Local and non-local measures of acceleration in cosmology
  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.
