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

Abstract

How does a smooth cosmic distance ladder emerge from observations made from a single location in a lumpy Universe? Distances to Type Ia supernovae 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 spacetime. We show that there is a non-negligible modification (about 11\%) to the background Friedmann-Lemaıtre Robertson-Walker 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 Type Ia supernova absolute magnitude in the Hubble flow. We show that it could potentially resolve the Type Ia supernova absolute magnitude and Hubble tensions simultaneously without the need for early or late dark energy.