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

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.

LaTeX file of the text (36 pages) and 3 ps files of 14 figures, few misprints are corrected and references added

References in corpus (9)

• (Anti-)Evaporation of Schwarzschild-de Sitter Black Holes
• Trace Anomaly of Dilaton Coupled Scalars in Two Dimensions
• Trace anomaly induced effective action for 2D and 4D dilaton coupled scalars
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• Exact solutions in two-dimensional string cosmology with back reaction
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• Two Two-Dimensional Supergravity Theories from Calabi-Yau Four-Folds
• Anomaly induced effective actions in even dimensions and reliability of s-wave approximation
• (Non) singular Kantowski-Sachs Universe from quantum spherically reduced matter
• On the Dimensional Reduction Procedure
• Transition from AdS universe to DS universe in the BPP model
• Unveiling horizons in quantum critical collapse
• Inflationary Dilatonic de Sitter Universe from cal N = 4 Super Yang - Mills Theory Perturbed by Scalars
• Anomaly Induced Effective Action Combined with Generalized Brans-Dicke Theory
• Inflationary Dilatonic de Sitter Universe from Super Yang - Mills Theory Perturbed by Scalars and Spinors