Constraints on modified gravity from the BOSS galaxy survey

We develop a pipeline to set new constraints on scale-independent modified gravity, from the galaxy power spectrum in redshift space of BOSS DR12. The latter is modelled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory. We test our pipeline on synthetic and simulated data, to assess systematic biases on the inferred cosmological parameters due to marginalization and theoretical errors, and we apply it to the normal branch of the DGP model with a $\Lambda$CDM background. When applied to synthetic data and cosmological simulations, we observe biased posteriors due to the strong degeneracy between the nDGP parameter $\Omega_{\rm rc}$ and the primordial amplitude of fluctuations $A_s$. Fixing the latter to the Planck central value, we obtain a posterior distribution with $\Omega_{\rm rc}\lesssim 0.65$ at 95$\%$ C.L., under the assumption of a flat prior on $\log_{10} \Omega_{\rm rc}$. This upper bound, however, depends strongly on the prior on $\Omega_{\rm rc}$. To alleviate this effect, we provide an upper bound based on the Bayes factor between the nDGP model and $\Lambda$CDM model, which gives $\Omega_{\rm rc}\lesssim 0.2$ at 95$\%$ C.L..