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Effects of inhomogeneities on observations have been vastly studied usingboth perturbative methods, N-body simulations and Swiss cheese solutions to theEinstein equations. In nearly all cases, such studied setups assume vanishingspatial background curvature. While a spatially flatFriedmann-Lemaitre-Robertson-Walker model is in accordance with observations, anon-vanishing curvature is not ruled out. It is therefore important to notethat, as has been pointed out in the literature, 1 dimensional averages mightnot converge to volume averages in non-Euclidean space. If this is indeed thecase, it will affect the interpretation of observations in spacetimes withnon-vanishing average spatial curvature. This possibility is therefore studiedhere by computing the integrated expansion rate and shear, the accumulateddensity contrast, and fluctuations in the redshift-distance relation in Swisscheese models with different background curvatures. It is found thatdifferences in mean and dispersion of these quantities in the different modelsare small and naturally attributable to differences in background expansionrate and density contrasts. Thus, the study does not yield an indication thatthe relationship between 1 dimensional spatial averages and volume averagesdepends significantly on background curvature.

Light path averages in spacetimes with non-vanishing average spatial curvature