  If captured by the gravitational field of stars or other compact objects,
dark matter can self-annihilate and produce a potentially detectable particle
flux. In the case of superheavy dark matter ($ m_{X} \gtrsim 10^{8} GeV $), a
large number of scattering events with nuclei inside stars are necessary to
slow down the dark matter particles below the escape velocity of the stars, at
which point the Dark Matter (DM) particle becomes trapped, or captured. Using
the recently developed analytical formalism for multiscatter capture, combined
with the latest results on the constraints of dark-matter-baryon scattering
cross-section, we calculate upper bounds on the capture rates for superheavy
dark matter particles by the first (Pop. III) stars. Assuming that a non-zero
fraction of the products of captured superheavy dark matter (SHDM)
annihilations can be trapped and thermalized inside the star we find that this
additional heat source could influence the evolutionary phase of Pop. III
stars. Moreover, requiring that Pop. III stars shine with sub-Eddington
luminosity, we find upper bounds on the masses of the Pop. III stars. This
implies a DM dependent cutoff on the initial mass function (IMF) of Pop. III
stars, thus opening up the intriguing possibility of constraining DM properties
using the IMF of extremely metal-poor stars.
