Converting dark matter to dark radiation does not solve cosmological tensions

Tensions between cosmological parameters (in particular the local expansion rate $H_0$ and the amplitude of matter clustering $S_8$) inferred from low-redshift data and data from the cosmic microwave background (CMB) and large-scale structure (LSS) experiments have inspired many extensions to the standard cosmological model, $\Lambda$CDM. Models which simultaneously lessen both tensions are of particular interest. We consider one scenario with the potential for such a resolution, in which some fraction of the dark matter has converted into dark radiation since the release of the CMB. Such a scenario encompasses and generalizes the more standard "decaying dark matter" model, allowing additional flexibility in the rate and time at which the dark matter converts into dark radiation. In this paper, we constrain this scenario with a focus on exploring whether it can solve (or reduce) these tensions. We find that such a model is effectively ruled out by low-$\ell$ CMB data, in particular by the reduced peak-smearing due to CMB lensing and the excess Integrated Sachs--Wolfe (ISW) signal caused by the additional dark energy density required to preserve flatness after dark matter conversion into dark radiation. Thus, such a model does not have the power to reduce these tensions without further modifications. This conclusion extends and generalizes related conclusions derived for the standard decaying dark matter model.