In this paper, we apply the statefinder diagnostic to the cosmology with the abnormally weighting energy hypothesis (AWE cosmology), in which dark energy in the observational (ordinary matter) frame results from the violation of the weak equivalence principle by pressureless matter. It is found that there exist closed loops in the statefinder plane, which is an interesting characteristic of the evolution trajectories of statefinder parameters and can be used to distinguish AWE cosmology from other cosmological models.
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Liu et al. (2008) studied this question.