Does dark matter fall in the same way as standard model particles? A direct constraint of Euler's equation with cosmological data

TL;DR

This study tests whether dark matter particles follow Euler's equation at cosmological scales by combining galaxy velocity data with gravitational potential measurements, constraining possible deviations or additional forces.

Contribution

First direct test of dark matter's motion governed by Euler's equation at cosmological scales using combined observational data.

Findings

Current data are consistent with Euler's equation at redshifts 0.3 to 0.8.

Constraints limit positive fifth force to 7% and negative to 21% of gravity.

Future surveys will improve constraints to 2% deviation from pure gravity.

Abstract

Since dark matter particles have never been directly detected, we do not know how they move, and in particular we do not know how they fall inside gravitational potential wells. Usually it is assumed that dark matter only interacts gravitationally with itself and with particles of the standard model, and therefore that its motion is governed by Euler's equation. In this paper, we test this assumption for the first time at cosmological scales, by combining measurements of galaxy velocities with measurements of gravitational potential wells, encoded in the Weyl potential. We find that current data are consistent with Euler's equation at redshifts $z\in [0.3,0.8]$, and we place constraints on the strength of a potential fifth force, which would alter the way dark matter particles fall. We find that a positive fifth force cannot exceed 7% of the gravitational interaction strength, while a negative fifth force is limited to 21%. The coming generation of surveys, including the Legacy Survey of Space and Time (LSST) of the Vera C. Rubin Observatory and the Dark Energy Spectroscopic Instrument (DESI) will drastically improve the constraints, allowing to constrain a departure from pure gravitational interaction at the level of 2%.