Gravitational backreaction of matter inhomogeneities

The non-linearity of Einstein’s equations makes it possible for small scale matter inhomogeneities to affect the universe at cosmological distances. We study the size of such effects using a simple heuristic model that captures the most important backreaction effect due to non-relativistic matter, as well as several exact solutions describing inhomogeneous and anisotropic expanding universes. We find that the effects are O(H2l2/c2) or smaller, where H is the Hubble parameter and l the typical size scale of inhomogeneities. For virialized structures this is of order v2/c2, where v is the characteristic peculiar velocity.