Approximate angular diameter distance in a locally inhomogeneous universe with nonzero cosmological constant

Abstract

We discuss the general and approximate angular diameter distance in the Friedman-Robertson-Walker cosmological models with nonzero cosmological constant. We modify the equation for the angular diameter distance by taking into account the fact that locally the distribution of matter is non homogeneous. We present exact solutions of this equation in a few special cases. We propose an approximate analytic solution of this equation which is simple enough and sufficiently accurate to be useful in practical applications.