A Complete Cosmological Solution to the Averaged Einstein Field Equations as found in Macroscopic Gravity

TL;DR

This paper develops a formalism for Macroscopic Gravity, derives a cosmological solution, and shows that under certain conditions, backreaction effects mimic positive spatial curvature in averaged Einstein equations.

Contribution

It provides a complete cosmological solution within Macroscopic Gravity formalism, extending previous work and offering a basis for future research.

Findings

Backreaction can be equivalent to positive spatial curvature.

Formalism completes the analysis of previous foundational work.

Conditions for the solution involve zero connection correlation tensor segment and flat Robertson-Walker metric.

Abstract

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 [Phys. Rev. Lett., vol. 95, 151102, (2005)] and the formalism developed provides a possible basis for future studies.