COSMO
In the literature: open
Does the growth rate of structure follow general relativity?
In plain words
In general relativity the rate at which clumps grow follows directly from the expansion history. Measuring both separately tests whether gravity on cosmic scales is the same as in the solar system.
Precise statement
Measure the growth index $\gamma$ in $f(z) = \Omega_m(z)^\gamma$, where f = dln(delta)/dln(a), over $0 < z < 2$ from redshift-space distortions, peculiar velocities and lensing; general relativity with LCDM gives $\gamma \sim 0.55$. An answer is $\gamma$ with uncertainty below 0.02 and a test of its redshift dependence.
What would settle it
DESI and Euclid redshift-space distortions combined with Rubin weak lensing and peculiar-velocity surveys.