Corrections to halo model in presence of primordial magnetic field

Abstract

We study the role played by the primordial magnetic field in the process of structure formation in the early universe. We have compared the halo mass abundance in the presence and absence of the magnetic field. We derive a modified Press-Schechter formula in presence of another source for matter perturbation and use it to study how this extra source affects halo count. This other source is the magnetic field with a given power spectrum. We find the ranges for the magnetic field strength over which the field enhances the halo formation for a mass range for spectral index \(n_{b} = -2.95\). We found that for field strength less than or equal to \(B = 7.0~\mbox{nG}\), which we call the cut-off field strength, the presence of magnetic field enhances halo formation at low mass scale while it disrupts for a stronger field. We further investigate the dependence of halo count on the spectral index of the magnetic field power spectrum. We observe that at the cut-off field strength, halo formation is disrupted for a spectral index larger than −2.9. We carry out similar investigation for the more generic ellipsoidal collapse where the mass function is given by the Sheth-Tormen formula. For this case we find the cut-off field strength is \(5.5~\mbox{nG}\).