Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation

TL;DR

This paper quantizes Friedmann-Robertson-Walker cosmological models with negative cosmological constant and radiation, showing that quantum effects prevent singularities by causing oscillating, non-vanishing scale factors.

Contribution

It introduces a method to solve Wheeler-DeWitt equations for these models using a quartic anharmonic oscillator approach, revealing non-singular quantum cosmological solutions.

Findings

Expected scale factors oscillate between maximum and minimum values.

Quantum models avoid classical singularities.

Eigenfunctions constructed for different curvature cases.

Abstract

We quantize three Friedmann-Robertson-Walker models in the presence of a negative cosmological constant and radiation. The models differ from each other by the constant curvature of the spatial sections, which may be positive, negative or zero. They give rise to Wheeler-DeWitt equations for the scale factor which have the form of the Schroedinger equation for the quartic anharmonic oscillator. We find their eigenvalues and eigenfunctions by using a method first developed by Chhajlany and Malnev, and use the eigenfunctions in order to construct wave packets for each case and evaluate the time-dependent expected value of the scale factors. We find for all of them that the expected values of the scale factors oscillate between maximum and minimum values. Since the expectation values of the scale factors never vanish, we conclude that these models do not have singularities.