Cosmological Newtonian limits on large spacetime scales
Seminar/Forum
Galaxies and clusters of galaxies are prime examples of large scale structures in our universe. Their formation requires nonlinear interactions and cannot be analyzed using perturbation theory alone. Currently, cosmological Newtonian Nbody simulations are the only well developed tool for studying structure formation. However, the Universe is fundamentally relativistic, and so the use of Newtonian simulations must be carefully justified. This leads naturally to the question: On what scales can Newtonian cosmological simulations be trusted to approximate realistic relativistic cosmologies? In this talk, I will describe recent work done in collaboration with Chao Liu in which we provide a rigorous answer to this question by establishing the existence of 1parameter families of \(\epsilon\)dependent solutions to the EinsteinEuler equations with a positive cosmological constant \(\Lambda >0\) and a linear equation of state \(p=\epsilon^2 K \rho, 0<K\leq 1/3\), for the parameter values \(0<\epsilon\leq \epsilon_0\). These solutions exist globally on the manifold \(M=[0,\infty) \times \mathbb{R}^3\), are future complete, and converge as \(\epsilon \searrow 0\) to solutions of the cosmological PoissonEuler equations. As I shall describe in the talk, these solutions represent inhomogeneous, nonlinear perturbations of a homogeneous fluid filled universe where the inhomogeneities are driven by localized matter fluctuations that evolve to good approximation according to Newtonian gravity. Time permitting, I will briefly discuss a number of new results in hyperbolic partial differential equations that were used to establish the global existence results described in the talk.
Presenter

Todd Oliynyk, Monash University