Gravity Seminar: Numerical construction of non-linear initial data sets for cosmological models, Alejandro Estrada Llesta, Universidad del Valle, Colombia

We explore the Algebraic-Hyperbolic Formulation (AHF) or 2+1 decomposition of the constraint equations in cosmological scenarios. We propose a pseudo-spectral method based on the Fourier transform to solve the evolution PDEs that the AHF provide. We use Gowdy and Perturbed-FLRW space-times as testbeds. Additionally, we review the error sources and propose modifications to the original system that allows us to find new and non-linear initial data sets.