A Multi-tracer Analysis for the eBOSS galaxy sample based on the Effective Field Theory of Large-scale Structure

We perform a multi-tracer full-shape analysis in Fourier space based on the effective field theory of large-scale structure (EFTofLSS) using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and emission line galaxy (ELG) samples. We study in detail the impact of the volume projection effect and different prior choices when doing the full-shape analysis based on the EFTofLSS model. We show that adopting a combination of Jeffreys prior and Gaussian prior can mitigate the volume effect and avoid exploring unphysical regions in the parameter space at the same time, which is crucial when jointly analysing the eBOSS LRG and ELG samples. We validate our pipeline using 1000 eBOSS EZmocks. By performing a multi-tracer analysis on mocks with comparable footprints, we find that cosmological constraints can be improved by $\sim10-40\%$ depending on whether we assume zero stochastic terms in the cross power spectrum, which breaks the degeneracy and boosts the constraints on the standard deviation of matter density fluctuation $\sigma_8$. Combining with the Big Bang Nucleosynthesis (BBN) prior and fixing the spectral tilt $n_s$ to Planck value, our multi-tracer full-shape analysis measures $H_0=70.0\pm2.3~{\rm km}~{\rm s}^{-1} {\rm Mpc}^{-1}$, $\Omega_m=0.317^{+0.017}_{-0.021}$, $\sigma_8=0.787_{-0.062}^{+0.055}$ and $S_8=0.809_{-0.078}^{+0.064}$, consistent with the Planck 2018 results. In particular, the constraint on $\sigma_8$ is improved beyond that obtained from the single tracer analysis by $18\%$, or by $27\%$ when assuming zero stochastic terms in the cross power spectrum.