  Context. Infrared Faint Radio Sources (IFRS) are extragalactic emitters
clearly detected at radio wavelengths but barely detected or undetected at
optical and infrared wavelengths, with 5 sigma sensitivities as low as 1 uJy.
Aims. Recent SED-modelling and analysis of their radio properties shows that
IFRS are consistent with a population of (potentially extremely obscured)
high-redshift AGN at 3<z<6. We demonstrate some astrophysical implications of
this population and compare them to predictions from models of galaxy evolution
and structure formation.
  Methods. We compiled a list of IFRS from four deep extragalactic surveys and
extrapolated the IFRS number density to a survey-independent value of (30.8 +-
15.0) per square degree. We computed the IFRS contribution to the total number
of AGN in the Universe to account for the Cosmic X-ray Background. By
estimating the black hole mass contained in IFRS, we present conclusions for
the SMBH mass density in the early universe and compare it to relevant
simulations of structure formation after the Big Bang.
  Results. The number density of AGN derived from the IFRS density was found to
be about 310 deg^-2, which is equivalent to a SMBH mass density of the order of
10^3 M_sun Mpc^-3 in the redshift range 3<z<6. This produces an X-ray flux of 9
10^-16 W m^-2 deg^-2 in the 0.5-2.0 keV band and 3 10^-15 W m^-2 deg^-2 in the
2.0-10 keV band, in agreement with the missing unresolved components of the
Cosmic X-ray Background. Concerning the problem of SMBH formation after the Big
Bang we find evidence for a scenario involving both halo gas accretion and
major mergers.
