  We explore the phenomenological consequences of general late-time
modifications of gravity in the quasi-static approximation, in the case where
cold dark matter is non-minimally coupled to the gravitational sector. Assuming
spectroscopic and photometric surveys with configuration parameters similar to
those of the Euclid mission, we derive constraints on our effective description
from three observables: the galaxy power spectrum in redshift space,
tomographic weak-lensing shear power spectrum and the correlation spectrum
between the integrated Sachs-Wolfe effect and the galaxy distribution. In
particular, with $\Lambda$CDM as fiducial model and a specific choice for the
time dependence of our effective functions, we perform a Fisher matrix analysis
and find that the unmarginalized $68\%$ CL errors on the parameters describing
the modifications of gravity are of order $\sigma\sim10^{-2}$--$10^{-3}$. We
also consider two other fiducial models. A nonminimal coupling of CDM enhances
the effects of modified gravity and reduces the above statistical errors
accordingly. In all cases, we find that the parameters are highly degenerate,
which prevents the inversion of the Fisher matrices. Some of these degeneracies
can be broken by combining all three observational probes.
