Inflation in quantum cosmology in higher dimensions

Quantum cosmology in Kaluza-Klein-type theories is investigated by using the fundamental equation of quantum gravity: the Wheeler-DeWitt equation. The Casimir stress tensor is considered as a prime source of compactification. By imposing the Hartle-Hawking boundary condition, we demonstrate that a fine-tuning of the boundary condition in the quantum regime is necessary, presumably at a moderate level of ${10}^{\mathrm{\ensuremath{-}}3}$, in order to obtain a sufficient inflation of our space.