The effective fluid approach for modified gravity
  Current and coming surveys will require sub-percent agreement in theoretical
accuracy to test the different cosmological and gravity scenarios. This can be
performed with Boltzmann solvers, i.e. codes that solve the linear evolution of
cosmological perturbations. Given the plethora of gravity models, it is crucial
to have a standardized unified way to describe all of them and take them into
account in a Boltzmann code. Dark Energy (DE) and Modified Gravity (MG) models,
although at a first glance quite dissimilar, are possible to unify them within
the same framework. In this paper we present a scenario, based on the effective
fluid approach that allows to map any modified gravity model as an effective
dark energy fluid and then we show how to implement it into existing Boltzmann
codes in a simple and straightforward way. This approach has also the advantage
that only a handful of variables are needed to compute, i.e the equation of
state $w(a)$ at the background level and the sound speed $c_s^2(a,k)$ and the
anisotropic stress $\pi(a,k)$ at the linear perturbation. In particular we show
that with simple modifications to the latter Cosmic Linear Anisotropy Solving
System (CLASS) code, which we called EFCLASS, we provide competitive results in
a much simpler and less error-prone approach in including the effects of
modified gravity models. To test our modifications, we particularize the
effective fluid approach to f(R) theories and a surviving class of Horndeski
models, the designer Horndeski (HDES) which have a background exactly to the
standard cosmological model $\Lambda$CDM.
