## [arXiv:2002.09293] Cosmological parameter analyses using transversal BAO data

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### [arXiv:2002.09293] Cosmological parameter analyses using transversal BAO data

This paper was commented on through 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:
1. 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.
2. 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.
3. 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).
4. 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.]

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### Re: [arXiv:2002.09293] Cosmological parameter analyses using transversal BAO data

[The following remark was shared by a cosmologist on the Slack CosmoDiscussion workspace. We considered it to be of general interest in this discussion.]

In addition to the points mentioned by the above post, I am quite puzzled by the MCMC results in this paper. When using just Planck data (not including their transverse BAO) why are not the published Planck results recovered?

Consider, for instance, Fig 1. The red contours on the left are not the same as Planck's for the same setup. These authors report $H_0= 68 \pm 0.56\,\mathrm{km/s/Mpc}$ for Planck alone, whereas Planck say $67.3\,\mathrm{km/s/Mpc}$, so that's a 1-sigma shift in the mean for exactly the same data.

Looking at the weird contours in the various plots, I suspect that the the chains have not actually converged.

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### Re: [arXiv:2002.09293] Cosmological parameter analyses using transversal BAO data

[The authors of the article replied to the above comments. We report their answers hereafter.]

Dear colleagues,

Answer to point 1: It is correct your claim that “It is not true that the approach adopted by the authors is model-independent.” In the improved updated version, soon to appear in arXiv and in the published version, we state that the transversal BAO data is weakly dependent on cosmological models. This is unavoidable dependence due to the well-known projection effect in a thin (but not null) redshift bin.

Answer to point 2: In the updated version, we improved the presentation of these new interesting BAO data, starting from a new abstract.

Answer to point 3: In this work, we did not analyze the SNIa data. Therefore, we cannot draw any conclusions on this point or provide an exact answer. But, realize that in any case, in general, our BAO data compilation increase expectations on H0 values.

Answer to point 4: One of us (AB) participated actively in the developing of the analyses that led to the 15 transversal BAO data. These measurements were not a coincidence, they were planned to be done some years ago. From the beginning our methodology excluded the possibility for covariance between BAO data because we analyzed the 2PACF in cosmic objects belonging to disjoint redshift bins (i.e., bins that are not overlapped and moreover separated by a minimum $\delta_z$, separation that excludes the possibility that errors in the redshifts could put one cosmic object belonging to one bin in a contagious bin).

About the second post comments: We verified the convergence of our chains and in the final version (published version), everything is fine. Perhaps some statistical fluctuations to be present (from our Planck data only, in comparation with papers by the Planck Collaboration), but now everything is fine.

Thank you very much for the comments and sorry for the delay in send a reply.

Best regards,
The authors.