Averaging in cosmology based on Cartan scalars

TL;DR

This paper introduces a novel averaging method in cosmology using Cartan scalars, demonstrating its application to LTB models and gravitational waves, revealing effects similar to cosmological constant and spatial curvature.

Contribution

It presents a new averaging approach based on Cartan scalars and applies it to different cosmological models and gravitational waves, showing novel effects.

Findings

Correlation term mimics a positive cosmological constant

Leading correlation term behaves like spatial curvature

Averaging nontriviality in linearized gravitational waves

Abstract

We present a new approach for averaging in general relativity and cosmology. After a short review of the theory originally taken from the equivalence problem, we consider two ways how to deal with averaging based on Cartan scalars. We apply the theory for two different LTB models. In the first one, correlation term behaves as a positive cosmological constant, in the second example leading correlation term behaves like spatial curvature. We also show nontriviality of averaging for linearized monochromatic gravitational wave.