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.

中文翻译：

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非欧牛顿宇宙学

我们在牛顿的绝对空间是非欧氏空间的假设下，制定并解决了牛顿宇宙学的问题。我们特别关注负弯曲双曲空间 H3。我们指出了欧几里得空间中牛顿宇宙学弗里德曼方程中出现的曲率项与曲率在 H3 空间中的作用之间的不等式。我们找到了平方反比定律的推广以及由此而来的牛顿宇宙学的解。我们在 H3 中找到了欧几里得米歇尔“黑洞”的推广，并表明它导致了与我们在广义相对论中发现的不同的最大力和面积结果。我们展示了如何将宇宙常数的对应物添加到 H3 的引力势中，并探索由此产生的宇宙学模型的解和渐近线。我们还讨论了在具有非负空间曲率的牛顿宇宙学中引入紧凑拓扑的问题。