Abstract
We present cosmological results inferred from the effective-field theory (EFT) analysis of the full-shape of eBOSS quasars (QSO) power spectrum. We validate our analysis pipeline against simulations, and find overall good agreement between the analyses in Fourier and configuration space. Keeping the baryon abundance and the spectral tilt fixed, we reconstruct at $68\%$ CL the fractional matter abundance $\Omega_m$, the reduced Hubble constant $h$, and the clustering amplitude $\sigma_8$, to respectively $\Omega_m=0.327\pm 0.035$, $h=0.655\pm 0.034$, and $\sigma_8=0.880\pm 0.083$ from eBOSS QSO alone. These constraints are consistent at $\lesssim 1.8\sigma$ with the ones from Planck and from the EFT analysis of BOSS full-shape. Interestingly $S_8$ reconstructed from eBOSS QSO is slightly higher than that deduced from Planck and BOSS, although statistically consistent. In combination with the EFT likelihood of BOSS, supernovae from Pantheon, and BAO from lyman-$\alpha$ and 6dF/MGS, constraints improve to $\Omega_m = 0.2985\pm 0.0069$ and $h = 0.6803\pm 0.0075$, in agreement with Planck and with similar precision. We also explore one-parameter extensions to $\Lambda$CDM and find that results are consistent with flat $\Lambda$CDM at $\lesssim 1.1\sigma$. We obtain competitive constraints on the curvature density fraction $\Omega_k=-0.039\pm 0.029$, the dark energy equation of state $w_0=-1.038\pm 0.041$, the effective number of relativistic species $N_{\rm eff}=3.44^{+0.44}_{-0.91}$ at $68\%$ CL, and the sum of neutrino masses $\sum m_\nu<0.274e$V at $95\%$ CL, without Planck data. Including Planck data, contraints significantly improve thanks to the large lever arm in redshift between LSS and CMB measurements. In particular, we obtain the stringent constraint $\sum m_\nu<0.093e$V, competitive with recent lyman-$\alpha$ forest power spectrum bound.