Local and non-local measures of acceleration in cosmology

TL;DR

This paper investigates how local and non-local measures of acceleration in inhomogeneous cosmological models relate to observations, revealing that observed acceleration does not necessarily imply dark energy or uniform acceleration.

Contribution

It clarifies the relationship between observed cosmic acceleration and local versus averaged measures in inhomogeneous universes, challenging the assumption that acceleration indicates dark energy.

Findings

Observation-based acceleration closely relates to averaged universe acceleration in homogeneous models.

In inhomogeneous models, observed acceleration may occur without actual spacetime acceleration.

Inhomogeneity can produce apparent acceleration effects without dark energy.

Abstract

Current cosmological observations, when interpreted within the framework of a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model, strongly suggest that the Universe is entering a period of accelerating expansion. This is often taken to mean that the expansion of space itself is accelerating. In a general spacetime, however, this is not necessarily true. We attempt to clarify this point by considering a handful of local and non-local measures of acceleration in a variety of inhomogeneous cosmological models. Each of the chosen measures corresponds to a theoretical or observational procedure that has previously been used to study acceleration in cosmology, and all measures reduce to the same quantity in the limit of exact spatial homogeneity and isotropy. In statistically homogeneous and isotropic spacetimes, we find that the acceleration inferred from observations of the distance-redshift relation is closely related to the acceleration of the spatially averaged universe, but does not necessarily bear any resemblance to the average of the local acceleration of spacetime itself. For inhomogeneous spacetimes that do not display statistical homogeneity and isotropy, however, we find little correlation between acceleration inferred from observations and the acceleration of the averaged spacetime. This shows that observations made in an inhomogeneous universe can imply acceleration without the existence of dark energy.