A Conformal Boundary Ansatz for Warm Inflation Initialization: A Toy Model

We present a theoretical framework demonstrating a deterministic initialization mechanism for Warm Inflation via classical conformal boundary conditions. A persistent challenge in dissipative inflationary models is the "cold start" paradox: initializing the requisite thermal bath to generate the dissipative friction that subsequently sustains radiation production. Postulating an idealized, asymptotically scale invariant pre-inflationary phase, we mathematically prove that a conformal Weyl mapping to the emergent metric furnishes a finite, analytically derived initial radiation density. Implementing a spontaneous conformal symmetry-breaking ansatz, an emergent inflaton field is subjected to this inherited thermal bath. We analytically derive the initial kinematics of this framework, demonstrating that for strict sub-Planckian temperatures, the universe naturally initializes in the weak dissipative regime (Q << 1). The initial Hubble friction provided by the boundary radiation enables a smooth, deterministic kinematic handoff to the warm slow-roll steady-state attractor. As a mathematical proof-of-concept, this mechanism provides a fully realized framework to bypass the bootstrap problem of warm inflation.