Early supersymmetric cold dark matter substructure

Earth-mass ``microhalos'' may be the first objects to virialize in the early universe. Their ability to survive the hierarchical clustering process as substructure in the larger halos that form subsequently has implications for dark matter detection experiments. We present a large N-body simulation of early substructure in a supersymmetric cold dark matter (SUSY-CDM) scenario characterized by an exponential cutoff in the power spectrum at M_c=10^-6 Msun. The simulation resolves a 0.014 Msun parent ``SUSY'' halo at z=75 with 14 million particles. On these scales the effective index of the power spectrum approaches -3, and a range of mass scales collapse almost simultaneously. Compared to a z=0 galaxy cluster substructure within our SUSY host is less evident both in phase-space and in physical space, and it is less resistant against tidal disruption. As the universe expands by a factor of 1.3, we find that between 20 and 40 percent of well-resolved SUSY substructure is destroyed, compared to only about 1 percent in the low-redshift cluster. Nevertheless SUSY substructure is just as abundant as in z=0 galaxy clusters, i.e. the normalized mass and circular velocity functions are very similar. The dark matter self-annihilation gamma-ray luminosity from bound subhalos and other deviations from a smooth spherical configuration is at least comparable to the spherically-averaged signal in the SUSY host, and at least three times larger than the spherically-averaged signal in the cluster host. Such components must be taken into account when estimating the total cosmological extragalactic gamma-ray annihilation background.(ABRIDGED)