  In the past few years, we built a Hubble diagram of quasars up to redshift
z$\sim$7, based on the nonlinear relation between quasars' x-ray and UV
luminosities. Such a Hubble diagram shows a >4$\sigma$ deviation from the
standard flat $\Lambda$CDM model at z>1.5. Given the important consequences of
this result, it is fundamental to rule out any systematic effect in the
selection of the sample and/or in the flux measurements, and to investigate
possible redshift dependences of the relation, that would invalidate the use of
quasars as standard candles. Here we review all the observational results
supporting our method: the match of the Hubble diagram of quasars with that of
supernovae in the common redshift range, the constant slope of the relation at
all redshifts, the redshift non-evolution of the spectral properties of our
sources both in the x-rays and in the UV. An independent test of our results
requires the observation of other standard candles at high redshift. In
particular, we expect that future observations of supernovas at z>2 will
confirm the deviation from the concordance model found with the Hubble diagram
of quasars.
