  Various models of modified gravity invoke ``screening'' mechanisms that are
sensitive to the value of the local gravitational potential. This could have
observable consequences for galaxies. These consequences might be seen by
comparing two proxies for galaxy mass -- their luminosity and their internal
kinematics -- as a function of local galaxy density. Motivated by this
prospect, we have compared the observed properties of luminous red galaxies
(LRGs) inside and outside of voids in the cosmic large scale structure. We used
archival measurements of line widths, luminosities, redshifts, colors, and
positions of galaxies in conjunction with recent void catalogs to construct
comparison LRG samples inside and outside of voids. We fitted these two samples
to the well-established fundamental plane of elliptical galaxies to constrain
any differences between the inferred value of the Newtonian gravitational
constant G for the two samples. We obtained a null result, with an upper limit
on any fractional difference in G within and outside of cosmological voids to
be $\alpha =\delta$$ G/G \sim$ 40\%. This upper bound is dominated by the
small-number statistics of our N $\sim $ 100 within-void LRG sample. With the
caveat that environmental effects could influence various parameters such as
star formation, we estimate that a 1\% statistical limit on $\alpha$ could be
attained with data from 10${^5}$ elliptical galaxies within voids. This is
within the reach of future photometric and spectroscopic surveys, both of which
are required to pursue this method.
