Newtonian versus relativistic cosmology

TL;DR

This paper compares relativistic and Newtonian cosmological models, introducing a gauge where their matter and velocity spectra match, but highlights the importance of relativistic effects on large scales beyond 10 Mpc.

Contribution

It constructs a new gauge where relativistic and Newtonian spectra coincide and emphasizes the significance of relativistic corrections on large cosmological scales.

Findings

Newtonian theory is inaccurate beyond 10 Mpc.

A new gauge aligns relativistic and Newtonian spectra.

Relativistic effects include geometric quantities absent in Newtonian theory.

Abstract

We show how the relativistic matter and velocity power spectra behave in different gauges. We construct a new gauge where both spectra coincide with Newtonian theory on all scales. However, in this gauge there are geometric quantities present which do not exist in Newtonian theory, for example the local variation of the Hubble parameter. Comparing this quantity to second order Newtonian quantities, we find that Newtonian theory is inaccurate on scales larger than 10 Mpc. This stresses the importance of relativistic corrections to Newtonian cosmological N-body simulations on these scales.