*Cosmo Comments*. The following comments can also be viewed as annotations on the paper via Hypothesis.

The paper updates previously published constraints (1505.05511) on the dark matter decay rate by including Planck SZ cluster counts and incorporating new WL data. In my opinion, several major points should be addressed before these constraints can be considered robust (some also apply to the previous paper):

1. The paper does not account for the nuisance parameters of the likelihoods that are used to constrain the DDM model. For the weak lensing side: Are the scale cuts identical to the fiducial analysis? How are intrinsic alignment or baryonic effects treated? I assume all of those are identical to the standard KiDS analysis, but why are the authors confident that the same assumptions hold in extended models that substantially change the growth of structures?

2. Concerning the BAO results: BOSS assumes a $\Lambda$CDM cosmology to reconstruct the BAO peak before fitting, and this procedure severely reduces error bars. This is not necessarily directly applicable in extended models, so the larger pre-reconstruction errors should be used.

3. The constraining power of the Planck SZ clusters depends sensitively on assumptions on the mass bias $(1-b)$, as discussed in the original Planck papers. At present, this paper does not discuss this. Since the major effect of DDM is a mass shift of the clusters, I expect $(1-b)$ to be degenerate with the decay rate constraint from clusters.

What are the mass bias priors used for this analysis? How do the results depend on choosing another prior?

4. When identifying the halos in the simulation, the authors use $\Delta=500$ and mention that this refers to the mean background density in DDM. Note that the Planck clusters are defined with $M_{\rm 500c} = 4\pi/3 R^3 \rho_{\rm crit}(z)$, compared to the critical density at the cluster redshift. Is this consistent with the definition used in the analysis?

Also: does defining the cluster mass compared to the DDM mean density (neglecting the dark radiation) induce an artificial time evolution in the cluster mass definition that can mirror a suppression?

5. The fitting formula describing the halo mass function suppression shown in Fig. 4 lacks error bars. Those may be substantial, since the mass function is almost consistent with no modification at all, judging from the figure for $1/\Gamma = 100$Gyr. A way to incorporate that would be to include errors for the fitting function parameters (which may be quite large) and marginalise over them.

6. I am very surprised by the $\omega_{\rm ddm}/\sigma_8$ contour in Figs. 2, 3. The WL likelihood should not be able to shift the CMB contour by that much. WL has basically no constraint on $\Omega h^2$ at all (since it does not constrain $H_0$), so I find this hard to believe. The authors may want to clarify what is actually shown in these figures.

7. The KiDS collaboration claims to be in tension with Planck results. It is possible that decaying dark matter models will weaken this tension, but this has to be checked explicitly before combining the likelihoods. It would be interesting to see a plot with KiDS and Planck constraints on $S_8/\Omega_{\rm m}$ within a $\Lambda$DDM model to check the compatibility of the probes.

As a general remark, I assume that the authors chose a decay channel into dark radiation to simplify the analysis, but it would be nice to comment briefly on how to achieve this in particle physics models without also creating a new light degree of freedom that is populated in the early universe.

*[These comments were shared with us by a member of the cosmology community. They do not necessarily reflect the opinion of the Cosmo Comments team.]*