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There is a no-go theorem forbidding flat and closed FLRW solutions in massivegravity on a flat reference metric, while open solutions are unstable. Recentlyit was shown that this no-go theorem can be overcome if at least some mattercouples to a hybrid metric composed of both the dynamical and the fixedreference metric. We show that this is not compatible with the standarddescription of cosmological sources in terms of effective perfect fluids, andthe predictions of the theory become sensitive either to the detailedfield-theoretical modelling of the matter content or to the presence ofadditional dark degrees of freedom. This is a serious practical complication.Furthermore, we demonstrate that viable cosmological background evolution witha perfect fluid appears to require the presence of fields with highly contrivedproperties. This could be improved if the equivalence principle is broken bycoupling only some of the fields to the composite metric, but viableself-accelerating solutions due only to the massive graviton are difficult toobtain.

Cosmological viability of massive gravity with generalized matter coupling