Symmetric Yang--Mills theory in FLRW universes

In this work, we set up the theoretical framework and indicate future applications of symmetric Yang–Mills fields to cosmology. We analyze the coset space dimensional reduction scheme to construct pure Yang–Mills fields on spacetimes given as cylinders over cosets. Particular cases of foliations using $H^n$, dS${}_n$ and AdS${}_n$ slices as non-compact symmetric spaces are solved, compared to previous results in the literature, and generalized in a structured fashion. Coupling to general relativity in FLRW-type universes is introduced via the cosmological scale factor. For the hyperbolic slicing in 4D, the dynamics of the Einstein–Yang–Mills system is analytically solved and discussed. Finally, we generalize the analysis to warped foliations of the cylinders, which enlarge the range of possible spacetimes while also introducing a Hubble friction-like term in the equation of motion for the Yang–Mills field.