Past Maximal Development of Near-FLRW Data for Einstein Scalar-Field Vlasov System

Explore a General Relativity seminar presentation examining the formation of Big Bang singularities and the past nonlinear stability of FLRW solutions in the Einstein scalar-field Vlasov system. Delve into how scalar-field matter suppresses geometric oscillations and investigate whether this characteristic remains when coupled with models that better represent our universe's matter content. Learn about the asymptotic velocity term dominated behavior of near-FLRW solutions toward the past, resulting in quiescent Big Bang singularities with stable Kretschmann scalar blow-up. Understand how the Vlasov distribution becomes highly anisotropic near the Big Bang singularity, concentrating in preferred momentum directions associated with shear eigendirections. Examine the scaling hierarchy between horizontal and vertical derivatives in the expansion normalized Vlasov equation, and discover how this analysis combines with Bel-Robinson energy formalism in four spacetime dimensions while finding a more direct proof in three dimensions. Gain insights into the Strong Cosmic Censorship conjecture for four-dimensional polarized U(1)-symmetric solutions to the Einstein vacuum equations with specific spatial topology conditions.