Multi-Scale Perturbation Theory for Cosmologies with Nonlinear Structure

Cosmological perturbation theory relies on the assumption that density contrasts are small. This assumption is valid for most of the history of the universe, but begins to break down at late times due to matter’s susceptibility to gravitational collapse. However, the post-Newtonian treatment of gravity is perfectly capable of dealing with highly nonlinear density contrasts, so long as the system under consideration is slow-moving and small in spatial extent - precisely the conditions present in large-scale structures such as superclusters! I will present a novel formalism for simultaneously applying a post-Newtonian expansion on short scales, while keeping a traditional approach to perturbation theory on large scales. This approach allows for the possibility of explicit coupling between terms from each sector. I will then use approximate solutions to calculate the matter bispectrum, using this statistic to highlight similarities and differences between traditional perturbation theory and our new multi-scale approach.