Quantum cosmology in the models of 2d and 4d dilatonic supergravity with WZ matter

TL;DR

This paper investigates quantum cosmological models derived from various 2d and 4d dilatonic supergravity theories, analyzing their solutions and singularity behavior through numerical methods and quantum corrections.

Contribution

It constructs and analyzes quantum-corrected equations of motion for multiple dilatonic supergravity models, exploring their cosmological solutions and singularity properties.

Findings

Most models exhibit quantum singular Universes.

Some models show non-singular early-time Universes.

Quantum matter back reaction unlikely to resolve singularities.

Abstract

We consider N=1 two-dimensional (2d) dilatonic supergravity (SG), 2d dilatonic SG obtained by dimensional reduction from N=1 four-dimensional (4d) SG, N=2 2d dilatonic SG and string-inspired 4d dilatonic SG. For all the theories, the corresponding action on a bosonic background is constructed and the interaction with $N$ (dilatonic) Wess-Zumino (WZ) multiplets is presented. Working in the large-N approximation, it is enough to consider the trace anomaly induced effective action due to dilaton-coupled conformal matter as a quantum correction (for 2d models s-waves approximation is additionally used). The equations of motion for all such models with quantum corrections are written in a form convenient for numerical analysis. Their solutions are numerically investigated for 2d and 4d Friedmann-Robertson-Walker (FRW) or 4d Kantowski-Sacks Universes with a time-dependent dilaton via exponential dilaton coupling. The evolution of the corresponding quantum cosmological models is given for different choices of initial conditions and theory parameters. In most cases we find quantum singular Universes. Nevertheless, there are examples of Universe non-singular at early times. Hence, it looks unlikely that quantum matter back reaction on dilatonic background (at least in large $N$ approximation) may really help to solve the singularity problem.