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

This paper presents a study of the observational implications of a non-gravitational coupling between cold dark matter and dark energy. The authors briefly discuss the cosmological phenomenology of the model, which is an interacting vacuum scenario, although it is difficult to see what is new in this analysis with respect to previous works, as this model has been extensively studied before (e.g., Guo et al. 1702.04189, and references therein). They then present the constraints on the model as obtained with several observational datasets by including the neutrino mass and effective number of neutrinos. They argue that such a coupling can resolve the Hubble tension and that the posterior on $M_\nu$ can be wider than in ΛCDM.

A few specific remarks:

In the introduction, the authors state that Interacting Dark Energy (IDE) models have been found to be able to solve the cosmic coincidence problem. This is an incorrect statement in my opinion. There has been an abundance of parameter estimation studies that showed that the coupling needed to solve the coincidence problem is too large (excluded by data). Furthermore, recent research on the QFT (D'Amico et al. 1605.00996, Marsh 1606.01538) of interacting dark energy seems to point out that, in general, coupled models with background energy exchange suffer from serious problems coming from huge quantum corrections. For this reason (and also because usually IDE models with background energy exchange are severely constrained from the currently available data), claims about such models being able to alleviate the coincidence problem should be reconsidered.

The authors claim that the interaction in the dark sector is an excellent way to alleviate/solve the $H_0$ and $\sigma_8$ tensions. This statement is optimistic: some IDE models are interesting phenomenologically, but they are based on ad hoc couplings and extra free parameters such that ΛCDM is clearly preferred if one performs a Bayesian model selection analysis.

The authors claim that their chosen interaction function, $Q$, is the most natural and simple, but in fact, several authors (e.g. Ref. [12] in the manuscript, 0804.0232) have argued for the opposite: this form of $Q$ can be seen as problematic, as it raises the question how an interaction rate expected to depend on local interactions, is determined by a global quantity like the Hubble expansion. Some discussion of this seems necessary.

The authors may want to consider adding discussion and calculations on the covariance and gauge-invariance properties of their model. This has been shown to be necessary (see e.g. Valiviita et al. 0804.0232 and Clemson et al. 1109.6234) to construct meaningful models. A previous paper by Guo et al. (1702.04189) seems to have done a more thorough investigation of this.

It is unclear what assumptions for the nonlinear behaviour of the considered models are taken in this work. For example, what exactly is assumed in order to perform the BAO analysis and for the impact of massive neutrinos? Likelihoods are usually constructed under the ΛCDM assumption. If nonlinear scales are considered, the behaviour of an exotic model might be completely different.

It would be interesting to compare the results of this analysis with an uncoupled model where $w$ is allowed to vary (and massive neutrinos are included). Then, one could see if the results are due to the coupling or if they can be mimicked by a very different assumption/model extension.

There are now lab-based (e.g. from KATRIN) constraints on the neutrino mass which are cosmology independent. Are the constraints presented in this paper consistent with the lab-based experiments?

*[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.]*