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If a fraction $f_{\rm dcdm}$ of the Dark Matter decays into invisible and massless particles (so-called "dark radiation") with the decay rate (or inverse lifetime) $\Gamma_{\rm dcdm}$, such decay will leave distinctive imprints on cosmological observables.
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O. Bertolami, F. Gil Pedro and M. Le Delliou, “Dark Energy-Dark Matter Interaction and the Violation of the Equivalence Principle from the Abell Cluster A586,” Phys. Lett. B
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F. D’Eramo, R. Z. Ferreira, A. Notari and J. L. Bernal, “Hot Axions and the H 0 H_{0} tension,” JCAP
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S. Tulin and H. B. Yu, “Dark Matter Self-interactions and Small Scale Structure,” Phys. Rept
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2019
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