On the Reliability of Quasars as Cosmological Distance Indicators

We assess the viability of quasars as cosmological distance indicators based on the non-linear $L_X$--$L_{\rm UV}$ relation. We calibrate this relation in a model-independent way by anchoring quasar luminosity distances to cosmic-chronometer $H(z)$ measurements over $z\leq 1.43$, and construct a quasar Hubble diagram extending up to $z\simeq 7.5$. We compare a traditional stepwise approach, in which the calibration is fixed before cosmological inference, with a joint QSO+SN calibration--cosmology framework where calibration and cosmological parameters are sampled simultaneously. The stepwise analysis, supplemented with DESI DR2 BAO measurements and Planck compressed CMB distance priors, is used as a diagnostic benchmark, while the joint framework, with and without the SH0ES $H_0$ information, provides our main cosmological results. We selected a low-$z$ quasar subsample ($z<1.43$), matching the redshift range of the cosmic-chronometer calibration, and found calibration parameters consistent with previous studies. However, the stepwise cosmological constraints can become unstable once quasars are included, reflecting the incomplete propagation of calibration uncertainties and calibration--cosmology degeneracies. In contrast, the joint analysis yields self-consistent constraints because the quasar calibration parameters are fitted simultaneously with the cosmological parameters, allowing these uncertainties and degeneracies to be propagated into the final posteriors. Our results indicate that the current limitations of quasar cosmology are driven mainly by intrinsic scatter and possible sample-dependent effects in the $L_X$--$L_{\rm UV}$ relation, rather than by a fundamental inconsistency with standard cosmology.