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In the standard approach to studying cosmological structure formation, theoverall expansion of the Universe is assumed to be homogeneous, with thegravitational effect of inhomogeneities encoded entirely in a Newtonianpotential. A topic of ongoing debate is to what degree this fully captures thedynamics dictated by general relativity, especially in the era of precisioncosmology. To quantitatively assess this, we directly compare standard N-bodyNewtonian calculations to full numerical solutions of the Einstein equations,for cold matter with various magnitude initial inhomogeneities on scalescomparable to the Hubble horizon. We analyze the differences in the evolutionof density, luminosity distance, and other quantities defined with respect tofiducial observers. This is carried out by reconstructing the effectivespacetime and matter fields dictated by the Newtonian quantities, and by takingcare to distinguish effects of numerical resolution. We find that the fullygeneral relativistic and Newtonian calculations show excellent agreement, evenwell into the nonlinear regime. They only notably differ in regions where theweak gravity assumption breaks down, which arise when considering extreme caseswith perturbations exceeding standard values.

Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation