The art of building a smooth cosmic distance ladder in a perturbed universe

Catching up on some literature on the inestimable arXiv I came across this paper by Obinna Umeh which I haven’t gone through in detail but which looks very interesting:

How does a smooth cosmic distance ladder emerge from observations made from a single location in a lumpy Universe? Distances to the Type Ia supernova (SN1A) in the Hubble flow are anchored on local distance measurements to sources that are very nearby. We described how this configuration could be built in a perturbed universe where lumpiness is described as small perturbations on top of a flat Friedmann-Lemaıtre Robertson-Walker (FLRW) spacetime. We show that there is a non-negligible modification (about 11%) to the background FLRW area distance due to the presence of inhomogeneities in the immediate neighbourhood of an observer. We find that the modification is sourced by the electric part of the Weyl tensor indicating a tidal deformation of the local spacetime of the observer. We show in detail how it could impact the calibration of the SN1A absolute magnitude in the Hubble flow. We show that it resolves the SN1A absolute magnitude and Hubble tensions simultaneously without the need for early or late dark energy.

The area distance here is what I usually call the angular-diameter distance; when one thinks of supernova measurements one usually thinks of the luminosity distance but these are related through the reciprocity relation discussed here which applies to each source regardless of whether the metric is of FLRW form or not. For a general discussion of cosmological distances see here.

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