Testing modified (Horndeski) gravity by combining intrinsic
  galaxyalignments with cosmic shear
  We study the impact of modified gravity of the Horndeski class, on intrinsic
shape correlations in cosmic shear surveys. As intrinsic shape correlations
(IAs) are caused by tidal gravitational fields acting on galaxies as a
collection of massive non-relativistic test particles, they are only sensitive
to the gravitational potential, which forms in conjunction with the curvature
perturbation. In contrast, the cosmic shear signal probes the sum of these two,
i.e. both Bardeen-potentials. Combining these probes therefore constitutes a
test of gravity, derived from a single measurement.
  Focusing on linear scales and alignments of elliptical galaxies, we study the
impact on inference of the braiding $\hat{\alpha}_B$ and the time evolution of
the Planck mass $\hat{\alpha}_M$ by treating IAs as a genuine signal
contributing to the overall ellipticity correlation. We find that for
\textsc{Euclid}, IAs can help to improve constraints on modified gravity of the
Horndeski-class by 10 per cent if the alignment parameter needed for the linear
alignment model is provided by simulations. If, however, the IA needs to be
self calibrated, all of the sensitivity is put into the inference of the
alignment strength $D$ since there is a very strong correlation with the
evolution of the Planck mass. Thus diminishing the benefit of IA for probing
modified gravitational theories. While the present paper shows results mainly
for modified gravity parameters, similar deductions can be drawn for the
investigation of anisotropic stresses, parameterised modifications to the
Poisson-equation, the phenomenology of gravitational slip and to breaking
degeneracies in a standard cosmology.
