Quantum cosmology of the multi-field scalar matter: some exact solutions

TL;DR

This paper derives exact solutions in quantum cosmology models with multiple scalar fields and exponential potentials, analyzing their semiclassical limits and boundary conditions for classical cosmology.

Contribution

It introduces a model with multiple scalar fields allowing variable separation in the Wheeler-DeWitt equation, leading to exact solutions in quantum cosmology.

Findings

Exact solutions to Wheeler-DeWitt equations for multi-field scalar models

Analysis of boundary conditions for classical cosmology emergence

Semiclassical approximation insights for quantum cosmological models

Abstract

We consider the gravity interacting with matter scalar fields and quantized in the minisuperspace approach in which the wave functional is described by the Wheeler-DeWitt equations (WdW). Assuming the domination of the homogeneous and isotropic geometry the leading contributions to the wave functional in the approximation of the minisuperspace with Friedmann-Robertson-Walker metric (FRW) and spatially uniform scalar fields are considered. The model of several scalar fields with exponential potentials and kinetic terms admitting such a special mixing that ultimately it is possible to separate the variables in the WdW equation and to find its exact solution in terms of the special functions is proposed. The semiclassical approximation is thoroughly investigated and the boundary conditions permitting the physical solution selection for classical cosmologies are chosen.