A Hubble Diagram for Quasars
  We present a new method to test the cosmological model, based on the
non-linear relation between ultraviolet and X-ray luminosity of quasars. We
built a data set of ~1,138 quasars by merging several literature samples with
X-ray measurements at 2 keV and SDSS photometry, which was used to estimate the
extinction-corrected 2500 Angstrom flux. We obtained three main results: (1) we
checked the relation between X-ray and UV luminosities in small redshift bins
up to z~6, confirming that it holds at all redshifts with the same slope; (2)
we built a Hubble diagram for quasars up to z~6, which is well matched to that
of supernovae in the common z=0-1.4 interval, and extends the test of the
cosmological model up to z~6; (3) we showed that this relation is a powerful
tool to estimate cosmological parameters. Assuming a LambdaCDM model, we obtain
Omega_M=0.22+0.08-0.10 and Omega_Lambda=0.92+0.18-0.30 (Omega_M=0.28+-0.04 and
Omega_\Lambda=0.73+-0.08 from a joint quasar-SNe fit). However, much more
precise measurements will be achieved in the future. A few thousands SDSS
quasars already have serendipitous X-ray observations with Chandra or
XMM-Newton, and at least 100,000 quasars with UV and X-ray data will be
available from the eROSITA all-sky survey in a few years. Euclid, LSST, and
Athena surveys will further increase the sample size to at least several
hundred thousands. Our simulations show that these samples will provide tight
constraints on the cosmological parameters, and will allow to test possible
deviations from the standard model with higher precisions than available today.
