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Résumé |
Modifications to 3+1d general relativity (GR) at high curvatures can eliminate the Big Bang singularity in favor of a bounce. Abstracting away microscopic details of the bounce, the spacetime is simply a GR solution on both sides of a singularity hypersurface, with some theory-dependent "singularity scattering map" relating the asymptotic metrics on both sides. The asymptotic metric near a singularity was studied by Belinsky, Khalatnikov and Lifshitz (BKL) and I will explain their finding that the time evolution at different points decouples. Motivated by this ultralocality property, we classify (in the absence of BKL oscillations) all singularity scattering maps that are ultralocal. By matching previous calculations on homogeneous spacetimes in f(R) gravity and in loop quantum cosmology with our classification we obtain a prediction for non-homogeneous bounces in these theories. Lastly, we construct a class of cyclic spacetimes by solving for the collision of plane gravitational waves (which may create infinitely many successive singularities). |
