Optimising growth of structure constraints on modified gravity
  We use growth of structure data to constrain the effective field theory of
dark energy. Considering as case study Horndeski theories with the speed of
gravitational waves equal to that of light, we show how constraints on the free
parameters and the large-scale structure phenomenological functions can be
improved by two ingredients: firstly by complementing the set of redshift-space
distortions data with the three recent measurements of the growth rate $f$ and
the amplitude of matter fluctuations $\sigma_8$ from the VIPERS and SDSS
collaborations; secondly by applying a local Solar System bound on the
variation of the Newton constant. This analysis allows us to conclude that:
$i)$ despite firmly restricting the predictions of weaker gravity, the
inclusion of the Solar System bound does not prevent suppressed growth relative
to the standard model $\Lambda$CDM at low redshifts; $ii)$ the same bound in
conjunction with the growth of structure data strongly restricts the redshift
evolution of the gravitational slip parameter to be close to unity and the
present value is constrained to one at the $10^{-3}$ level; $iii)$ the growth
of structure data favours a fifth force contribution to the effective
gravitational coupling at low redshifts and at more than one sigma at present
time.
