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 behaviour of fσ8and EG that, unlike the Λ cold dark matter (ΛCDM) 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 cosmic microwave background lensing, the WiggleZ galaxy survey and the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), weak-lensing survey measurements. We find that while WiggleZ data favour a non-vanishing value of the Hu-Sawicki model parameter, log10(-fR0, and consequently a large value of σ8, CFHTLenS drags the estimate of log10(-fR0back to the ΛCDM limit.