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/c ²) or smaller, where H is the Hubble parameter and l the typical size scale of inhomogeneities. For virialized structures this is of order v ²/c², where v is the characteristic peculiar velocity.