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Register a new userCosmic No-hair Conjecture and Inflation with an SU(3) Gauge Field
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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.
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We study the cosmic no-hair in the presence of spin-2 matter, i.e. in bimetric gravity. We obtain stable de Sitter solutions with the cosmological constant in the physical sector and find an evidence that the cosmic no-hair is correct. In the presence of the other cosmological constant, there are two branches of de Sitter solutions. Under anisotropic perturbations, one of them is always stable and there is no violation of the cosmic no-hair at the linear level. The stability of the other branch depends on parameters and the cosmic no-hair can be violated in general. Remarkably, the bifurcation point of two branches exactly coincides with the Higuchi bound. It turns out that there exists a de Sitter solution for which the cosmic no-hair holds at the linear level and the effective mass for the anisotropic perturbations is above the Higuchi bound.
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