Measuring anisotropic stress with relativistic effects

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.

6 pages, no figures. V2 is the published version

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• Modified Einstein versus Modified Euler for Dark Matter
• Combining gravitational lensing and gravitational redshift to measure the anisotropic stress with future galaxy surveys
• Testing gravity with gravitational wave friction and gravitational slip
• Measuring the distortion of time with relativistic effects in large-scale structure
• Disentangling modified gravity from a dark force with gravitational redshift
• Euclid: Relativistic effects in the dipole of the 2-point correlation function
• Using relativistic effects in large-scale structure to constrain astrophysical properties of galaxy populations
• Model-Independent Test for Gravity using Intensity Mapping and Galaxy Clustering
• A Light-Cone Approach to Higher-Order Cosmological Observables