Post-Newtonian Cosmological Modelling

Abstract

We develop a new approach to building cosmological models, in which small pieces of perturbed Minkowski space are joined together at reflection-symmetric boundaries in order to form a global, dynamical space-time. Each piece of this patchwork universe is described using post-Newtonian gravitational physics, with the large-scale expansion of the universe being an emergent phenomenon. This approach to cosmology does not require any assumptions about non-local averaging processes. Our framework clarifies the relation between the weak-field limit of general relativity, and the cosmological solutions that result from solving Einstein's equations with a set of symmetry assumptions. It also allows the effects of structure formation on the large-scale expansion of the universe to be investigated in an unambiguous way. As an explicit example, we use this formalism to investigate the cosmological behaviour of a large number of regularly arranged point-like masses. In this case we find that the large-scale expansion is well modelled by a Friedmann-like equation that contains terms that take the form of dust, radiation, and spatial curvature. The radiation term, while small compared to the dust term, is purely a result of the non-linearity of Einstein's equations.

22 pages, 5 figures, v2: Published version, v4: Corrections to published version

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• Parametrizing theories of gravity on large and small scales in cosmology
• The Magnetic Part of the Weyl Tensor, and the Expansion of Discrete Universes
• CMB seen through random Swiss Cheese
• Exact Initial Data for Black Hole Universes with a Cosmological Constant
• Perturbation theory for cosmologies with non-linear structure
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• Cosmological gravity on all scales III: non-linear matter power spectrum in phenomenological modified gravity
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• The momentum constraint equation in Parameterised Post-Newtonian Cosmology
• Cosmological Solutions with Charged Black Holes
• Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude
• Post-Newtonian Gravity in Cosmology
• Second-order dust perturbations of the non-flat FLRW model with the positive cosmological constant
• The perturbed FLRW metric on all scales: Newtonian limit and top-hat collapse
• Les Houches on Dark Universe 2025: Elements of cosmology beyond FLRW