# Prof. Florian Beyer (University of Otago) Nonlinear stability of Einstein-matter models near the big bang singularity

In our recent work, we have made significant progress in understanding the complex mathematical landscape surrounding the big bang singularity in classical general relativity. Utilizing Fuchsian partial differential equation techniques, we have established rigorous nonlinear stability results for certain Friedmann cosmological models, particularly focusing on solutions to the fully coupled Einstein-matter equations in the non-oscillatory regime. This not only reinforces some of the standard cosmological model’s simpler assumptions in certain scenarios but also brings to light new critical phenomena that have yet to be fully understood. This research was conducted in collaboration with Todd Oliynyk from Monash University.