Inflationary Dynamics with a Non-Abelian Gauge Field

TL;DR

This paper explores how a non-Abelian SU(2) gauge field coupled with a scalar field can induce power-law inflation, with the magnetic component aiding cosmic acceleration and revealing stable attractor solutions.

Contribution

It demonstrates that non-Abelian gauge fields can facilitate inflation even with steep potentials, highlighting the role of magnetic components and stability analysis in such models.

Findings

Magnetic component of Yang-Mills field aids inflation

Power-law inflation is a stable attractor under certain conditions

Electric component inflationary solutions are unstable due to non-linear couplings

Abstract

We study the dynamics of the universe with a scalar field and an SU(2) non-Abelian Gauge (Yang-Mills) field. The scalar field has an exponential potential and the Yang-Mills field is coupled to the scalar field with an exponential function of the scalar field. We find that the magnetic component of the Yang-Mills field assists acceleration of the cosmic expansion and a power-law inflation becomes possible even if the scalar field potential is steep, which may be expected from some compactification of higher-dimensional unified theories of fundamental interactions. This power-law inflationary solution is a stable attractor in a certain range of coupling parameters. Unlike the case with multiple Abelian gauge fields, the power-law inflationary solution with the dominant electric component is unstable because of the existence of non-linear coupling of the Yang-Mills field. We also analyze the dynamics for the non-inflationary regime, and find several attractor solutions.