Cosmology with quasars: predictions for eROSITA from a quasar Hubble
  diagram
  Our group has developed a technique that makes use of the observed non-linear
relation between the ultraviolet and the X-ray luminosity in quasars to provide
an independent measurement of their distances, thus turning quasars into
standardizable candles. This technique, at present, it is mostly based upon
quasar samples with data from public catalogues both in the X-rays and in the
optical/ultraviolet and extends the Hubble diagram of supernovae to a redshift
range still poorly explored (z>2). From the X-ray perspective, we are now on
the eve of a major change, as the upcoming mission eROSITA is going to provide
us with up to ~3 millions of active galactic nuclei across the entire sky. Here
we present predictions for constraining cosmological parameters such as the
amount of dark matter ($\Omega_{\rm m}$), dark energy ($\Omega_\Lambda$) and
the evolution of the equation of state of dark energy ($w$) through the Hubble
diagram of quasars, based on the 4-year eROSITA all-sky survey. Our simulations
show that the eROSITA quasars, complemented by redshift and broad-band
photometric information, will supply the largest quasar sample at z<2, but with
very few objects available for cosmology at higher redshifts that survives the
cut for the Malmquist bias, as eROSITA will sample the brighter end of the
X-ray luminosity function. The power of the quasar Hubble diagram for precision
cosmology lies in the high-redshift regime, where quasars can be observed up to
redshift ~7.5, essential to discriminate amongst different model
extrapolations. Therefore, to be competitive for cosmology, the eROSITA quasar
Hubble diagram must be complemented with the already available quasar samples
and dedicated (deep) large programmes at redshift z>3.
