Interpretation of the Hubble diagram in a nonhomogeneous universe

TL;DR

This paper investigates how small-scale inhomogeneities in the universe, modeled by a Swiss-cheese cosmology, affect the interpretation of the Hubble diagram, revealing significant biases that diminish with a dominant cosmological constant.

Contribution

It introduces an exact Swiss-cheese cosmological model to quantify the impact of inhomogeneities on Hubble diagram interpretations, highlighting their effect on cosmological parameter estimation.

Findings

Inhomogeneities cause biases and dispersion in the Hubble diagram.

Effects are significant but decrease in a universe dominated by a cosmological constant.

Swiss-cheese models can accurately simulate inhomogeneous universe effects.

Abstract

In the standard cosmological framework, the Hubble diagram is interpreted by assuming that the light emitted by standard candles propagates in a spatially homogeneous and isotropic spacetime. However, the light from "point sources"--such as supernovae--probes the Universe on scales where the homogeneity principle is no longer valid. Inhomogeneities are expected to induce a bias and a dispersion of the Hubble diagram. This is investigated by considering a Swiss-cheese cosmological model, which (1) is an exact solution of the Einstein field equations, (2) is strongly inhomogeneous on small scales, but (3) has the same expansion history as a strictly homogeneous and isotropic universe. By simulating Hubble diagrams in such models, we quantify the influence of inhomogeneities on the measurement of the cosmological parameters. Though significant in general, the effects reduce drastically for a universe dominated by the cosmological constant.