$N$-body simulation of early structure formation from cosmic string loops

By means of $N$-body simulations, we study early structure formation in the presence of a scaling distribution of cosmic string loops. Cosmic string loops dominate the high redshift halo mass function while the fluctuations seeded by the standard structure formation scenario dominate structure at low redshifts. In our study, the effects of the cosmic string loops are taken into account by displacing the dark matter particles and their velocities at the initial time of the simulation by amounts determined by the analytical analysis which makes use of the Zel'dovich approximation. We find that the resulting halo mass function is to a good approximation given by the sum of the analytically determined cosmic string halo mass function and the halo mass function obtained from the standard $\Lambda \mathrm{CDM}$ model.