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Despite the ever growing observational evidence for the existence of thelarge scale magnetic fields, their origin and the evolution are not fullyunderstood. If the magnetic fields are of primordial origin, they result in thegeneration of the secondary matter density perturbations and the previousstudies show that such density perturbations enhance the number of dark matterhalos. We extend the conventional spherical collapse model by including theLorentz force which has not been implemented in the previous analysis to studythe evolution of density perturbations produced by primordial magnetic fields.The critical over-density $\delta_{\rm c}$ characterizing the halo massfunction turns out to be a bigger value, $\delta_{\rm c}\simeq 1.78$, than theconventional one $\delta_{\rm c}\simeq 1.69$ for the perturbations evolved onlyby the gravitational force.  The difference in $\delta_{\rm c}$ between our model and the fully matterdominated cosmological model is small at a low redshift and, hence, only thehigh mass tail of the mass function is affected by the magnetic fields. At ahigh redshift, on the other hand, the difference in $\delta_{\rm c}$ becomeslarge 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 $z=9$.

The influence of primordial magnetic fields on the spherical collapse model in cosmology