A bstract We study a phenomenological model where the lightest dark matter (DM) particles are the pseudo-Goldstone excitations associated with a spontaneously broken symmetry, and transforming linearly with respect to an unbroken group $ {{mathcal{H}}_{mathrm{DM}}} $ . For definiteness we take $ {{mathcal{H}}_{mathrm{DM}}} $ = SU( N ) and assume the Goldstone particles are bosons; in parallel with QCD, we refer to these particles as dark-matter pions. This scenario is in contrast to the common assumption that DM fields transform linearly under the full symmetry of the model. We illustrate the formalism by treating in detail the case of $ {{mathcal{H}}_{mathrm{DM}}} $ = SU(2), in particular we calculate all the interactions relevant for the Boltzmann equations, which we solve numerically; we also derive approximate analytic solutions and show their consistency with the numerical results. We then compare the results with the constraints derived from the cold DM and direct detection experiments and derive the corresponding restrictions on the model parameters. We also briefly comment on constraints from indirect detection of DM.
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