Measuring the distortion of time with relativistic effects in large-scale structure

TL;DR

This paper proposes a new method to measure time distortions caused by relativistic effects in large-scale structures, enabling more precise tests of gravity theories and distinguishing between modifications of gravity and dark forces.

Contribution

It introduces a novel approach to isolate and measure time distortions independently, enhancing the capability of upcoming galaxy surveys like SKA to test gravity models.

Findings

Projected measurement accuracy of 10-30% with future surveys

Ability to distinguish between gravity modifications and dark forces

Provides a model-independent test of space-time distortions

Abstract

To test the theory of gravity one needs to test, on one hand, how space and time are distorted by matter and, on the other hand, how matter moves in a distorted space-time. Current observations provide tight constraints on the motion of matter, through the so-called redshift-space distortions, but they only provide a measurement of the sum of the spatial and temporal distortions, via gravitational lensing. In this Letter, we develop a method to measure the time distortion on its own. We show that the coming generation of galaxy surveys, like the Square Kilometer Array, will allow us to measure the distortion of time with an accuracy of 10-30%. Such a measurement will be essential to test deviations from the $\Lambda$CDM model in a fully model-independent way. In particular, it can be used to compare the spatial and temporal distortions of space-time and to unambiguously distinguish between modifications of gravity and dark fifth forces acting on dark matter.