Light path averages in spacetimes with non-vanishing average spatial
  curvature
  Effects of inhomogeneities on observations have been vastly studied using
both perturbative methods, N-body simulations and Swiss cheese solutions to the
Einstein equations. In nearly all cases, such studied setups assume vanishing
spatial background curvature. While a spatially flat
Friedmann-Lemaitre-Robertson-Walker model is in accordance with observations, a
non-vanishing curvature is not ruled out. It is therefore important to note
that, as has been pointed out in the literature, 1 dimensional averages might
not converge to volume averages in non-Euclidean space. If this is indeed the
case, it will affect the interpretation of observations in spacetimes with
non-vanishing average spatial curvature. This possibility is therefore studied
here by computing the integrated expansion rate and shear, the accumulated
density contrast, and fluctuations in the redshift-distance relation in Swiss
cheese models with different background curvatures. It is found that
differences in mean and dispersion of these quantities in the different models
are small and naturally attributable to differences in background expansion
rate and density contrasts. Thus, the study does not yield an indication that
the relationship between 1 dimensional spatial averages and volume averages
depends significantly on background curvature.
