Solutions for gravity coupled to Higgs–Yang–Mills dark sector with Jacobi elliptical functions

We discuss the equations that arise from a Higgs–Yang–Mills dark sector coupled to gravity on a flat Friedmann–Lemaitre–Robertson–Walker metric. We choose the simplest SU(2) representation, which we show to be compatible with the Cosmological Principle. We devise a multiple time scale approach to solve the equations of motion through a hierarchy of the couplings, utilizing exact solutions in terms of Jacobi elliptic functions. This novel method implements the dynamical system approach used in the literature and can shed new light on the possibility that this model can describe dark energy.