Abstract
We study inflationary universes with an SU(3) gauge field coupled to an inflaton through a gauge kinetic function. Although the SU(3) gauge field grows at the initial stage of inflation due to the interaction with the inflaton, nonlinear self-couplings in the kinetic term of the gauge field become significant and cause nontrivial dynamics after sufficient growth. We investigate the evolution of the SU(3) gauge field numerically and reveal attractor solutions in the Bianchi type I spacetime. In general cases where all the components of the SU(3) gauge field have the same magnitude initially, they all tend to decay eventually because of the nonlinear self-couplings. Therefore, the cosmic no-hair conjecture generically holds in a mathematical sense. Practically, however, the anisotropy can be generated transiently in the early universe, even for an isotropic initial condition. Moreover, we find particular cases for which several components of the SU(3) gauge field survive against the nonlinear self-couplings. It occurs due to flat directions in the potential of a gauge field for Lie groups whose rank is higher than one. Thus, an SU(2) gauge field has a specialty among general non-Abelian gauge fields.
Highlights
No matters can survive in an expanding homogeneous universe in the presence of a positive cosmological constant except for the Bianchi type-IX spacetime [1]
We study inflationary universes with an SU(3) gauge field coupled to an inflaton through a gauge kinetic function
A healthy counterexample to the conjecture motivated by supergravity was found in [8], where a vector field is coupled to an inflaton through a gauge kinetic function
Summary
No matters can survive in an expanding homogeneous universe in the presence of a positive cosmological constant except for the Bianchi type-IX spacetime [1]. We study a general Bianchi type-I universe having the metric of the form gμνdxμdxν 1⁄4 −dt þ gijðtÞdxidxj; ð38Þ accompanied by homogeneous scalar and gauge fields, φ 1⁄4 φðtÞ; Aaμdxμ 1⁄4 Aai ðtÞdxi; ð39Þ where we used the gauge symmetry to fix the time component of the gauge field. In this setup, the system of EOMs consists of the Hamiltonian constraint, six EOMs for gij, eight Yang-Mills constraints, 24 EOMs for Aai , one EOM for φ. Since A8 has no coupling with the SU(2) sector, this state is stable
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