On (cosmological) singularity avoidance in loop quantum gravity

Abstract

Loop quantum cosmology (LQC), mainly due to Bojowald, is not the cosmological sector of loop quantum gravity (LQG). Rather, LQC consists of a truncation of the phase space of classical general relativity to spatially homogeneous situations which is then quantized by the methods of LQG. Thus, LQC is a quantum-mechanical toy model (finite number of degrees of freedom) for LQG (a genuine QFT with an infinite number of degrees of freedom) which provides important consistency checks. However, it is a non-trivial question whether the predictions of LQC are robust after switching on the inhomogeneous fluctuations present in full LQG. Two of the most spectacular findings of LQC are that: (1) the inverse scale factor is bounded from above on zero-volume eigenstates which hints at the avoidance of the local curvature singularity and (2) the quantum Einstein equations are nonsingular which hints at the avoidance of the global initial singularity. This rests on (1) a key technique developed for LQG and (2) the fact that there are no inhomogeneous excitations. We display the result of a calculation for LQG which proves that the (analogon of the) inverse scale factor, while densely defined, is not bounded from above on zero-volume eigenstates. Thus, in full LQG, if curvature singularity avoidance is realized, then not in this simple way. In fact, it turns out that the boundedness of the inverse scale factor is neither necessary nor sufficient for the curvature singularity avoidance and that non-singular evolution equations are neither necessary nor sufficient for initial singularity avoidance because none of these criteria are formulated in terms of observable quantities. After outlining what would be required, we present the results of a calculation for LQG which could be a first indication that our criteria at least for curvature singularity avoidance are satisfied in LQG.

Critical Behaviour in Quantum Gravitational Collapse

“…The corresponding quantum corrected equation will have a power of the spectrum function of the corresponding operator as in Eqn. (19). Given the form of this function, it is apparent that the large x limit gives the classical equation as shown in Figure 2, and that the small x region represents a "repulsion," if the eigenvalue represents a potential energy.…”

Loop quantum gravity: an outside view

“…to the inverse volume is not bounded from above when acting on zero-volume spin network states [41] (in marked contrast to the symmetry reduced models of [38], where the avoidance of an initial singularity hinges on the fact that the operator corresponding to the 'inverse volume' is bounded from above 13 ). Nevertheless, the resulting formulas remain very complicated.…”

Semiclassical dynamics of horizons in spherically symmetric collapse

“…Results from LQC leads to the conclusion that the cosmological singularities are resolved in quantum gravity [11]. However, in view of the full theory, there is still considerable ambiguity and none of those results are fully satisfactory [12,13].…”