Screened fifth forces in parity-breaking correlation functions
  Cross-correlating two different types of galaxy gives rise to parity breaking
in the correlation function that derives from differences in the galaxies'
properties and environments. This is typically associated with a difference in
galaxy bias, describing the relation between galaxy number density and dark
matter density, although observational effects such as magnification bias also
play a role. In this paper we show that the presence of a screened fifth force
adds additional degrees of freedom to the correlation function, describing the
effective coupling of the force to the two galaxy populations. These are also
properties of the galaxies' environments, but with different dependence in
general to galaxy bias. We derive the parity-breaking correlation function
analytically as a function of fifth-force strength and the two populations'
fifth-force charges, and explore the result numerically using Hu-Sawicki $f(R)$
as a toy model of chameleon screening. We find that screening gives rise to an
octopole, which, in the absence of magnification bias, is not present in any
gravity theory without screening and thus is a qualitatively distinct
signature. The modification to the dipole and octopole can be
$\mathcal{O}(10\%)$ and $\mathcal{O}(100\%)$ respectively at redshift $z
\gtrsim 0.5$ due to screening, but decreases towards lower redshift. The change
in the background power spectrum in $f(R)$ theories induces a change in the
dipole of roughly the same size, but dominant to the effect of screening at low
$z$. While current data is insufficient to measure the parity-breaking dipole
or octopole to the precision required to test these models, future surveys such
as DESI, Euclid and SKA have the potential to probe screened fifth forces
through the dipole.
