Finite states in four dimensional quantum gravity. The isotropic minisuperspace Asktekar--Klein--Gordon model

Abstract

In this paper we construct the generalized Kodama state for the case of a Klein--Gordon scalar field coupled to Ashtekar variables in isotropic minisuperspace by a new method. The criterion for finiteness of the state stems from a minisuperspace reduction of the quantized full theory, rather than the conventional techniques of reduction prior to quantization. We then provide a possible route to the reproduction of a semiclassical limit via these states. This is the result of a new principle of the semiclassical-quantum correspondence (SQC), introduced in the first paper in this series. Lastly, we examine the solution to the minisuperspace case at the semiclassical level for an isotropic CDJ matrix neglecting any quantum corrections and examine some of the implications in relation to results from previous authors on semiclassical orbits of spacetime, including inflation. It is suggested that the application of nonperturbative quantum gravity, by way of the SQC, might potentially lead to some predictions testable below the Planck scale.