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

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 Kilometre Array, will allow us to measure the distortion of time with an accuracy of 10-30 per cent. 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.

Automated summary

In order to test the theory of gravity, it is necessary to investigate the distortion of space and time caused by matter, as well as how matter moves in a distorted space-time. Current observations have provided constraints on the motion of matter using redshift-space distortions, but only the combined measurement of spatial and temporal distortions through gravitational lensing. This letter introduces a method to measure time distortion independently, which will be possible with upcoming galaxy surveys like the Square Kilometre Array, allowing for an accuracy of 10-30 percent. This measurement will be crucial for testing deviations from the Lambda CDM model in a model-independent manner, particularly for distinguishing between modifications of gravity and dark fifth forces acting on dark matter.