of their extensions to more general settings. In order to make the presentation of the studies clearer to the reader, some details of the mathematical studies as well as the details of the numerical analysis used in the article are moved to Appendix \[app:math\] and \[app:num\] respectively.

The framework of LQC and its WDW analog {#sec:frame}
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In this section we briefly sketch the specification, quantization program and relevant properties of the models we are going to study. We discuss only those elements of the theory, which are relevant for our analysis. For the detailed description of the quantization and the properties of the systems the reader is referred to [@abl; @aps-imp] and [@awe].

Since the considered systems are constrained ones, they are quantized via Dirac program, which consists of the following steps: kinematical quantization ignoring the constraints, promoting the constraints to quantum operators and finding the physical Hilbert space built out of the states annihilated by the quantum constraint. In accordance to this procedure this section has the following structure: First we introduce the classical models, LQC kinematics and quantization of the constraint for the FRW and Bianchi I models separately in Sec. \[sec:frame-FRW\] and \[sec:frame-B1\] respectively. Next we 