  The observed acceleration of the Universe can be explained by modifying
general relativity. One such attempt is the nonlocal model of Deser and
Woodard. Here we fix the background cosmology using results from the Planck
satellite and examine the predictions of nonlocal gravity for the evolution of
structure in the universe, confronting the model with three tests:
gravitational lensing, redshift space distortions, and the estimator of gravity
$E_G$. Current data favor general relativity (GR) over nonlocal gravity: fixing
primordial cosmology with the best fit parameters from Planck leads to weak
lensing results favoring GR by 5.9 sigma; redshift space distortions
measurements of the growth rate preferring GR by 7.8 sigma; and the single
measurement of $E_G$ favoring GR, but by less than 1-sigma. The significance
holds up even after the parameters are allowed to vary within Planck limits.
The larger lesson is that a successful modified gravity model will likely have
to suppress the growth of structure compared to general relativity.
