The Limited Accuracy of Linearized Gravity

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.