Quantum Cosmology Close to the Classical Big Bang Singularity and in the Semiclassical Limit

TL;DR

This paper explores quantum cosmology models with a Chaplygin gas, solving the Wheeler-DeWitt equation exactly in key limits, and demonstrates how quantum wave functions can avoid the big bang singularity while matching classical behavior in the semiclassical limit.

Contribution

It provides exact solutions to the Wheeler-DeWitt equation for cosmological models with Chaplygin gas and dust, showing how quantum states can circumvent the big bang singularity and align with classical cosmology.

Findings

Wave function vanishes at the classical singularity, avoiding the big bang.

Exact solutions describe universe evolution with dust, avoiding singularities.

Wave packets are peaked at classical configurations in the semiclassical limit.

Abstract

We investigate a cosmological model whose energy content is described by a Chaplygin gas represented by a scalar field $\phi$ with an associated potential producing a big bang singularity such that for vanishing scale factor, $a\to 0$, one has $|\phi|\to \infty$. The classical version of the model is discussed in detail, however, our main interest lies in its quantization. Upon quantization of this model in the Schr\"odinger picture, we get the Wheeler--DeWitt equation which can be solved exactly in the two limits $a\to 0$ and $a\to\infty$, respectively. Employing the DeWitt criterium that the wave function should vanish at the classical singularity in order to avoid the big bang, we show that a solution to the Wheeler-DeWitt equation fulfilling this condition can indeed be found. In addition to DeWitt's initial condition at the big bang, we postulate an asymptotic condition to be imposed on the wave function which guarantees that the quantum wave function is strongly peaked at the classical field configurations in the semiclassical limit. We also investigate a universe filled with dust (describing baryonic and dark matter) and show that in this case there exists an exact solution to the Wheeler-DeWitt equation which describes the evolution of the universe during its whole history. Also for this model one can construct a wave packet which avoids the big bang singularity at small scale factors and is strongly peaked at the classical field in the far future of the universe. Finally, we discuss the significance of our treatment of the Wheeler-DeWitt equation and mention some open problems.