Cosmological backreaction in the presence of radiation and a cosmological constant

Abstract

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 non-linear, and the cosmological expansion is treated as an emergent phenomenon. This is achieved by employing a generalised 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 "back-reaction", in the literature). We then proceed to specialize our models to the case where the matter fields are given by a regular array of point-like 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 back-reaction effects, while the existence of a cosmological constant has only a negligible effect.

14 pages, 12 figures, v2: matches published version, v3: typo corrected in Eq. (59)

References in corpus (3)

• The influence of structure formation on the cosmic expansion
• Black Hole Universe with $\Lambda$
• Averaging Robertson-Walker Cosmologies

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