Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation

TL;DR

This study compares fully relativistic and Newtonian simulations of cosmic structure formation, finding they agree well except in extreme, strongly gravitating regions, thus validating Newtonian approaches in most cosmological scenarios.

Contribution

It provides a direct numerical comparison between Einstein-based and Newtonian simulations, assessing their agreement across different regimes of structure formation.

Findings

Excellent agreement between relativistic and Newtonian calculations in most regimes.

Differences only appear in regions with extreme, strong gravity.

Validates the use of Newtonian simulations for standard cosmological modeling.

Abstract

In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic of ongoing debate is to what degree this fully captures the dynamics dictated by general relativity, especially in the era of precision cosmology. To quantitatively assess this, we directly compare standard N-body Newtonian calculations to full numerical solutions of the Einstein equations, for cold matter with various magnitude initial inhomogeneities on scales comparable to the Hubble horizon. We analyze the differences in the evolution of density, luminosity distance, and other quantities defined with respect to fiducial observers. This is carried out by reconstructing the effective spacetime and matter fields dictated by the Newtonian quantities, and by taking care to distinguish effects of numerical resolution. We find that the fully general relativistic and Newtonian calculations show excellent agreement, even well into the nonlinear regime. They only notably differ in regions where the weak gravity assumption breaks down, which arise when considering extreme cases with perturbations exceeding standard values.