Phase Space Analysis of Quintessence Cosmologies with a Double Exponential Potential

TL;DR

This paper uses phase space analysis to classify the late-time behaviors of various cosmological models with a double exponential scalar potential, revealing conditions for acceleration, deceleration, or crunch scenarios.

Contribution

It introduces the concept of a 'quasi fixed point' to analyze asymptotic behaviors in quintessence cosmologies with a double exponential potential.

Findings

Classifies solutions into accelerating, decelerating, or crunching.

Identifies conditions for multiple periods of accelerated expansion.

Provides a complete late-time behavior classification.

Abstract

We use phase space methods to investigate closed, flat, and open Friedmann-Robertson-Walker cosmologies with a scalar potential given by the sum of two exponential terms. The form of the potential is motivated by the dimensional reduction of M-theory with non-trivial four-form flux on a maximally symmetric internal space. To describe the asymptotic features of run-away solutions we introduce the concept of a `quasi fixed point.' We give the complete classification of solutions according to their late-time behavior (accelerating, decelerating, crunch) and the number of periods of accelerated expansion.