  We derive the details of a new screening mechanism where the interactions of
baryons and dark matter can be screened according to the local dark matter
density. In this mechanism, the value of Newton's constant is dark matter
density-dependent, allowing for the possibility that astrophysical phenomena
are very different in galaxies less dense than the Milky Way. The parameterized
post Newtonian parameter $\gamma$, which quantifies the difference between
kinematical and lensing probes, also depends on dark matter density. We
calculate the effects of varying $G$ on various stages of stellar evolution,
focusing on observables that impact cosmology: the Cepheid period--luminosity
relation and the supernova Ia magnitude--redshift relation. Other potential
tests of the model are also investigated including main-sequence, post-main
sequence, and low mass dwarf stars. Finally, we discuss how extragalactic tests
of $\gamma$ could provide complementary constraints.
