Non-Abelian Born--Infeld cosmology

TL;DR

This paper explores cosmological solutions with an SU(2) gauge field described by the Born-Infeld Lagrangian, revealing how the universe's expansion behavior transitions from acceleration to deceleration depending on the field strength.

Contribution

It provides a detailed dynamical systems analysis of SU(2) Born-Infeld cosmology, including the effective equation of state and asymptotic behaviors, which was not previously studied.

Findings

The effective equation of state interpolates between -1/3 and 1/3.

The universe transitions from zero acceleration to deceleration.

Solutions asymptotically approach the Tolman solution.

Abstract

We investigate homogeneous and isotropic cosmological solutions supported by the SU(2) gauge field governed by the Born-Infeld lagrangian. In the framework of the Friedmann-Robertson-Walker cosmology, with or without cosmological constant $\lambda$, we derive dynamical systems that give rather complete description of the space of solutions. For $\lambda=0$ the effective equation of state $\ve(p)$ is shown to interpolate between $p=-\ve/3$ in the regime of the strong field and $p=\ve/3$ for the weak field. Correspondingly, the Universe starts with zero acceleration and gradually enters the decelerating regime, asymptotically approaching the Tolman solution.