A comparison of the R_h=ct and LCDM cosmologies based on the observed
  halo mass function
  The growth of structure probes the re-ionization history and quasar abundance
in the Universe, constituting an important probe of the cosmological
predictions. Halos are not directly observable, however, so their mass and
evolution must be inferred indirectly. Studies based on the assumption of a
constant halo to stellar mass ratio M_h/M_* (extrapolated from z<4) reveal
significant tension with LCDM---a failure known as "The Impossibly Early Galaxy
Problem". But whether this ratio evolves or remains constant through redshift
4<z<10 is still being debated. To eliminate the tension with LCDM, it would
have to change by about 0.8 dex over this range, an issue that may be settled
by upcoming observations with the James Webb Space Telescope. In this paper, we
study this problem in the context of another
Friedmann-Lemaitre-Robertson-Walker (FLRW) model known as the R_h=ct universe,
and use our previous measurement of sigma_8 from the cosmological growth rate,
together with new solutions to the Einstein-Boltzmann equations, to interpret
these recent halo measurements. We demonstrate that the predicted mass and
redshift dependence of the halo distribution in R_h=ct is consistent with the
data, even assuming a constant M_h/M_* throughout the observed redshift range
(4<z<10), contrasting sharply with the tension in LCDM. We conclude that---if
M_h/M_* turns out to be constant---the massive galaxies and their halos must
have formed earlier than is possible in LCDM.
