On the dynamics of a quadratic scalar field potential

TL;DR

This paper analyzes the inflationary dynamics of a scalar field with a quadratic potential using a new autonomous system approach, extending beyond traditional slow-roll approximations.

Contribution

It introduces a novel formalism for studying inflation dynamics through autonomous equations, providing deeper insights into attractor properties of quadratic scalar field models.

Findings

Identifies critical points corresponding to inflationary solutions.

Demonstrates the formalism's ability to analyze beyond slow-roll conditions.

Provides a comprehensive phase space analysis of quadratic inflation models.

Abstract

We review the attractor properties of the simplest chaotic model of inflation, in which a minimally coupled scalar field is endowed with a quadratic scalar potential. The equations of motion in a flat Friedmann-Robertson-Walker universe are written as an autonomous system of equations, and the solutions of physical interest appear as critical points. This new formalism is then applied to the study of inflation dynamics, in which we can go beyond the known slow-roll formalism of inflation.