The influence of primordial magnetic fields on the spherical collapse
  model in cosmology
  Despite the ever growing observational evidence for the existence of the
large scale magnetic fields, their origin and the evolution are not fully
understood. If the magnetic fields are of primordial origin, they result in the
generation of the secondary matter density perturbations and the previous
studies show that such density perturbations enhance the number of dark matter
halos. We extend the conventional spherical collapse model by including the
Lorentz force which has not been implemented in the previous analysis to study
the evolution of density perturbations produced by primordial magnetic fields.
The critical over-density $\delta_{\rm c}$ characterizing the halo mass
function turns out to be a bigger value, $\delta_{\rm c}\simeq 1.78$, than the
conventional one $\delta_{\rm c}\simeq 1.69$ for the perturbations evolved only
by the gravitational force.
  The difference in $\delta_{\rm c}$ between our model and the fully matter
dominated cosmological model is small at a low redshift and, hence, only the
high mass tail of the mass function is affected by the magnetic fields. At a
high redshift, on the other hand, the difference in $\delta_{\rm c}$ becomes
large enough to suppress the halo abundance over a wide range of mass scales.
The halo abundance is reduced for instance by as large a factor as $\sim10^5$
at $z=9$.
