Asymptotics and singularities in cosmological models with positive cosmological constant

Understand

This thesis is concerned with global properties of those cosmological solutions of Einstein's field equations which obey accelerated expansion into the future driven by a non-vanishing cosmological constant, as suggested by current cosmological observations.

• In particular, the strong cosmic censorship and BKL conjecture are investigated in special classes of spacetimes.
• For this, a new numerical technique based on spectral methods is introduced to be able to deal with situations where the spatial topology is non-trivial from the numerical point of view, such as the 3-sphere.
• Therefor, an explicit spectral regularization at the - in single patch approaches inevitable - coordinate singularities is worked out.