Observational Quantities in Quasi-Newtonian Descriptions of Cosmological Space-Times

TL;DR

This paper develops a quasi-Newtonian framework for analyzing cosmological space-times, enabling the study of relativistic structures using Newtonian concepts and providing insights into cosmological tensions.

Contribution

It introduces a new formulation of relativistic cosmologies with non-perturbative structures using Newtonian-like quantities derived from shear-free foliations.

Findings

Provides fundamental results for kinematics and light propagation in quasi-Newtonian cosmologies.

Quantifies deviations of observables from Friedmann cosmology predictions.

Illustrates the approach with the Kasner solution and discusses implications for cosmological tensions.

Abstract

We investigate measures of distance and redshift in cosmological space-times that admit a shear-free foliation, which we henceforth refer to as `quasi-Newtonian'. Space expands isotropically in this description, and small-scale gravitational physics has a natural Newtonian limit, which makes it ideal for considering the physics of wide classes of cosmological models. By assuming that the energy-momentum tensor is dominated by rest-mass density, and that the 3-velocity of matter is small in the quasi-Newtonian frame, we derive fundamental results for kinematics and light propagation. Our results provide a new way of formulating general-relativistic cosmologies with non-perturbative structures in terms of quantities that can be understood from cosmological perturbation theory and post-Newtonian expansions, and allow us to quantify departures of observables from the predictions of Friedmann cosmology. It thereby provides a route to understanding inherently relativistic space-time structures, such as those that occur in Lema\^{i}tre-Tolman-Bondi, Szekeres solutions, and Bianchi cosmologies in terms of Newtonian degrees of freedom. We illustrate our results using the degenerate Kasner solution as an example, and explain how our approach can be used to provide new insights into the current cosmological tensions.