(1992) that the coarse-grained closed-time-path effective action formalism is equivalent to the Feynman-Vernon (1963) influence functional which was popularized by Caldeira and Leggett (1983) in their study of quantum macroscopic dissipative processes. Paz and Sinha (1991, 1992) have used this paradigm for a detailed analysis of the relation of quantum cosmology with semiclassical gravity. We like to illustrate this development with two problems, initially proposed and studied by Misner. One is on the validity of minisuperspace approximation, the other is on the classical limit of quantum cosmology.

Validity of the Minisuperspace Approximation
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In quantum cosmology, the principal object of interest is the wave function of the universe $\Psi(h_{ij}, \phi)$, which is a functional on superspace. It obeys the Wheeler DeWitt equation, which is an infinite-dimensional partial differential equation. Its solution is a formidable task in the general case. To make the problem more tractable, Misner suggested looking at only a finite number of degrees of freedom (usually obtained by imposing a symmetry requirement), and coined the word minisuperspace (Misner 1972) quantization. We note that such a tremendous simplification has its preconditions. Since in the process of this transition one is truncating an infinite number of modes, nonlinear interactions of 