Summary: | There are compelling evidences of gravitational effects from dark matter in cosmology and astronomy. By studying other imprints besides gravity, we might be able to infer its properties and interactions with Standard Model particles. This thesis explores how different dark matter models generate interesting observables and what can be learned by looking into various datasets. I demonstrate that novel techniques and datasets from indirect searches can be combined to set stringent constraints on the model parameters. In particular, this thesis details the calculations of constraints from two directions: on the one hand I will show how to constrain the rate of scattering, decay, and annihilation by taking advantage of cosmological observables including the Cosmic Microwave Background and the 21-cm neutral hydrogen line; on the other hand I will exploit astronomical datasets to infer properties of dark matter substructures and halo structures. The sources of the observables span a wide of range of cosmological time from cosmological recombination to the late-time universe, and they can be applied to probe complementary parameter space. With the upcoming precision measurements of astronomy, these novel ideas and calculations of indirect detections will lead insight into the nature of dark matter.
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