  We present a new catalogue of ~2,400 optically selected quasars with
spectroscopic redshifts and X-ray observations from either Chandra or
XMM-Newton. The sample can be used to investigate the non-linear relation
between the UV and X-ray luminosity of quasars, and to build a Hubble diagram
up to redshift z~7.5. We selected sources that are neither reddened by dust in
the optical/UV nor obscured by gas in the X-rays, and whose X-ray fluxes are
free from flux-limit related biases. After checking for any possible
systematics, we confirm, in agreement with our previous works, that (i) the
X-ray to UV relation provides distance estimates matching those from supernovae
up to z~1.5, and (ii) its slope shows no redshift evolution up to z~5. We
provide a full description of the methodology for testing cosmological models,
further supporting a trend whereby the Hubble diagram of quasars is well
reproduced by the standard flat $\Lambda$CDM model up to z~1.5-2, but strong
deviations emerge at higher redshifts. Since we have minimized all
non-negligible systematic effects, and proven the stability of the $L_{\rm
X}-L_{\rm UV}$ relation at high redshifts, we conclude that an evolution of the
expansion rate of the Universe should be considered as a possible explanation
for the observed deviation, rather than some systematic (redshift-dependent)
effect associated with high-redshift quasars.
