Spatially averaged cosmology in an arbitrary coordinate system

TL;DR

This paper develops a general averaging method for tilted observers in cosmology, revealing new backreaction terms related to peculiar velocities and coordinate shifts, enhancing understanding of inhomogeneous universe models.

Contribution

It introduces a novel averaging procedure applicable to tilted observers, incorporating effects of peculiar velocities and coordinate shifts into cosmological backreaction analysis.

Findings

New backreaction terms identified due to peculiar velocities.

Averaging procedure applicable to arbitrary coordinate systems.

Enhanced understanding of inhomogeneity effects in cosmology.

Abstract

This paper presents a general averaging procedure for a set of observers which are tilted with respect to the cosmological matter fluid. After giving the full set of equations describing the local dynamics, we define the averaging procedure and apply it to the scalar parts of Einstein's field equations. In addition to the standard backreaction, new terms appear that account for the effect of the peculiar velocity of the matter fluid as well as the possible effect of a shift in the coordinate system.