Liam Urban: On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system

While Vlasov matter has proven itself as a robust model in
describing the late universe, what we know about its past evolution
indicates that we should expect instability in general cosmological
settings. On the other hand, a series of recent works have shown that
scalar fields are uniquely suited to cause stable, quiescent Big Bang
formation.

In this talk, I will discuss recent joint work with David Fajman, in
which we show the past nonlinear stability of FLRW solutions to the
Einstein scalar-field Vlasov system without symmetry assumptions. For
such near-FLRW solutions, spacetime variables and the scalar field
exhibit asymptotically velocity term dominated (AVTD) behaviour towards
the Big Bang. While the components of the Vlasov energy momentum tensor
remain close to their FLRW counterparts up to a small offset, we
observed that the distribution function asymptotically concentrates in
certain preferred momentum directions. To ensure that the scalar field
sufficiently controls the anisotropic asymptotics of Vlasov matter, we
crucially exploit a scaling hierarchy between horizontal and vertical
derivatives in the expansion normalised Vlasov equation.