there has been a lot of interest in this subject, and two basic criteria for classicality have emerged (see Halliwell 1991 and references therein) from these endeavors. The first is [*decoherence*]{} – which requires that quantum interference between distinct alternatives must be suppressed. The second is that of [*correlation*]{}, which requires that the wave function or some distribution constructed from it (e.g. Wigner 1932) predicts correlations between coordinates and momenta in accordance with classical equations of motion. We will study the emergence of a semiclassical limit with the help of a quantum open system paradigm applied in the context of quantum cosmology. The basic mechanism for achieving decoherence and the appearance of correlations is by coarse-graining certain variables acting as an environment coupled to the system of interest.

Reduced Density Matrix
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We will consider a $D$-dimensional minisuperspace with coordinates $r^m$ ($m=1,\ldots,D$) as our system for which the Hamiltonian can be written as: $$H_g= {1\over{2M}}G^{mm'}p_mp_{m'} + M V(r^m)$$ where $G^{mm'}$ is the (super)metric of the minisuperspace and $M $ is related to the square of the Planck mass. The minisuperspace modes are coupled to other degrees of freedom $\Phi$, such as the modes of a scalar field, or the gravitational 