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Abstract:
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 they
found 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).