We construct high-precision models of the Universe that contain radiation, a cosmological constant, and periodically distributed inhomogeneous matter. The density contrasts in these models are allowed to be highly nonlinear, and the cosmological expansion is treated as an emergent phenomenon. This is achieved by employing a generalized version of the post-Newtonian formalism, and by joining together inhomogeneous regions of space-time at reflection symmetric junctions. Using these models, we find general expressions that precisely and unambiguously quantify the effect of small-scale inhomogeneity on the large-scale expansion of space (an effect referred to as “backreaction” in the literature). We then proceed to specialize our models to the case where the matter fields are given by a regular array of pointlike particles. This allows us to derive extremely simple expressions for the emergent Friedmann-like equations that govern the large-scale expansion of space. It is found that the presence of radiation tends to reduce the magnitude of backreaction effects, while the existence of a cosmological constant has only a negligible effect.

• Received 25 April 2016

DOI:https://doi.org/10.1103/PhysRevD.94.023505