not been observed?). In orthodox cosmology, inflation is driven by a scalar field — the inflaton — whose potential energy dominates the energy budget and produces a nearly de Sitter expansion.

Category τ agrees that the early universe underwent rapid expansion. But it disagrees on the mechanism. The inflationary epoch is a regime of the same τ-Einstein equation — not a new phase driven by a new field. The Regime Invariance Theorem

states that the τ-Einstein equation is invariant across all regimes. The Inflaton No-Go Corollary (Corollary [cor:ch47-inflaton-no-go]) follows immediately from the Sector Exhaustion Theorem (Part V, the relevant chapter): no sixth sector exists, so no inflaton sector exists. The flatness and horizon problems are resolved not by inflation but by the compactness of τ³.