## Two-parameter Perturbation Theory for Cosmologies with Non-linear Structure

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We propose and construct a two-parameter expansion around a Friedmann-Lemaitre-
Robertson-Walker geometry which uses both large-scale and small-scale perturbations
analogous to cosmological perturbation theory and post-Newtonian gravity.
We justify this observationally, derive a set of fi eld equations valid on a fraction
of the horizon size and perform a detailed investigation of the associated gauge
problem. We fi nd only the Newtonian gauge, out of the standard gauges used in
cosmological perturbation theory, is applicable to post-Newtonian perturbations; we
can identify a consistent set of perturbed quantities in the matter and gravity sectors
and construct corresponding gauge-invariant quantities. The fi eld equations,
written in terms of these quantities, takes on a simpler form, and allows the effects
of small-scale structure on the large-scale properties of the Universe to be clearly
identified and discussed for different physical scenarios. With a defi nition 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 Newton-Poisson
equation { even though both originate from the same equation. There exists eld
equations at new orders in our formalism, such as a frame-dragging eld equation
a hundred times larger than expected from using cosmological perturbation theory
alone. Moreover, we fi nd non-linear gravity, mode-mixing and a mixing-of-scales
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
non-linearities lead to, for example, a large-scale effective pressure and anisotropic
stress. We expect our formalism to be useful for accurately modelling our Universe,
and for investigating the effects of non-linear gravity in the era of ultra-large-scale
surveys.

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Goldberg, Sophie Rachel##### Collections

- Theses [2616]