The physics of gravity on cosmological scales affects both the rate of assembly of large-scale structure , and the gravitational lensing of background light through this cosmic web .
By comparing the amplitude of these different observational signatures , we can construct tests that can distinguish General Relativity from its potential modifications .
We use the latest weak gravitational lensing dataset from the Kilo-Degree Survey , KiDS-1000 , in conjunction with overlapping galaxy spectroscopic redshift surveys BOSS and 2dFLenS , to perform the most precise existing amplitude-ratio test .
We measure the associated E _ { \mathrm { G } } statistic with 15 - 20 \% errors , in five \Delta z = 0.1 tomographic redshift bins in the range 0.2 < z < 0.7 , on projected scales up to 100 h ^ { -1 } Mpc .
The scale-independence and redshift-dependence of these measurements are consistent with the theoretical expectation of General Relativity in a Universe with matter density \Omega _ { \mathrm { m } } = 0.27 \pm 0.04 .
We demonstrate that our results are robust against different analysis choices , including schemes for correcting the effects of source photometric redshift errors , and compare the performance of angular and projected galaxy-galaxy lensing statistics .