Research in Astronomy and Astrophysics Perturbations of the Yang-Mills field in the universe ∗

Abstract It has been suggested that the Yang-Mills (YM) field can be a kind of candidate for the inflationary field at high energy scales or dark energy at very low energy scales, which can naturally give the equation of state −1 < ω < 0 or ω < −1. We discuss the zero order and first order Einstein equations and YM field kinetic energy equations of the free YM field models. From the zero order equations, we find that ω + 1 ∝ a−2, from which it follows that the equation of state of the YM field always goes to−1, independent of the initial conditions. By solving the first order Einstein equations and the YM field equations, we find that in the YM field inflationary models, the scale-invariant primordial perturbation power spectrum cannot be generated. Therefore, only using this kind of YM field is not enough to account for inflationary sources. However, as a kind of candidate for dark energy, the YM field has the ‘sound speed ’ c 2s = −1/3 < 0, which makes the perturbation φ have a damping behavior at large scales. This provides a way to distinguish the YM field dark energy models from other kinds of models