Initial state in quantum cosmology

Canonical quantum gravity admits an initial state of the Universe which is independent of all variables (except for the ‘‘timelike’’ expansion factor a) in the field representation. This is achieved by means of a symmetrical initial condition (SIC). The consequences of the SIC are investigated in detail within some models. Thereby an additional potential, significantly contributing in the Planck era only, is introduced ad hoc into the potential of the Wheeler-DeWitt equation. Apart from technical advantages it allows the wave function to vanish at the initial singularity, and to satisfy the SIC. Decoherence with respect to the expansion factor is analyzed in the perturbed Friedmann model with various versions of such a ‘‘Planck potential.’’ A rather complex one is required in order to derive ultraviolet cutoffs for the considered fields. It is also possible to justify the linear approximation for the perturbed Friedmann model, and to estimate the region where the minisuperspace approximation is valid. The SIC is compared with the ‘‘no boundary’’ condition of Hartle and Hawking.