While the expansion rate of a homogeneous isotropic universe is simply proportional to the square-root of the energy density, the expansion rate of an inhomogeneous universe also depends on the nature of the density inhomogeneities. In this paper we calculate to second order in perturbation variables the expansion rate of an inhomogeneous universe and demonstrate corrections to the evolution of the expansion rate. While we find that the mean correction is small, the variance of the correction on the scale of the Hubble radius is sensitive to the physical significance of the unknown spectrum of density perturbations beyond the Hubble radius.
Physical Review D
- Pub Date:
- January 2005
- Particle-theory and field-theory models of the early Universe;
- High Energy Physics - Phenomenology;
- General Relativity and Quantum Cosmology
- 19 pages, 2 figures Version 2 includes some changes in numerical factors and corrected typos. It is the version accepted for publication in Physical review D