Measuring anisotropic stress with relativistic effects

TL;DR

This paper introduces a new method to directly measure anisotropic stress in the universe by using relativistic effects in galaxy counts, bypassing assumptions about dark matter and enabling tests of gravity theories.

Contribution

The paper proposes a novel observational technique that directly measures anisotropic stress using relativistic effects, independent of dark matter assumptions.

Findings

Method enables direct measurement of anisotropic stress.

Relativistic effects in galaxy counts are key to the measurement.

Provides a new test for theories of gravity.

Abstract

One of the main goal of large-scale structure surveys is to test the consistency of General Relativity at cosmological scales. In the $\Lambda$CDM model of cosmology, the relations between the fields describing the geometry and the content of our Universe are uniquely determined. In particular, the two gravitational potentials -- that describe the spatial and temporal fluctuations in the geometry -- are equal. Whereas large classes of dark energy models preserve this equality, theories of modified gravity generally create a difference between the potentials, known as anisotropic stress. Even though measuring this anisotropic stress is one of the key goals of large-scale structure surveys, there are currently no methods able to measure it directly. Current methods all rely on measurements of galaxy peculiar velocities (through redshift-space distortions), from which the time component of the metric is inferred, assuming that dark matter follows geodesics. If this is not the case, all the proposed tests fail to measure the anisotropic stress. In this letter, we propose a novel test which directly measures anisotropic stress, without relying on any assumption about the unknown dark matter. Our method uses relativistic effects in the galaxy number counts to provide a direct measurement of the time component of the metric. By comparing this with lensing observations our test provides a direct measurement of the anisotropic stress.