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We study cosmological applications of extended vector-tensor theories, whoseLagrangians contain up to two derivatives with respect to metric and vectorfield. We derive background equations under the assumption of homogeneous andisotropic universe and study the nature of cosmological perturbations on top ofthe background. We found an example of healthy cosmological solutions innon-trivial degenerate theory of gravity for the first time, where thoseperturbations do not suffer from any instabilities, that is, ghost and gradientinstabilities.

Stable cosmological solutions in degenerate theory of gravity