Unstable Fluids in Expanding Cosmologies

The FLRW solution is the simplest cosmological model in general relativity, describing a fluid-filled, spatially homogeneous universe. While there is extensive literature in the physics community on cosmological models with a linear equation of state p=K\rho, rigorous stability results have, until recently, been limited to FLRW models with accelerated expansion and small sound speeds. In this talk, I will discuss numerical work on two types of instabilities which can occur in non-linearly perturbed FLRW models outside of this regime. The first concerns a longstanding conjecture of Alan Rendall on FLRW models with positive cosmological constant and super-radiative (K>1/3) equations of state. Our numerical work, in collaboration with F. Beyer and T.A. Oliynyk, supports Rendall’s conjecture and highlights the underlying mechanism for the instability. In the second case, I will discuss evidence that perturbations of slowly expanding (decelerated) FLRW models generically form shocks in finite time. This contrasts with known results for accelerated models where shock formation is suppressed for suitably small perturbations.

Via Zoom: https://harvard.zoom.us/j/7855806609