Testing Hu-Sawicki f(R) gravity with the Effective Field Theory approach
  We show how to fully map a specific model of modified gravity into the
Einstein-Boltzmann solver EFTCAMB. This approach consists in few steps and
allows to obtain the cosmological phenomenology of a model with minimal effort.
We discuss all these steps, from the solution of the dynamical equations for
the cosmological background of the model to the use of the mapping relations to
cast the model into the effective field theory language and use the latter to
solve for perturbations. We choose the Hu-Sawicki f(R) model of gravity as our
working example. After solving the background and performing the mapping, we
interface the algorithm with EFTCAMB and take advantage of the effective field
theory framework to integrate the full dynamics of linear perturbations,
returning all quantities needed to accurately compare the model with
observations. We discuss some observational signatures of this model, focusing
on the linear growth of cosmic structures. In particular we present the
behavior of $f\sigma_8$ and $E_G$ that, unlike the $\Lambda$CDM scenario, are
generally scale dependent in addition to redshift dependent. Finally, we study
the observational implications of the model by comparing its cosmological
predictions to the Planck 2015 data, including CMB lensing, the WiggleZ galaxy
survey and the CFHTLenS weak lensing survey measurements. We find that while
WiggleZ data favor a non-vanishing value of the Hu-Sawicki model parameter,
$\log_{10}(-f^0_{R})$, and consequently a large value of $\sigma_8$, CFHTLenS
drags the estimate of $\log_{10}(-f^0_{R})$ back to the $\Lambda$CDM limit.
