In the cold dark matter (CDM) picture of structure formation, galaxy mass distributions are predicted to have a considerable amount of structure on small scales. Strong gravitational lensing has proven to be a useful tool for studying this small-scale structure. Much of the attention has been given to detecting individual dark matter subhalos through lens modeling, but recent work has suggested that the full population of subhalos could be probed using a power spectrum analysis. In this paper we quantify the power spectrum of small-scale structure in simulated galaxies, with the goal of understanding theoretical predictions and setting the stage for using measurements of the power spectrum to test dark matter models. We use a sample of simulated galaxies generated from the texttt{Galacticus} semi-analytic model to determine the power spectrum distribution first in the CDM paradigm and then in a warm dark matter scenario. We find that a measurement of the slope and amplitude of the power spectrum on galaxy strong lensing scales ($ksim 1$ kpc$^{-1}$) could be used to distinguish between CDM and alternate dark matter models, especially if the most massive subhalos can be directly detected via gravitational imaging.
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