I am certainly not suggesting anything negative about the character or reputation of the authors of the work. I think that work on alternatives to the accepted

I am certainly not suggesting anything negative about the character or reputation of the authors of the work. I think that work on alternatives to the accepted concordance cosmology model (LCDM) should definitely be explored, and David Wiltshire et al. should pursue this if they deem it promising. As an aside: You may not find this compelling, which is understandable, but I will note that the vast majority of cosmologists (very conservatively 95%) do not question the FLRW aspect of the cosmological concordance model (which is what the paper here does away with in the alternative timescape cosmology), even if they question other parts of it (i.e. by considering dynamical dark energy, neutrino interactions, etc.). I agree that timescape is an interesting idea, but it seems like only a few people have been working on it for over a decade now - unless you have a very (and I think unfairly) dim view of professional cosmologists, if there was a strong case to be made for the timescape model based in data, the greater community would have adopted it by now. Finally, and independent of the sociological points above, an answer to your question about specifics aside from the types of statistical/modeling issues of the type I mentioned above. Again this is not exactly my area and I have not done the analysis myself, so I will refrain from strong opinions. However, my immediate reaction to this is that it is easy to fit one particular dataset (in this case part of the Pantheon+ supernovae sample) with a more complicated model than LCDM, but often these types of models fail when other cosmological datasets are included. Considering such joint constraints with multiple datasets is not an “extra ask” of alternatives to LCDM - to be taken seriously any alternative model should hold up in a joint analysis of precision cosmological datasets (see, for example, the tests of a more seriously considered alternative model in the community, early dark energy [0]). These days, this is often the combination of Cosmic Microwave Background (CMB) Anisotropies, galaxy Baryon Acoustic Oscillations (BAO), and one of several supernovae samples - see e.g. [1] for a somewhat pedagogical overview. The failure to fit several datasets is a common issue e.g. with many MOND papers. In this case, the authors do not try to fit data to anything but a single (modified) supernovae dataset. I would expect that if they included a fit to CMB/BAO data, there would be trouble with the timescape model, as this is exactly what was found in an analysis of the timescape model in another state-of-the-art supernova dataset [2] - there the timescape model could not accommodate the supernova data when combined with CMB/BAO data [2]. [0] https://arxiv.org/abs/2302.09032 https://arxiv.org/abs/2302.09032 [1] https://arxiv.org/pdf/2007.08991 https://arxiv.org/pdf/2007.08991 [2] https://arxiv.org/pdf/2406.05048 https://arxiv.org/pdf/2406.05048