Combining gravitational lensing and gravitational redshift to measure the anisotropic stress with future galaxy surveys

Understand

Galaxy surveys provide one of the best ways to constrain the theory of gravity at cosmological scales.

• They can be used to constrain the two gravitational potentials encoding time, $\Psi$, and spatial, $\Phi$, distortions, which are exactly equal at late time within general relativity.
• Hence, any small variation leading to a nonzero anisotropic stress, i.e.
• a difference between these potentials, would be an indication for modified gravity.