Cosmic Growth Signatures of Modified Gravitational Strength
  Cosmic growth of large scale structure probes the entire history of cosmic
expansion and gravitational coupling. To get a clear picture of the effects of
modification of gravity we consider a deviation in the coupling strength
(effective Newton's constant) at different redshifts, with different durations
and amplitudes. We derive, analytically and numerically, the impact on the
growth rate and growth amplitude. Galaxy redshift surveys can measure a product
of these through redshift space distortions and we connect the modified gravity
to the observable in a way that may provide a useful parametrization of the
ability of future surveys to test gravity. In particular, modifications during
the matter dominated era can be treated by a single parameter, the "area" of
the modification, to an accuracy of $\sim0.3\%$ in the observables. We project
constraints on both early and late time gravity for the Dark Energy
Spectroscopic Instrument and discuss what is needed for tightening tests of
gravity to better than 5% uncertainty.
