Light Propagation in a Clumpy Universe

Abstract

The propagation of light in an inhomogeneous universe is a long standing problem. Its resolution requires, first, a realistic description of the geometry of a clumpy universe and, second, solutions to the null geodesic equations given the metric of such a universe. The Friedmann-Robertson-Walker metric has become the standard description of the large scale geometry of the universe. However, the observable universe today is manifestly inhomogeneous. The weakly perturbed Friedmann-Robertson-Walker metric is often used to describe such a universe. But its validity is only guaranteed for a weakly inhomogeneous universe, where, for instance, overdensities are small , which is not true for sufficiently small scales in the universe today. It is well known, however, that the metric perturbations can still be small even if the overdensity is not small, given the right conditions and coordinates. However, spatial gradients of metric perturbations are not necessarily small any more. Here we estimate whether the second-order corrections involving them can affect significantly the expansion of the universe or the light propagation in it.