Tomographic-spectral approach for dark matter detection in the cross-correlation between cosmic shear and diffuse γ-ray emission

We recently proposed to cross-correlate the diffuse extragalactic gamma-ray background with the gravitational lensing signal of cosmic shear. This represents a novel and promising strategy to search for annihilating or decaying particle dark matter (DM) candidates. In the present work, we demonstrate the potential of a tomographic-spectral approach: measuring the cross-correlation in separate bins of redshift and energy significantly improves the sensitivity to a DM signal. Indeed, the technique proposed here takes advantage of the different scaling of the astrophysical and DM components with redshift and, simultaneously of their different energy spectra and different angular extensions. The sensitivity to a particle DM signal is extremely promising even when the DM-induced emission is quite faint. We first quantify the prospects of detecting DM by cross-correlating the Fermi Large Area Telescope (LAT) diffuse gamma-ray background with the cosmic shear expected from the Dark Energy Survey. Under the hypothesis of a significant subhalo boost, such a measurement can deliver a 5 sigma detection of DM, if the DM particle is lighter than 300 GeV and has a thermal annihilation