A DIRECT ESTIMATE OF THE SPATIAL CURVATURE OF THE UNIVERSE

The main idea of this contribution is to calculate the average spatial curvature directly from the observed mass distribution of the universe. In short, our philosophy is that the curvature of the universe is generated solely by the matter it contains. Although this may seem as self-evident in the context of general relativity, the usual practice in cosmology is rather to use a top-down approach in which the curvature is calculated indirectly using a prescribed matter distribution as a source of the Einstein equations. By contrast, our approach may be seen as part of a bottom-up approach. In practical terms, we first calculate the far field spatial curvature generated by an isolated matter distribution which is in arbitrary motion. At this stage we obtain the result that the sign of the spatial curvature is necessarily positive. For the spatial curvature generated by multiple sources we show that it is sufficient to use linearized theory to compute the leading contributions. In the matter dominated era the spatial curvature is then seen to be generated by local sources at small redshifts. This fact makes it possible to calculate the total spatial curvature just by summing up the contributions from the observed discrete mass distribution. A crude estimate gives a very small value for the curvature.