Preheating in an Expanding Universe: Analytic Results for the Massless Case

TL;DR

This paper analyzes resonant preheating after chaotic inflation in both flat and open FRW spacetimes for a massless inflaton decaying into inflaton quanta. Using Hartree factorization and conformal time, it derives analytic equations for the coupled zero-mode and quantum fluctuations, showing that $m=0$ yields conformal equivalence to Minkowski space and a single narrow resonance band, with backreaction ending preheating when $3\lambda\Sigma$ rivals $3\psi^2$. It demonstrates that open and flat models differ by only about $10^{-2}$ under chaotic initial conditions, with open inflation exciting only subcurvature modes. The results provide a clear, analytic benchmark for preheating in open inflation and clarify how conformal invariance shapes resonant particle production, while noting that a nonzero mass would break conformal symmetry and suppress resonance in many regimes.

Abstract

Analytic results are presented for preheating in both flat and open models of chaotic inflation, for the case of massless inflaton decay into further inflaton quanta. It is demonstrated that preheating in both these cases closely resembles that in Minkowski spacetime. Furthermore, quantitative differences between preheating in spatially-flat and open models of inflation remain of order $10^{-2}$ for the chaotic inflation initial conditions considered here.