Cosmological inference from the eBOSS QSO full-shape analysis with optimal redshift weights
We present a full-shape power-spectrum analysis of the eBOSS DR16 quasar sample with optimal redshift weights. The DR16 QSO catalog contains 343,708 quasars over $0.8<z<2.2$, a redshift interval broad enough to contain useful light-cone evolution but not naturally captured by a single effective-redshift measurement. We construct Karhunen--Lo\`eve weights for the parameters of interest and measure the resulting monopole and quadrupole with a cross-correlation estimator, which remains well defined for sign-changing weights. The theoretical spectra are convolved with the measured Fourier-space survey-window kernels for each Galactic cap and weighting scheme, and both the covariance matrix and the end-to-end validation are based on 1000 EZ light-cone mock catalogs. In $\Lambda$CDM, the redshift-weighted and standard analyses give consistent constraints, as expected from the near-standard effective redshifts of the weights targeting $h$, $\Omega_{\rm m}$, and $A_s$. In the Chevallier--Polarski--Linder (CPL) model, the redshift-weighted DR16 analysis reduces the marginalized uncertainties on $H_0$, $\sigma_8$, and $w_0$ by $43.3\%$, $19.7\%$, and $20.5\%$, respectively, and turns the standard one-sided constraint on $w_a$ into a bounded posterior, $w_a=-0.98^{+1.0}_{-1.3}$. The gain is therefore concentrated where the model contains genuine redshift evolution, demonstrating that optimal redshift weighting can recover tomographic information from a wide QSO light cone while keeping the full-shape data vector compact.