Dynamical systems applied to cosmology: dark energy and modified gravity

Bahamonde, Sebastian; B�hmer, Christian G.; Carloni, Sante; Copeland, Edmund J.; Fang, Wei; Tamanini, Nicola

Abstract

The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late time cosmology.

Citation

Bahamonde, S., Böhmer, C. G., Carloni, S., Copeland, E. J., Fang, W., & Tamanini, N. (2018). Dynamical systems applied to cosmology: dark energy and modified gravity. Physics Reports, 775-777, 1-122. https://doi.org/10.1016/j.physrep.2018.09.001

• Journal Article Type: Article
• Acceptance Date: Sep 11, 2018
• Online Publication Date: Oct 5, 2018
• Publication Date: Nov 24, 2018
• Deposit Date: Dec 4, 2018
• Publicly Available Date: Oct 6, 2020
• Journal: Physics Reports
• Print ISSN: 0370-1573
• Electronic ISSN: 0370-1573
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 775-777
• Pages: 1-122
• DOI: https://doi.org/10.1016/j.physrep.2018.09.001
• Public URL: https://nottingham-repository.worktribe.com/output/1364762
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0370157318302242?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Dynamical systems applied to cosmology: Dark energy and modified gravity; Journal Title: Physics Reports; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.physrep.2018.09.001; Content Type: article; Copyright: © 2018 Elsevier B.V. All rights reserved.
• Contract Date: Dec 5, 2018