A Reanalysis of the Latest SH0ES Data for H0: Effects of New Degrees of Freedom on the Hubble Tension
Round 1
Reviewer 1 Report
This manuscript reanalyzes the most recent release of SH0ES data which contains a large collection of Cepheids observed in around 40 different galaxies. The authors provided an interesting review of the parameters involved in the Cepheids and SNe Ia modeling, testing the possibility of a transitional phase for the MB parameter of SNe Ia - in correspondence of a distance value Dc~50 Mpc - which could lead to a measured value of the Hubble constant compatible in 1 sigma with the Planck CMB value. I found the manuscript properly written and the work correctly performed and presented, thus I strongly encourage its publication after some comments of mine have been addressed.
COMMENTS
1) In Section 2.1 (pag. 11) it is specified how a linear solution of the system has been chosen as an alternative approach to the Monte Carlo Markov Chain given the huge number of data and free parameters involved in the analysis. This discussion is provided in detail in the Appendix B through an analytical demonstration. Nevertheless, to test the reliability of the numerical results it would be a good proof if the authors provided a comparison. To be more specific, a small sample of arbitrary entries (up to a maximum of 1000 data points) allowing to vary 1 or 2 parameters would not require large computation times and could be used as a benchmark to compare the results of the MCMC and the linear fitting for parameters, showing how in the two aforementioned approaches the results are compatible. To this end, the addition in the Appendix of one graphic that contains this comparison would be sufficient.
2) The reanalysis of the SH0ES data is performed rigorously and it is appreciated that the authors added some new comments (at the end of Section 2.1) that were not specified in the original release of the SH0ES data. A complete discussion of the Cepheids observables (period, metallicity) is provided inside this manuscript (Section 2.2). In my opinion, to give a further general insight into this sample, the histograms or distributions of the period and metallicity in the Cepheids sample can be added to the manuscript. It would be interesting to add:
a) the distributions of the period and metallicity in the sample at distances smaller than the transition threshold (Dc < 50 Mpc)
b) the distributions of the same observables at Dc > 50 Mpc
c) the distributions of the same observables for the whole sample [thus merging a) and b)]
d) a Kolmogorov-Smirnov test to assess if the a) and b) distributions can be drawn from the same sample.
e) plotting a), b), and c) together and discussing the results of d).
FURTHER IMPROVEMENTS
The structure of the paper is clear and complete but the Introduction concerning the Hubble constant tension can be further expanded. I suggest the authors to add the following reference https://www.mdpi.com/2075-4434/10/1/24 where the Hubble tension has been analyzed with a binned analysis on the Pantheon sample of SNe Ia through a multidimensional MCMC analysis (varying the Hubble constant together with a second cosmological parameter). Furthermore, given that a transition of the MB parameter occurs at low redshift (also in Alestas, Kazantzidis, and Perivolaropoulos 2021 is specified a threshold of z~0.1) the need for new standardizable candles with redshift values far beyond the SNe Ia (z~3 up to 9) can be discussed by including the following: https://arxiv.org/abs/2201.05245,
https://arxiv.org/abs/2204.08710,
https://arxiv.org/abs/2206.07479,
https://arxiv.org/abs/2203.15538, and
https://arxiv.org/abs/1308.1918 for GRBs;
https://arxiv.org/abs/2111.02420 and
https://arxiv.org/abs/2203.12914 for quasars.
Author Response
Please see attached pdf file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors reanalyze in a simple and comprehensive manner the recently released SH0ES data for the determination of current Hubble rate H0. They mainly focus on testing the homogeneity of the Cepheid+SnIa sample and to check the robustness of the results in the presence of new degrees of freedom in the modeling of Cepheids and SnIa. The article is very well written, and scientifically sound. I thus recommend acceptance as it is.
Author Response
Please see attached pdf file
Author Response File: Author Response.pdf
