Decay of multiple dark matter particles to dark radiation in different epochs does not alleviate the Hubble tension

Decaying cold dark matter (CDM) has been considered as a mechanism to tackle the tensions in the Hubble expansion rate and the clustering of matter. However, polarization measurements of the cosmic microwave background (CMB) severely constrain the fraction of dark matter decaying before recombination, and lensing of the CMB anisotropies by large-scale structure set strong constraints on dark matter decaying after recombination. Together, these constraints make an explanation of the Hubble tension in terms of decaying dark matter unlikely. In response to this situation, we investigate whether a dark matter ensemble with CDM particles decaying into free streaming dark radiation in different epochs can alleviate the problem. We find that it does not.