Exact isotropic cosmologies with local fractal number counts

Abstract

We construct an exact relativistic cosmology in which an inhomogeneous but isotropic local region has fractal number counts and matches to a homogeneous background at a scale of the order of $10^2$ Mpc. We show that Einstein's equations and the matching conditions imply either a nonlinear Hubble law or a very low large-scale density.

revised version, to appear Class. Q. Grav.; minor corrections following eqn 16, additional comments on relation to other work, some new references