A Theory of Self-Resonance After Inflation, Part 1: Adiabatic and Isocurvature Goldstone Modes

TL;DR

This paper develops a theoretical framework for self-resonance phenomena after inflation, analyzing the behavior of adiabatic and isocurvature Goldstone modes in multi-field inflation models, focusing on long-wavelength instabilities.

Contribution

It introduces a comprehensive theory of post-inflation self-resonance, deriving conditions for instabilities of adiabatic and isocurvature modes in multi-field models with internal symmetry.

Findings

Long-wavelength modes govern key physics of self-resonance.

Instability bands depend on sound speeds derived from averaged potentials.

Typically, only one class of modes exhibits instability at a time.

Abstract

We develop a theory of self-resonance after inflation. We study a large class of models involving multiple scalar fields with an internal symmetry. For illustration, we often specialize to dimension 4 potentials, but we derive results for general potentials. This is the first part of a two part series of papers. Here in Part 1 we especially focus on the behavior of long wavelengths modes, which are found to govern most of the important physics. Since the inflaton background spontaneously breaks the time translation symmetry and the internal symmetry, we obtain Goldstone modes; these are the adiabatic and isocurvature modes. We find general conditions on the potential for when a large instability band exists for these modes at long wavelengths. For the adiabatic mode, this is determined by a sound speed derived from the time averaged potential. While for the isocurvature mode, this is determined by a speed derived from a time averaged auxiliary potential. Interestingly, we find that this instability band usually exists for one of these classes of modes, rather than both simultaneously. We focus on backgrounds that evolve radially in field space, as setup by inflation, and also mention circular orbits, as relevant to Q-balls. In Part 2 [1] we derive the central behavior from the underlying description of many particle quantum mechanics, and introduce a weak breaking of the symmetry to study corrections to particle-antiparticle production from preheating.