Interpretation of the Hubble diagram in a nonhomogeneous universe

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the light from "point sources"-such as supernovae-probes the Universe on scales where the homogeneity principle is no longer valid.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.

Primordial black holes survive SN lensing constraints

“…This effect is essentially equivalent to reducing the mean density of the Universe [43][44][45] (or adding spatial curvature). Indeed, the denser the Universe, the more matter is encountered by light beams, and hence the more magnified they are.…”

Impact of small-scale inhomogeneities on observations of standard candles

“…First, other origins of uncertainty in SNe observations, such as absorption effects and bias from poor understanding of the explorsion mechanism, must be resolved. Besides those effects, our analysis is based on the "opacity hypothesis" [3] which states that all observed SNe have path through the region far from clumps. Nevertheless, our proposal is unique one which has potential to probe extremely small scale (> 10 15 cm) inhomogeneities…”

“…This tension would originate from small scale inhomogeneities as is reported in Refs. [2,3]. The real universe is inhomogeneous on the scales smaller than 100Mpc.…”

“…This hypothesis states that all observed SNe have passed through the region far from clumps. It might be justified by the following reasons [3]: the probability of passing through near clumps is too small, clumps may be bright enough to hide SNe behind it, strong gravitational lensing due to a clump makes it so bright that it is regarded as isolated exceptional source. Throughout this paper, we assume that the distance redshift relation of SNe is given by the DR distance with true cosmological parameters which describe global aspect of the universe.…”

Impact of cosmic variance on the local measurement of $H_0$

“…Other relativistic approaches were proposed in [13,14]. In [13] a "Swiss cheese" model was used in modeling the local Universe, in [14] a "Hubble bubble" model was used and the perturbation of the expansion rate, which is not directly measurable, was considered.…”