  We consider a modified gravity model with a massive graviton, but which
nevertheless only propagates two gravitational degrees of freedom and which is
free of ghosts. We show that non-singular bouncing cosmological background
solutions can be generated. In addition, the mass term for the graviton
prevents anisotropies from blowing up in the contracting phase and also
suppresses the spectrum of gravitational waves compared to that of the scalar
cosmological perturbations. This addresses two of the main problems of the
matter bounce scenario.
