Hans Ringström: Formation of quiescent big bang singularities

Abstract:

A basic question in general relativity is if big bang singularities appear naturally in solutions to Einstein's equations. In the early days of general relativity, explicit solutions with such singularities were found. Later, the singularity theorem of Hawking was demonstrated. It provides an indication that big bang singularities should appear naturally but does not say much about their nature. Recently, many results concerning stable big bang formation have appeared. Most of the results concern stability of spatially homogeneous and isotropic solutions. However, a recent result of Fournodavlos, Rodnianski and Speck (FRS) covers the full regime in which stability is to be expected. On the other hand, it is restricted to the stability of spatially homogeneous and spatially flat solutions. In this talk, I will present a new result (joint work with Hans Oude Groeniger and Oliver Petersen) in which we identify a general condition on initial data ensuring big bang formation. The solutions need, in this case, not be close to symmetric background solutions. Moreover, the result reproduces previous results in the Einstein-scalar field and Einstein-vacuum settings. Finally, the result is in the Einstein-non-linear scalar field setting, and therefore yields future and past global non-linear stability of large classes of spatially locally homogeneous solutions.