Absence of Singularity in Loop Quantum Cosmology

TL;DR

It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry and the correct semiclassical behavior is obtained.

Abstract

It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstation comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.

Figures (1)

• Figure 1: The classical expectation $V_j^{-\frac{1}{3}}$ (dashed line) and eigenvalues $m_{II,j}$, $j\geq0$ of the inverse scale factor ($\times$). Contrary to the classical curve, the latter peak at $j=\frac{1}{2}$ and decrease for $j=0$ and $j=-\frac{1}{2}$ ($m_{II,-\frac{1}{2}}=0$ is not shown).