General covariance violation and the gravitational dark matter: Scalar graviton

The violation of the general covariance is proposed as a resource of the gravitational dark matter. The minimal violation of the covariance to the unimodular one is associated with the massive scalar graviton as the simplest representative of such matter. The Lagrangian formalism for a continuous medium, a perfect fluid in particular, in the scalar graviton environment is developed. The implications for cosmology are briefly indicated