A complete cosmological solution to the averaged Einstein field equations as found in macroscopic gravity

A formalism for analyzing the complete set of field equations describing macroscopic gravity is presented. Using this formalism, a cosmological solution to the macroscopic gravity equations is determined. It is found that if a particular segment of the connection correlation tensor is zero and if the macroscopic geometry is described by a flat Robertson–Walker metric, then the effective correction to the averaged Einstein field equations of general relativity i.e., the backreaction, is equivalent to a positive spatial curvature term. This investigation completes the analysis of Coley et al. [Phys. Rev. Lett. 95, 151102 (2005)], and the formalism developed provides a possible basis for future studies.