inertial forces

The equivalence principle suggests that inertial forces are in fact gravitational in nature, and that any inertial force which is observed in accelerating frames of reference is generated by the gravitomagnetic potentials of the matter distribution relative to which the frame is accelerated: Would that imply that e.g. the centrifugal force depends on cosmic time because of the varying matter density \(\Omega_m(a)\)? Would these forces be absent in the case of an empty universe?