Singularity resolution from polymer quantum matter

Abstract

We study the polymeric nature of quantum matter fields using the example of a FriedmannLemaître-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.

Collapse and dispersal of a homogeneous spin fluid in Einstein–Cartan theory

“…Besides the model presented here, non-singular scenarios have been reported in the literature within various models such as f (R) theories of gravity in the Palatini [86] and metric [87] formalisms, nonsingular cosmological settings in the presence of a spinning fluid in the context of EC theory [88], bouncing scenarios in brane models [89][90][91][92][93], and modified Gauss-Bonnet gravity [94] (see also [95] for recent review). While the spacetime singularities could generically occur as the end-product of a continual gravitational collapse, it is widely believed that in the very final stages of the collapse where the scales are comparable to the Planck length and extreme gravity regions are dominant, quantum corrections could generate a strong negative pressure in the interior of the cloud to finally resolve the classical singularity [96][97][98][99][100][101][102][103][104][105][106][107]. Finally, as we come near the end of this paper we should point out that quantum effects due to particle creation could possibly avoid the cosmological [108][109][110][111] as well as astrophysical singularities [112].…”

Loop quantum cosmology of a radiation-dominated flat FLRW universe

“…An alternative possibility to construct a separable Hilbert space is to use the construction given in Appendix C of [45] or to exploit the natural fibration of H gr and the Lebesgue measure on the fiber space inherited from superselection labels. The latter method leads to the fiber-integral Hilbert space which is again separable [26,46]. For the remaining part of this paper we choose the first approach and work with one superselection sector.…”

“…The matter sector is usually dealt with in a perfunctory manner, although there do exist some studies on the polymeric matter sector in the literature [25,26] (including attempts to describe the perturbative degrees of freedom [27]). Most of the space-times studied to date in LQC are either vacuum space-times [12,14] or with the particularly simple choice of a massless scalar field [3, 5-7, 11, 13, 15].…”

Separable Hilbert space for loop quantization

“…On the other hand, the reasoning presented in Sec. 4 of [17] and references therein shows that-in the context of LQC-a similar approach based on working within the subspaces S ϵ may be problematic because the dynamics may connect different sectors. To avoid this kind of problem one should take into account all the sectors.…”