Decoherence on the Onset of Inflation in Quantum Cosmology

We consider the problem of ultraviolet divergences in the decoherence factor in quantum cosmology. It is shown that using dimensional regularization it is not possible to obtained the consistent reduced density matrix. In the case of tracing out the bosonic inhomogeneous degrees of freedom one can get a reasonable reduced density matrix showing decoherence properties using a conformal reparametrization of fields, which suppresses ultraviolet divergences. In the case of fermionic fields such a suppression can be achieved by performing of a non-local Bogoliubov transformation of Grassmann variables.