  We construct the gauge-invariant electric and magnetic charges in Yang-Mills
theory coupled to cosmological General Relativity (or any other geometric
gravity), extending the flat spacetime construction of Abbott and Deser. For
non-vanishing background gauge fields, the charges receive non-trivial
contribution from the gravity part. In addition, we study the constraints on
the first order perturbation theory and establish the conditions for
linearization instability: that is the validity of the first order perturbation
theory.
