  Recent results on the decoherent histories quantization of simple
cosmological models (minisuperspace models) are described. The most important
issue is the construction, from the wave function, of a probability
distribution answering various questions of physical interest, such as the
probability of the system entering a given region of configuration space at any
stage in its entire history. A standard but heuristic procedure is to use the
flux of (components of) the wave function in a WKB approximation as the
probability. This gives sensible semiclassical results but lacks an underlying
operator formalism. Here, we supply the underlying formalism by deriving
probability distributions linked to the Wheeler-DeWitt equation using the
decoherent histories approach to quantum theory, building on the generalized
quantum mechanics formalism developed by Hartle. The key step is the
construction of class operators characterizing questions of physical interest.
Taking advantage of a recent decoherent histories analysis of the arrival time
problem in non-relativistic quantum mechanics, we show that the appropriate
class operators in quantum cosmology are readily constructed using a complex
potential. The class operator for not entering a region of configuration space
is given by the $S$-matrix for scattering off a complex potential localized in
that region. We thus derive the class operators for entering one or more
regions in configuration space. The class operators commute with the
Hamiltonian, have a sensible classical limit and are closely related to an
intersection number operator. The corresponding probabilities coincide, in a
semiclassical approximation, with standard heuristic procedures.
