Wavefunction of anisotropic inflationary universes with no-boundary conditions

We study the emergence of anisotropic (Bianchi IX) inflationary universes with no-boundary conditions in the path integral approach to quantum gravity. In contrast to previous work, we find no evidence for any limit to how large the anisotropies can become, although for increasing anisotropies the shape of the instantons becomes significantly different from Hawking's original no-boundary instanton. In all cases an inflationary phase is reached, with the anisotropies decaying away. Larger anisotropies are associated with a much larger imaginary part of the action, implying that the highly anisotropic branches of the wavefunction are heavily suppressed. Interestingly, the presence of anisotropies causes the wavefunction to become classical much more slowly than for isotropic inflationary universes. We derive the associated scaling of the WKB classicality conditions both numerically and analytically.