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

This paper looks at the very interesting idea of combining Planck data with

**transversal BAO data**, i.e. measurements of the angular diameter distance $D_{\rm A}(z)$ at certain redshifts. Crucially, transversal BAO measurements are not obtained in the usual way, i.e. looking at the 2-point correlation function in redshift space, and separating radial and transverse modes, but instead are indirectly obtained by looking at the 2-point

*angular*correlation function, fitting for the BAO angular scale $\theta_{\rm BAO}(z)$, and then obtaining $D_{\rm A}(z)$ from there, see Eq. (2.1). The idea is that this should be more model-independent than "usual" BAO analyses, because computing the 2-point correlation function in redshift-space requires assuming a fiducial cosmology for converting angles and redshifts to comoving coordinates, which instead is not required if one simply looks at angular separations within different redshift bins.

However, some aspects of the discussion were unclear and I would like the authors to clarify a few points:

- It is not true that the approach adopted by the authors is model-independent. The interpretation of the $\theta_{\rm BAO}(z)$ measurements adopted still requires assuming a model for determining $r_{\rm drag}$. In fact, in their subsequent analyses, the authors do assume specific models (e.g. $\Lambda$CDM and extensions thereof), so in my opinion the statements in the introduction that transversal BAO data are "quasi model independent" could be misleading. It is true that these new measurements remove a layer of model independence at the earliest stage of data reduction, but they are not model-independent.
- I think the title and abstract of the paper can be improved to make the novel aspects of the analysis clearer. When I first read the title and abstract, I did not understand what was new because transversal BAO measurements are already used in most analyses. What is crucial is how these transversal BAO distances are obtained, i.e. using the 2-point
*angular*correlation function. I think that should be reflected somewhere in the title or abstract. - All statements throughout the paper of the $H_0$ tension being resolved in various models (e.g. $w_0w_a$CDM) when considering the combination of Planck+transverse BAO are made on an incorrect basis. Indeed, this combination does not consider cosmographic SN data, which are crucial in fixing the late-time expansion rate. I suspect that the addition of SN data would pull $H_0$ again towards lower values, as found by various studies using a semi-model-independent inverse distance ladder approach (e.g. 1607.05617, 1707.06547, 1806.06781).
- The authors do not mention whether and how they treat the covariance between the transversal BAO measurements reported in Table 1. Presumably, the measurements across different bins are not independent (and thus the covariance not diagonal), but it is not clear from the text how this is taken into account. In general, regardless of whether they treat the covariance as diagonal or not, it would be interesting if the authors could clarify how they treat their BAO likelihood, i.e., is it a multivariate Gaussian, a product of univariate Gaussians, or something else altogether?

*[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.]*