Combined full shape analysis of BOSS galaxies and eBOSS quasars using an iterative emulator

Standard full-shape clustering analyses in Fourier space rely on a fixed power spectrum template, defined at the fiducial cosmology used to convert redshifts into distances, and compress the cosmological information into the Alcock-Paczynski parameters and the linear growth rate of structure. In this paper, we propose an analysis method that operates directly in the cosmology parameter space and varies the power spectrum template accordingly at each tested point. Predictions for the power spectrum multipoles from the TNS model are computed at different cosmologies in the framework of $\Lambda \rm{CDM}$. Applied to the final eBOSS QSO and LRG samples together with the low-z DR12 BOSS galaxy sample, our analysis results in a set of constraints on the cosmological parameters $\Omega_{\rm cdm}$, $H_0$, $\sigma_8$, $\Omega_{\rm b}$ and $n_s$. To reduce the number of computed models, we construct an iterative process to sample the likelihood surface, where each iteration consists of a Gaussian process regression. This method is validated with mocks from N-body simulations. From the combined analysis of the (e)BOSS data, we obtain the following constraints: $\sigma_8=0.877\pm 0.049$ and $\Omega_{\rm m}=0.304^{+0.016}_{-0.010}$ without any external prior. The eBOSS quasar sample alone shows a $3.1\sigma$ discrepancy compared to the Planck prediction.