Cosmology on all scales: a two-parameter perturbation expansion

Understand

We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure.

• This framework reduces to the weak-field and slow-motion post-Newtonian treatment of gravity in the appropriate limits, but also includes the low-amplitude large-scale fluctuations that are important for cosmological modelling.
• We derive a set of field equations that can be applied to the late Universe, where non-linear structure exists on supercluster scales, and perform a detailed investigation of the associated gauge problem.
• This allows us to identify a consistent set of perturbed quantities in both the gravitational and matter sectors, and to construct a set of gauge-invariant quantities that correspond to each of them.