Abstract
Cosmological models and their parameters are widely debated because of
theoretical and observational mismatches of the standard cosmological model,
especially the current discrepancy between the value of the Hubble constant,
$H_0$, obtained by Type Ia supernovae (SNe Ia), and the Cosmic Microwave
Background Radiation (CMB). Thus, considering high-redshift probes like quasars
(QSOs), having intermediate redshifts between SNe Ia and CMB, is a necessary
step. In this work, we use SNe Ia and the most updated QSO sample, reaching
redshifts up to $z\sim7.5$, applying the Risaliti-Lusso QSO relation based on a
non-linear relation between ultraviolet and X-ray luminosities. We consider
this relation both in its original form and corrected for selection biases and
evolution in redshift through a reliable statistical method also accounting for
the circularity problem. We also explore two approaches: with and without
calibration on SNe Ia. We then investigate flat and non-flat standard
cosmological models and a flat $w$CDM model, with a constant dark energy
equation of state parameter $w$. Remarkably, when correcting for the evolution
as a function of cosmology, we obtain closed constraints on $Ømega_M$ using
only non-calibrated QSOs. We find that considering non-calibrated QSOs combined
with SNe Ia and accounting for the same correction, our results are compatible
with a flat $Łambda$CDM model with $Ømega_M = 0.3$ and $H_0 = 70 \,
km\,s^-1\,Mpc^-1$. Intriguingly, the $H_0$ values obtained place
halfway between the one from SNe Ia and CMB, paving the way for new insights
into the $H_0$ tension.
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