Cosmological constraints with the Effective Fluid approach for Modified Gravity

We utilise the latest cosmological data and EFCLASS, our modified version of the Boltzmann solver CLASS following the Effective Fluid Approach, to derive constraints on three modified gravity models using a Markov Chain Monte Carlo method. In particular, we analyse the Designer $f(R)$ (DES-fR) and Designer Horndeski (HDES) models, but also the Hu $\&$ Sawicki $f(R)$ model (HS). We find tight constraints on the modified gravity parameters that parametrize the deviation from the $\Lambda$CDM model. For both the DES-fR and the HS model we obtain $\log_{10}b -5$ at $68\%$ confidence. We also examine the degeneracy between modified gravity and the neutrino mass and we find that the presence of the neutrino mass as a free parameter loosens the constraints. Compared to other standard analyses our Effective Fluid Approach has a couple of advantages. First, we model the background expansion for the various models correctly, something which is not always done in other codes and second, we examine the degeneracy with the sum of the neutrinos masses.