Nonmarginal Lemaitre-Tolman-Bondi-like models with inverse triad corrections from loop quantum gravity

Marginal Lemaitre-Tolman-Bondi (LTB) models with corrections from loop quantum gravity have recently been studied with an emphasis on potential singularity resolution. This paper corroborates and extends the analysis in two regards: (i) the whole class of LTB models, including nonmarginal ones, is considered, and (ii) an alternative procedure to derive anomaly-free models is presented which first implements anomaly freedom in spherical symmetry and then the LTB conditions rather than the other way around. While the two methods give slightly different equations of motion, not altogether surprisingly given the ubiquitous sprawl of quantization ambiguities, final conclusions remain unchanged: compared to quantizations of homogeneous models, bounces seem to appear less easily in inhomogeneous situations, and even the existence of homogeneous solutions as special cases in inhomogeneous models may be precluded by quantum effects. However, compared to marginal models, bouncing solutions seem more likely with nonmarginal models.

Figure 1

The correction functions $\alpha (\Delta )$ (solid line) and $f(\Delta )$ (dashed line) where $\Delta$ is taken relative to ${\Delta }_{*}≔\sqrt{\gamma /2}{\ell }_{\mathrm{P}}$.