On the Limit Cycle of an Inflationary Universe

TL;DR

This paper rigorously proves the existence and stability of a limit cycle in the phase space of a scalar inflaton field with a double-well potential, providing an analytical formula for its period.

Contribution

It introduces a rigorous proof of a stable limit cycle in inflationary universe models with a double-well potential, combining analytical and numerical methods.

Findings

Existence of a stable limit cycle in the inflaton phase space

Analytical expression for the period of the limit cycle

Numerical validation of the limit cycle stability

Abstract

We study the dynamics of a scalar inflaton field with a symmetric double--well potential and prove rigorously the existence of a limit cycle in its phase space. By using analytical and numerical arguments we show that the limit cycle is stable and give an analytical formula for its period.