Singularity resolution from polymer quantum matter

We study the polymeric nature of quantum matter fields using the example of a Friedmann-Lemaître-Robertson-Walker universe sourced by a minimally coupled massless scalar field. The model is treated in the symmetry reduced regime via deparametrization techniques, with the scale factor playing the role of time. Subsequently, the remaining dynamic degrees of freedom corresponding to the matter are polymer quantized. The analysis of the resulting genuine quantum dynamic shows that the big bang singularity is resolved, although with the form of the resolution differing significantly from that in the models with matter clocks: dynamically, the singularity is made passable rather than avoided. Furthermore, this analysis exposes crucial limitations to the so-called effective dynamic in loop quantum cosmology when applied outside of the most basic isotropic settings.

Figure 1

An illustration of the quantum evolution of the scalar field is presented in (a). In (b) we display the $p_{\varphi }^{\star }=5$ quantum evolution along with the corresponding classical evolution over a subset of the $v$ interval used in (a). The circles, triangles, and squares correspond to actual measurements made using the software Matlab and GNU Octave. The time interval between two consecutive measurements becomes smaller as $|v|$ approaches 0. In this plot, the smallest value of $|v|$ is 0.25 but values as small as ${10}^{-4}$ have been considered with the same outcome. Namely, there is semiclassicality for $|v|\gg 1$ and the big bang singularity at $v=0$ is resolved.

Figure 2

Expectation values of the spacetime Ricci operator for various values of $v$ are plotted in this figure. As in Fig. 1, measurements are taken the more often the closer $|v|$ is to 0 with the smallest values given by $|v|=0.25$. It follows that the big bang curvature singularity is resolved and the branches $v\in {\mathbb{R}}^{\pm }$ are connected.

Figure 3

In this figure an illustration of the fluctuations of the scalar field operator is presented. For $|v|\to \infty$ the fluctuations increase but remain nonetheless finite.

Figure 4

This figure provides an illustration of the fluctuations of the polymeric momentum operator. Just like for the scalar field fluctuations in Fig. 3, the behavior for $|v|\gg 1$ indicates semiclassicality.