Asymptotic Properties of a Supposedly Regular (Dirac-Born-Infeld) Modification of General Relativity

TL;DR

This paper investigates a Dirac-Born-Infeld type modification of General Relativity using dynamical systems, revealing a complex phase space with multiple attractors, bifurcations, and the persistence of initial singularities.

Contribution

It provides a detailed dynamical analysis of a non-linear gravity model, highlighting rich behaviors and the non-removal of the big bang singularity in this framework.

Findings

Multiple equilibrium points including matter-dominated and de Sitter solutions

Existence of multi-attractor structures depending on parameters

Initial singularity persists as a past attractor in phase space

Abstract

We apply the dynamical systems tools to study the asymptotic properties of a cosmological model based on a non-linear modification of General Relativity in which the standard Einstein-Hilbert action is replaced by one of Dirac-Born-Infeld type. It is shown that the dynamics of this model is extremely rich: there are found equilibrium points in the phase space that can be associated with matter-dominated, matter-curvature scaling, de Sitter, and even phantom-like solutions. Depending on the value of the overall parameters the dynamics in phase space can show multi-attractor structure into the future (multiple future attractors may co-exist). This is a consequence of bifurcations in control parameter space, showing strong dependence of the model's dynamical properties on the free parameters. Contrary to what is expected from non-linear modifications of general relativity of this kind, removal of the initial spacetime singularity is not a generic feature of the corresponding cosmological model. Instead, the starting point of the cosmic dynamics -- the past attractor in the phase space -- is a state of infinitely large value of the Hubble rate squared, usually associated with the big bang singularity.