Noether Symmetry in Non-Minimally Coupled Yang-Mills Cosmology

This paper investigates a cosmological model based on a non-minimally coupled Yang-Mills field in the framework of a spatially flat FLRWuniverse. The model includes general functions describing the coupling between the Yang-Mills field and gravity, as well as its self-interaction potential. To further analyze the model, the Noether symmetry approach is used as a systematic method to identify conserved quantities and reduce the complexity of the dynamical system. By imposing the existence of a Noether symmetry, the initially arbitrary coupling functions are constrained, and the exact cosmological solutions compatible with observational data are found. It is shown that, under suitable conditions, Yang-Mills field behaves as a dark-energy component capable of driving the accelerated expansion of the universe.