  The Alcock-Paczynski (AP) effect uses the fact that, when analyzed with the
correct geometry, we should observe structure that is statistically isotropic
in the Universe. For structure undergoing cosmological expansion with the
background, this constrains the product of the Hubble parameter and the angular
diameter distance. However, the expansion of the Universe is inhomogeneous and
local curvature depends on density. We argue that this distorts the AP effect
on small scales. After analyzing the dynamics of galaxy pairs in the Millennium
simulation, we find an interplay between peculiar velocities, galaxy properties
and local density that affects how pairs trace cosmological expansion. We find
that only low mass, isolated galaxy pairs trace the average expansion with a
minimum "correction" for peculiar velocities. Other pairs require larger, more
cosmology and redshift dependent peculiar velocity corrections and, in the
small-separation limit of being bound in a collapsed system, do not carry
cosmological information.
