The Averaging Problem in Cosmology and Macroscopic Gravity

TL;DR

This paper discusses the averaging problem in cosmology and introduces macroscopic gravity as a method to modify Einstein's equations, providing solutions that can model open or closed universes with flat spatial geometry.

Contribution

It presents an exact cosmological solution within macroscopic gravity, showing how correlation tensor terms can mimic spatial curvature effects.

Findings

Correlation tensor can act as effective spatial curvature.

Macroscopic gravity solutions include open and closed universe models.

Provides a new approach to averaging in cosmology.

Abstract

The averaging problem in cosmology and the approach of macroscopic gravity to resolve the problem is discussed. The averaged Einstein equations of macroscopic gravity are modified on cosmological scales by the macroscopic gravitational correlation tensor terms as compared with the Einstein equations of general relativity. This correlation tensor satisfies a system of structure and field equations. An exact cosmological solution to the macroscopic gravity equations for a constant macroscopic gravitational connection correlation tensor for a flat spatially homogeneous, isotropic macroscopic space-time is presented. The correlation tensor term in the macroscopic Einstein equations has been found to take the form of either a negative or positive spatial curvature term. Thus, macroscopic gravity provides a cosmological model for a flat spatially homogeneous, isotropic Universe which obeys the dynamical law for either an open or closed Universe.