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Using a new procedure based on Kummer's Confluent Hypergeometric Functions,we investigate the question of singularity avoidance in loop quantum gravity(LQG) in the context of U$(1)^3$ complexifier coherent states and compareobtained results with already existing ones. Our analysis focuses on thedynamical operators, denoted by q(r), whose products are the analogue of theinverse scale factor in LQG and also play a pivotal role for other dynamicaloperators such as matter Hamiltonians or the Hamiltonian constraint. For graphsof cubic topology and linear powers in q(r), we obtain the correct classicallimit and demonstrate how higher order corrections can be computed with thismethod. This extends already existing techniques in the way how the involvedfractional powers are handled. We also extend already existing formalisms tographs with higher-valent vertices. For generic graphs and products of q(r),using estimates becomes inevitable and we investigate upper bounds for thesesemiclassical expectation values. Compared to existing results, our methodallows to keep fractional powers involved in q(r) throughout the computations,which have been estimated by integer powers elsewhere. Similar to formerresults, we find a non-zero upper bound for the inverse scale factor at theinitial singularity. Additionally, our findings provide some insights intoproperties and related implications of the results that arise when usingestimates and can be used to look for improved estimates.

Analysing (cosmological) singularity avoidance in loop quantum gravity using U$(1)^3$ coherent states and Kummer's functions