Abstract: Recent work on quantum cosmology has led to a plethora of semiclassical no-boundary wave functions. Moreover it was argued that all no-boundary states receive non-perturbative corrections due to singular off-shell configurations, which render large perturbations in de Sitter space unsuppressed. We will review the original Hartle-Hawking no-boundary proposal and show that when it is carefully defined and evaluated, it receives no such corrections. We calculate the no-boundary wave function in anisotropic Bianchi IX cosmologies by the method of steepest descent, taking into account the non-linear backreaction of perturbations. We find large anisotropies are suppressed, in agreement with holographic calculations in dual vector toy models. This suggests that the requirement that the state fits into a proper quantum mechanical framework selects a unique no-boundary wave function.
This work was done in collaboration with Juan Diaz, Jonathan Halliwell, Jim Hartle, Thomas Hertog and Yannick Vreys, and, aside from work done on quantum cosmology mainly in the late 80â€™s and begin 90â€™s, is based on 1703.02076, 1705.00192, 1705.05340, 1708.05104, and an upcoming paper.