Non-Euclidean Newtonian Cosmology
  We formulate and solve the problem of Newtonian cosmology under the
assumption that the absolute space of Newton is non-Euclidean. In particular,
we focus on the negatively-curved hyperbolic space, H3. We point out the
inequivalence between the curvature term that arises in the Friedmann equation
in Newtonian cosmology in Euclidean space and the role of curvature in the H3
space. We find the generalisation of the inverse-square law and the solutions
of the Newtonian cosmology that follow from it. We find the generalisations of
the Euclidean Michell 'black hole' in H3 and show that it leads to different
maximum force and area results to those we have found in general relativity. We
show how to add the counterpart of the cosmological constant to the
gravitational potential in H3 and explore the solutions and asymptotes of the
cosmological models that result. We also discuss the problems of introducing
compact topologies in Newtonian cosmologies with non-negative spatial
curvature.
