Quintessence from a state space perspective

Artur Alho; Claes Uggla; John Wainwright

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arXiv · 2209.09684

Quintessence from a state space perspective

Artur Alho·Claes Uggla·John Wainwright

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Abstract

We use dynamical systems methods to study quintessence models in a spatially flat and isotropic spacetime with matter and a scalar field with potentials for which $λ(φ)=-V_{,φ}/V$ is bounded, thereby going beyond the exponential potential for which $λ(φ)$ is constant. The scalar field equation of state parameter $w_φ$ plays a central role when comparing quintessence models with observations, but with the dynamical systems used to date $w_φ$ is an indeterminate, discontinuous, function on the state space in the asymptotically matter dominated regime. Our first main result is the introduction of new variables that lead to a \emph{regular} dynamical system on a \emph{bounded} three-dimensional state space on which $w_φ$ is a \emph{regular} function. The solution trajectories in the state space then provide a visualization of different types of quintessence evolution, and how initial conditions affect the transition between the matter and scalar field dominated epochs; this is complemented by graphs $w_φ(N)$, where $N$ is the $e$-fold time, which enables characterizing different types of quintessence evolution.

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Artur Alho, Claes Uggla, John Wainwright. 2022-12-07. Quintessence from a state space perspective. https://arxiv.org/abs/2209.09684

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