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We present cosmological results inferred from the effective-field theory(EFT) analysis of the full-shape of eBOSS quasars (QSO) power spectrum. Wevalidate our analysis pipeline against simulations, and find overall goodagreement between the analyses in Fourier and configuration space. Keeping thebaryon abundance and the spectral tilt fixed, we reconstruct at $68\%$ CL thefractional matter abundance $\Omega_m$, the reduced Hubble constant $h$, andthe 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. Theseconstraints are consistent at $\lesssim 1.8\sigma$ with the ones from Planckand from the EFT analysis of BOSS full-shape. Interestingly $S_8$ reconstructedfrom eBOSS QSO is slightly higher than that deduced from Planck and BOSS,although statistically consistent. In combination with the EFT likelihood ofBOSS, supernovae from Pantheon, and BAO from lyman-$\alpha$ and 6dF/MGS,constraints improve to $\Omega_m = 0.2985\pm 0.0069$ and $h = 0.6803\pm0.0075$, in agreement with Planck and with similar precision. We also exploreone-parameter extensions to $\Lambda$CDM and find that results are consistentwith flat $\Lambda$CDM at $\lesssim 1.3\sigma$. We obtain competitiveconstraints on the curvature density fraction $\Omega_k=-0.039\pm 0.029$, thedark energy equation of state $w_0=-1.038\pm 0.041$, the effective number ofrelativistic species $N_{\rm eff}=3.44^{+0.44}_{-0.91}$ at $68\%$ CL, and thesum of neutrino masses $\sum m_\nu<0.274e$V at $95\%$ CL, without Planck data.Including Planck data, contraints significantly improve thanks to the largelever arm in redshift between LSS and CMB measurements. In particular, weobtain the stringent constraint $\sum m_\nu<0.093e$V, competitive with recentlyman-$\alpha$ forest power spectrum bound.

Cosmological inference from the EFTofLSS: the eBOSS QSO full-shape analysis