  We present a systematic exploration of dark energy and modified gravity
models containing a single scalar field non-minimally coupled to the metric.
Even though the parameter space is large, by exploiting an effective field
theory (EFT) formulation and by imposing simple physical constraints such as
stability conditions and (sub-)luminal propagation of perturbations, we arrive
at a number of generic predictions. (1) The linear growth rate of matter
density fluctuations is generally suppressed compared to $\Lambda$CDM at
intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction
of an attractive long-range scalar force. This is due to the fact that, in
self-accelerating models, the background gravitational coupling weakens at
intermediate redshifts, over-compensating the effect of the attractive scalar
force. (2) At higher redshifts, the opposite happens; we identify a period of
super-growth when the linear growth rate is larger than that predicted by
$\Lambda$CDM. (3) The gravitational slip parameter $\eta$ - the ratio of the
space part of the metric perturbation to the time part - is bounded from above.
For Brans-Dicke-type theories $\eta$ is at most unity. For more general
theories, $\eta$ can exceed unity at intermediate redshifts, but not more than
about $1.5$ if, at the same time, the linear growth rate is to be compatible
with current observational constraints. We caution against phenomenological
parametrization of data that do not correspond to predictions from viable
physical theories. We advocate the EFT approach as a way to constrain new
physics from future large-scale-structure data.
