A spherically symmetric and stationary universe from a weak modification of general relativity

It is shown that a weak modification of general relativity, in the linearized approach, renders a spherically symmetric and stationary model of the universe. This is due to the presence of a third mode of polarization in the linearized gravity in which a "curvature" energy term is present. Such an energy can, in principle, be identified as the Dark Energy. The model can also help to a better understanding of the framework of the Einstein-Vlasov system.