https://doi.org/10.1140/epjc/s10052-019-7082-z
Regular Article - Theoretical Physics
A comparison of the 
and 
CDM cosmologies based on the observed halo mass function
1
Department of Physics, The University of Arizona, Tucson, AZ, 85721, USA
2
The Applied Math Program, Department of Physics, The University of Arizona, Tucson, AZ, 85721, USA
3
Department of Astronomy, The University of Arizona, Tucson, AZ, 85721, USA
* e-mail: fmelia@email.arizona.edu
Received:
5
June
2019
Accepted:
27
June
2019
Published online:
8
July
2019
The growth of structure may be traced via the redshift-dependent halo mass function. This quantity 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. The most common approach is to presume a relationship with galaxies and halos. Studies based on the assumption of a constant halo to stellar mass ratio 
(extrapolated from 
) reveal significant tension with CDM – a failure known as “The Impossibly Early Galaxy Problem”. But whether this ratio evolves or remains constant through redshift 
is still being debated. To eliminate the tension with CDM, 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 explore the possibility that this major inconsistency may instead be an indication that the cosmological model is not completely correct. We study this problem in the context of another Friedmann–Lemaître–Robertson–Walker (FLRW) model known as the universe, and use our previous measurement of 
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 is consistent with the data, even assuming a constant throughout the observed redshift range (
), contrasting sharply with the tension in CDM. We conclude that – if turns out to be constant – the massive galaxies and their halos must have formed earlier than is possible in CDM.
© The Author(s), 2019
