| Speaker: Florian Beyer Affiliation: University of Otago Time: 3:00 pm Wednesday, 2 February, 2022 Location: https://massey.zoom.us/j/89209863327?pwd=OGtnamR1anZDTFNJc1ZpbXZFYTVDQT09 |
| The Einstein equations are a complicated nonlinear system of geometric wave-type partial differential equations defined on Lorentzian “spacetime" manifolds. In cosmology, these equations describe the dynamics of gravity and therefore the history of the universe as a whole. While the observationally very successful “Lambda-CDM” cosmological model restricts to very simple settings, the full nonlinear regime of these equations is still full of mysteries. Several fundamental issues (“Mixmaster behavior”, “cosmic censorship” etc) especially related to the “early universe” in the vicinity of the “initial big bang singularity” (a domain of the spacetime manifold near a spacelike singularity of the Riemann curvature tensor) remain open. Tackling these issues boils down to the singular analysis of these nonlinear partial differential equations, while exploiting their geometric nature, with the hope to obtain sufficiently detailed rigorous estimates of the global behaviour of generic solutions. In this talk I present recent global nonlinear stability results providing sufficiently sharp estimates which (to a point) confirm that the simple description of the early universe given by the Lambda-CDM model is a good approximation. However our results also indicate the existence of new dynamical phenomena not covered by that model. This is work done in collaboration with Todd Oliynyk (Monash University). |