The Limited Accuracy of Linearized Gravity

TL;DR

This paper assesses the accuracy of linearized gravity in cosmology using fully relativistic simulations, finding it generally reliable for small perturbations but with notable gauge-dependent corrections at large scales.

Contribution

It provides a detailed evaluation of linearized gravity's precision in cosmological models through relativistic simulations, highlighting gauge effects and correction amplitudes.

Findings

Linear theory accurately describes the metric in Newtonian and harmonic gauges for standard perturbations.

Corrections can reach or exceed percent-level for the largest cosmic structures.

Gauge dependence significantly affects the interpretation of linearized gravity corrections.

Abstract

Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate predictions sufficiently accurate for comparison to observations, and can we draw meaningful conclusions about properties of our Universe from them? In this work we examine the accuracy of linearized gravity in the presence of collisionless matter and a cosmological constant utilizing fully general relativistic simulations. We observe the gauge-dependence of corrections to linear theory, and note the amplitude of these corrections. For perturbations whose amplitudes are in line with expectations from the standard $\Lambda$CDM model, we find that the full, general relativistic metric is well-described by linear theory in Newtonian and harmonic gauges, while the metric in comoving-synchronous gauge is not. For the largest observed structures in our Universe, our results suggest that corrections to linear gravitational theory can reach or surpass the percent-level.