  We calculate the reduced density matrix for the inflaton field in a model of
chaotic inflation by tracing out degrees of freedom corresponding to various
bosonic fields. We find a qualitatively new contribution to the density matrix
given by the Euclidean effective action of quantum fields. We regularise the
ultraviolet divergences in the decoherence factor. Dimensional regularisation
is shown to violate the consistency conditions for a density matrix as a
bounded operator. A physically motivated conformal redefinition of the
environmental fields leads to well-defined expressions. They show that due to
bosonic fields the Universe acquires classical properties near the onset of
inflation.
