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Extragalactic gamma-ray signal from Dark Matter annihilation: a power spectrum based computation

We revisit the computation of the extragalactic gamma-ray signal from cosmological dark matter annihilations. The prediction of this signal is notoriously model dependent, due to different descriptions of the clumpiness of the dark matter distribution at small scales, responsible for an enhancement with respect to the smoothly distributed case. We show how a direct computation of this "flux multiplier" in terms of the nonlinear power spectrum offers a conceptually simpler approach and may ease some problems, such as the extrapolation issue. In fact very simple analytical recipes to construct the power spectrum yield results similar to the popular Halo Model expectations, with a straightforward alternative estimate of errors. For this specific application, one also obviates to the need of identifying (often literature-dependent) concepts entering the Halo Model, to compare different simulations.