Forecasted constraints on modified gravity from Sunyaev Zel'dovich
  tomography
  Observational cosmology has become an important laboratory for testing
General Relativity, with searches for modified gravity forming a significant
portion of the science case for existing and future surveys. In this paper, we
illustrate how future measurements of the Cosmic Microwave Background (CMB)
temperature and polarization anisotropies can be combined with large galaxy
surveys to improve constraints on modified gravity using the technique of
Sunyaev Zel'dovich (SZ) tomography. SZ tomography uses the correlations between
the kinetic/polarized SZ contributions to the small-angular scale CMB and the
distribution of structure measured in a galaxy redshift survey to reconstruct
the remote dipole and quadrupole fields, e.g. the CMB dipole and quadrupole
observed throughout the Universe. We compute the effect of a class of
modifications of gravity on the remote dipole and quadrupole fields,
illustrating that these observables combine a number of the desirable features
of existing probes. We then perform a fisher forecast of constraints on a
two-parameter class of modifications of gravity for next-generation CMB
experiments and galaxy surveys. By incorporating information from the
reconstructed remote dipole and quadrupole fields, we find that it is possible
to improve the constraints on this model by a factor of $\sim 2$ beyond what is
possible with a galaxy survey alone. We conclude that SZ tomography is a
promising method for testing gravity with future cosmological datasets.
