The Effects of Inhomogeneities on Cosmic Expansion

We evaluate the effect of inhomogeneity energy on the expansion rate of the universe. Our method is to expand to Newtonian order in potential and velocity but to take into account fully nonlinear density inhomogeneities. To linear order in density, kinetic and gravitational potential energy contribute to the total energy of the universe with the same scaling with expansion factor as spatial curvature. In the strongly nonlinear regime, growth saturates, and the net effect of the inhomogeneity energy on the expansion rate remains negligible at all times. In particular, inhomogeneity contributions never mimic the effects of dark energy or induce an accelerated expansion.