The Perturbation Theory of the Yang-Mills Field

We have suggested that the Yang-Mills(YM) field can be a kind of candidate of inflation at high energy scale or dark energy at the very low energy scale, which can naturally give the matter state of ω < 0, even it can give ω < −1. In this paper, we discuss the perturbation theory of the YM field, and give a series of equations which can describe the evolution of the YM field’s perturbation in the Robertson-Walker space-time. Then for example we discuss solution of the only ”electric” field, and find that this field can not generate the scale-invariant initial scalar perturbation spectrum, so it can not as a kind of inflation field, although it can give a nearly de Sitter expansion. But as a kind of dark energy, we find ω+1 ∝ 1/a2, so it will give a nearly de Sitter expansion which is same with the observation results. We also research the perturbation of this kind of dark energy, and find that if not considering the field perturbation δE, then the dark energy will be no perturbation δp = δρ = 0, which is different with the scalar field dark energy, but fit well with the observation. If there are field perturbation, the sound velocity is cs = −1/3, which will alter the evolution of the cosmic scalar perturbation, this should have obvious effect on the large scale power spectrum of Cosmic Microwave Background Radiation(CMB). PACS numbers: 98.80.-k, 98.80.Es, 04.30.-w, 04.62+v,