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 show that the parity-breaking correlation function can be calculated analytically, under simplifying approximations, 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 is thus a qualitatively distinct signature. The modification to the dipole and octopole can be O(10%) and O(100%) respectively at redshift z greater than or similar to 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 dark energy spectroscopic survey, Euclid and square kilometre array have the potential to probe screened fifth forces through the parity breaking correlation function.