Effects of primordial magnetic field on the formation rate of dark matter halos

We construct and demonstrate a method for computing the formation rate of the dark matter halo in the hierarchical model set up. This method uses the Press-Schecter distribution for the halos and hence applies only to the spherical halos. But this can be generalized to ellipsoidal structures also if one uses the Sheth-Torman distribution. After obtaining the formation rate, we study the effect of primordial magnetic field on the dynamics of these halos. We investigate the effect for different field strengths and conclude that a magnetic field stronger than 10 nG would impact the halos larger than (10^{8}) solar masses while a weaker field affects the formation rate of smaller halos.