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

TL;DR

This paper investigates how local inhomogeneities in a perturbed universe affect the cosmic distance ladder, revealing an 11% modification in distance measurements that could resolve key cosmological tensions.

Contribution

It demonstrates the impact of local inhomogeneities on distance calibration and proposes a potential solution to the Hubble and supernova magnitude tensions without dark energy.

Findings

11% modification to area distance due to inhomogeneities

Tidal deformation influences local spacetime measurements

Potential resolution of Hubble and supernova magnitude tensions

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-Lema{\i}tre Robertson-Walker spacetime. We show that there is a non-negligible modification (about 11\%) to the background Friedmann-Lema{\i}tre 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.