Approximate Canonical Quantization for Cosmological Models

In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this in mind, we present a scheme for the (approximate) quantization of perturbed, nonintegrable, time-reparametrization invariant systems that uses (approximate) gauge invariant quantities. We apply the scheme to a couple of simple quantum cosmological models. Pac(s) numbers: 03.20.+i, 04.60.Ds, 98.80.Hw, 04.60.Kz. Keyword(s): Canonical Quantization, Quantum Cosmology, Minisuperspace Models.