Liam Urban - On the past maximal development of near-FLRW data for the Einstein scalar-field Vla....

This talk was part of the Thematic Programme on "Nonlinear Waves and Relativity" held at the ESI April 29 -- June 21, 2024.
In this talk, I will discuss recent joint work with David Fajman, in which we prove the past nonlinear stability of FLRW solutions to the Einstein scalar-field Vlasov equations. For near-FLRW solutions, the spacetime variables and the scalar field are shown to be asymptotically velocity term dominated (AVTD) toward the Big Bang, causing stable Kretschmann scalar blow-up. While components of the Vlasov energy-momentum tensor remain close to that of the FLRW solution up to a small offset, the distribution function itself generically becomes highly anisotropic. To ensure that this behaviour is sufficiently mitigated by the quiescent background, we crucially exploit a scaling hierarchy between horizontal and vertical derivatives in the Vlasov equation.