Abstract: Modified gravity theory is known to violate Birkhoff's theorem. We explore a
key consequence of this violation, the effect of distant matter in an
Einstein-de Sitter universe on the motion of test particles. We find that when
a particle is accelerated, a force is experienced that is proportional to the
particle's mass and acceleration and acts in the direction opposite to that of
the acceleration. We identify this force with inertia. At very low
accelerations, our inertial law deviates slightly from that of Newton, yielding
a testable prediction that may be verified with relatively simple experiments.