Generating spatial curvature in an inhomogeneous universe: a bottom-up approach to cosmology

We take the first steps towards a new bottom-up approach to cosmology. The dynamics is described in terms of the world lines of the cosmic grains (galaxies or clusters of galaxies). The description is microscopic in the sense that there is no fluid assumption. The motion of each grain is geodesic ensuring the presence of gravitational interactions only. The scheme is fully general in that there is no restriction to homogeneous or isotropic models. Our approach is mathematically similar to Buchert's averaging method, but there are important differences. In particular, we use statistical averages, when needed, not volume averages. For example, a crucial ingredient in any cosmological framework is the spatial curvature. Here we give an estimate of the scalar curvature based on statistical averages of the actual mass distribution in the universe.