Dimension of the Universe

The dynamical evolution of the Universe is represented by the wave packet of Hartle and Hawking’s ‘‘ground state.’’ Its most probable trajectory arises by a quantum tunneling from a gravitational instanton. We discuss the dimensionality of the Universe within the framework of eleven-dimensional supergravity as a true Kaluza-Klein theory. By using some minisuperspace ansatz, it is proved that only $S_4$×$S_7$ instantons are possible. From the viewpoint of quantum cosmology, it seems that the main reason the apparent spacetime is four-dimensional is simply that there does not exist any gravitational instanton without a four-dimensional sector in the theory.