Cosmological Newtonian limits on large spacetime scales


Galaxies and clusters of galaxies are prime examples of large scale structures in our universe. Their formation requires non-linear interactions and cannot be analyzed using perturbation theory alone. Currently, cosmological Newtonian N-body 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 1-parameter families of \(\epsilon\)-dependent solutions to the Einstein-Euler 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 Poisson-Euler 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.


  •  Todd  Oliynyk
    Todd Oliynyk, Monash University