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

TL;DR

This paper introduces a deterministic, conformal boundary condition-based initialization method for warm inflation, addressing the cold start problem by deriving initial radiation density and inflaton dynamics analytically.

Contribution

It presents a novel theoretical framework using conformal boundary conditions to naturally initialize warm inflation without the cold start paradox.

Findings

Analytically derived initial radiation density from conformal Weyl mapping.

Demonstrated universe naturally starts in weak dissipative regime (Q << 1).

Provided a mathematical proof-of-concept for warm inflation initialization.

Abstract

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.