Observational constraints on dark matter models

In this short course, which complements the lecture on Dark Matter alternatives, I provide concrete examples of how Dark Matter (DM) models can be tested, whether for generic DM properties, or specific scenarios. First, I review searches for WIMPs, one of the most well-studied DM candidates. I also showcase some constraints on DM models that predict a modification of the cosmological matter power spectrum at high k <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>k</mml:mi> </mml:math> . To this end, I focus primarily on bounds derived from the Lyman- \alpha <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> forest observations, which I will present in a brief overview beforehand.