Title:

Twoparameter perturbation theory for cosmologies with nonlinear structure

We propose and construct a twoparameter expansion around a FriedmannLemaitre RobertsonWalker geometry which uses both largescale and smallscale perturbations analogous to cosmological perturbation theory and postNewtonian gravity. We justify this observationally, derive a set of field equations valid on a fraction of the horizon size and perform a detailed investigation of the associated gauge problem. We find only the Newtonian gauge, out of the standard gauges used in cosmological perturbation theory, is applicable to postNewtonian perturbations; we can identify a consistent set of perturbed quantities in the matter and gravity sectors and construct corresponding gaugeinvariant quantities. The field equations, written in terms of these quantities, takes on a simpler form, and allows the effects of smallscale structure on the largescale properties of the Universe to be clearly identified and discussed for different physical scenarios. With a definition of statistical homogeneity, we find that the cosmological constant and the average energy density, of radiation and dust, source the Friedmann equation, whereas only the inhomogeneous part of the Newtonian energy density sources the NewtonPoisson equation { even though both originate from the same equation. There exists field equations at new orders in our formalism, such as a framedragging field equation a hundred times larger than expected from using cosmological perturbation theory alone. Moreover, we find nonlinear gravity, modemixing and a mixingofscales at orders one would not expect from intuition based on cosmological perturbation theory. By recasting the field equations as an effective fluid we observe that these nonlinearities lead to, for example, a largescale effective pressure and anisotropic stress. We expect our formalism to be useful for accurately modelling our Universe, and for investigating the effects of nonlinear gravity in the era of ultralargescale surveys.
