The fully non-linear post-Friedmann frame-dragging vector potential: Magnitude and time evolution from N-body simulations

TL;DR

This paper calculates the magnitude and evolution of the post-Friedmann vector potential from N-body simulations, revealing it is significantly smaller than the scalar potential but can be larger than perturbative estimates on small scales.

Contribution

It provides a detailed method to extract the fully non-linear vector potential from simulations and compares it to perturbative predictions across scales and redshifts.

Findings

Vector potential is ~10^5 times smaller than scalar potential at z=0.

Fully non-linear vector potential can exceed perturbative estimates on small scales.

The ratio of vector to scalar potential remains consistent over various redshifts.

Abstract

Newtonian simulations are routinely used to examine the matter dynamics on non-linear scales. However, even on these scales, Newtonian gravity is not a complete description of gravitational effects. A post-Friedmann approach shows that the leading order correction to Newtonian theory is a vector potential in the metric. This vector potential can be calculated from N-body simulations, requiring a method for extracting the velocity field. Here, we present the full details of our calculation of the post-Friedmann vector potential, using the Delauney Tesselation Field Estimator (DTFE) code. We include a detailed examination of the robustness of our numerical result, including the effects of box size and mass resolution on the extracted fields. We present the power spectrum of the vector potential and find that the power spectrum of the vector potential is $\sim 10^5$ times smaller than the power spectrum of the fully non-linear scalar gravitational potential at redshift zero. Comparing our numerical results to perturbative estimates, we find that the fully non-linear result can be more than an order of magnitude larger than the perturbative estimate on small scales. We extend the analysis of the vector potential to multiple redshifts, showing that this ratio persists over a range of scales and redshifts. We also comment on the implications of our results for the validity and interpretation of Newtonian simulations.