  Effects from nonstandard corrections to Newtonian gravity, at large scale,
can be investigated using the cosmological structure formation. In particular,
it is possible to show if and how a logarithmic correction (as that induced
from nonlocal gravity) modifies the clustering properties of galaxies and of
clusters of galaxies. The thermodynamics of such systems can be used to obtain
important information about the effects of such modification on clustering. We
will compare its effects with observational data and it will be demonstrated
that the observations seem to point to a characteristic scale where such a
logarithmic correction might be in play at galactic scales. However, at larger
scales such statistical inferences are much weaker, so that a fully reliable
statistical evidence for this kind of corrections cannot be stated without
further investigations and the use of more varied and precise cosmological and
astrophysical probes.
