Cosmology with exponential potentials

TL;DR

This paper analyzes the dynamics of a flat universe with a scalar field and matter, showing conditions for early or late acceleration and deriving relations between cosmological parameters.

Contribution

It provides a first-order differential equation framework for understanding acceleration phases in scalar field cosmologies with exponential potentials.

Findings

Passage into acceleration can occur at early times even with decelerating late-time attractors.

Necessary conditions on the potential parameter or acceleration are derived independently of initial conditions.

A general relation between  and the scalar field density parameter  is obtained for late-time evolution.

Abstract

We examine in the context of general relativity the dynamics of a spatially flat Robertson-Walker universe filled with a classical minimally coupled scalar field \phi of exponential potential ~ e^{-\mu\phi} plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation, providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints on the present values of \Omega_{m}, w_{\phi} provide, independently of initial conditions and other parameters, necessary conditions on \mu. Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w_{\phi} ~ -1, as well as, for the generic late-times evolution, the general relation \Omega_{\phi}(w_{\phi}) is obtained.