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# Modified Einstein versus Modified Euler for Dark Matter

Camille Bonvin and Levon Pogosian

Submitted on 8 September 2022

## Abstract

Modifications of General Relativity generically contain additional degrees of freedom that can mediate forces between matter particles. One of the common manifestations of a fifth force in alternative gravity theories is a difference between the gravitational potentials felt by relativistic and non-relativistic particles, also known as the gravitational slip''. In contrast, a fifth force between dark matter particles, due to dark sector interaction, does not cause a gravitational slip, making the latter a possible smoking gun of modified gravity. In this article, we point out that a force acting on dark matter particles, as in models of coupled quintessence, would also manifest itself as a measurement of an effective gravitational slip by cosmological surveys of large-scale structure. This is linked to the fact that redshift-space distortions due to peculiar motion of galaxies do not provide a measurement of the true gravitational potential if dark matter is affected by a fifth force. Hence, it is extremely challenging to distinguish a dark sector interaction from a modification of gravity with cosmological data alone. Future observations of gravitational redshift from galaxy surveys can help to break the degeneracy between these possibilities, by providing a direct measurement of the distortion of time. We discuss this and other possible ways to resolve this important question.

## Preprint

Comment: 13 pages, 2 figures

Subjects: Astrophysics - Cosmology and Nongalactic Astrophysics; General Relativity and Quantum Cosmology