Extension of Newton's theory to non-Euclidean topologies (webcam+audio)

Constructing an extension of Newton's theory which is defined on a non-Euclidean topology, called a non-Euclidean Newtonian theory, would be a powerful tool to study the influence of global topology on structure formation, especially studying the influence of other topologies than the 3-torus currently used in Newtonian cosmological simulations. That theory would be simpler to use than general relativity, but would still be physical on cosmological scales as is the case with Newton's theory. We will see that a natural way of defining such a non-Euclidean Newtonian theory is to use the concept of Galilean manifolds along with a minimal modification of the Newton-Cartan equations. The resulting theory has a gravitational system of equations which is algebraically equivalent to cosmological Newton's equations, but with the presence of a non-zero spatial curvature in the spatial connection present in these equations. While the theory predicts no additional effects (with respect to ΛCDM) of