Quantum cosmology for inflationary scenary

Abstract

We study quantum and super quantum cosmology for a Friedman-Robertson Walker (FRW) flat universe in the presence of an inflation exponential potential with the corresponding kinetic term for the scalar field. We exhibit exact solutions for the corresponding Wheeler-DeWitt (WDW) equation and its square root. In both cases, solutions, as is known for the Bianchi models, of the form $e^{i\Phi}$ exist, where $\Phi$ is the Hamilton-Jacobi function. For a particular factor ordering of the standard Wheeler-DeWitt equation we show a ``wave packet" in which for large $x$ (with the radius of expansion of the universe $a \sim e^{-x}$), $\varphi$ the scalar field and $x$ ``compete" modulating the behaviour of the ``wave packet".