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SU(3)ゲージ場を伴うインフレーション

髙, 鵬遠 神戸大学

2022.03.25

概要

A coupling between the inflaton and the U(1) gauge field with a kinetic gauge function can give a stable anisotropic attractor solution, which is a counter-example for the cosmic no-hair conjecture. If the gauge field is of conventional SU(2) (with Pauli matrices as the generators), the nonlinear coupling will destabilize the anisotropic solution, which takes back the solution to no-hair(energy density of gauge field tends to 0). As there is SU(3) gauge field in the standard model of particle physics, it is natural to consider an SU(3) gauge field in inflation. From the viewpoint of group theory, that the di↵erences of the structure constants in the SU(3) group may give di↵erent e↵ective coupling between di↵erent gauge components and the inflaton, which may give di↵erent behavior compared to that of SU(2). Also, there are other two SU(2) subgroups in the SU(3) group. In each of the two SU(2) subgroups, there is one generator which is a combination of the Cartan generators. This di↵erence may also give di↵erent behavior compared to the conventional SU(2).

Thus in this thesis, we study inflationary universes with an SU(3) gauge field coupled to an inflaton through a gauge kinetic function. In the general case, similar to that of SU(2), the nonlinear coupling between gauge components destabilizes the anisotropic solution. However, we found several features in inflation with an SU(3) gauge field, which do not appear in inflation with an conventional SU(2) gauge field. Firstly, in some special cases, anisotropy can generate transiently even from an isotropic initial condition. This is di↵erent from that of conventional SU(2) in which isotropy solution will keep on from isotropic condition. Secondly, we found for the other two SU(2) subgroups in the SU(3) group, in which there is one generator which is a combination of the Cartan generators, the gauge components corresponding to the Cartan generators can survive from the nonlinear coupling, which results in an anisotropic solution. It occurs due to flat directions in the potential of the gauge field. This can be generalized to Lie groups whose rank is higher than one. Thus, the conventional SU(2) gauge field has a specialty among general non-Abelian gauge fields in inflation.

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