- Conceptual issues:
- This has already been mentioned above. Isotropic models provide simpler settings to analyze, e.g., the physical inner product [184, 243, 26, 33], observables, different interpretations of quantum aspects or the emergence of a classical world.
- Effective equations:
- Even in isotropic models, effective equations have only been derived completely in one special class of models [70]. A general scheme exists, shown to be analogous to standard effective-action techniques [105], but it remains to be applied in detail to quantum cosmology, as done for an interacting scalar in [87]. If successful, this will lead to a complete set of correction terms and their ranges of validity and importance. In addition, the question of whether a covariant effective action for quantum cosmology exists and what its form is can be addressed.
- Properties of states:
- In some isotropic models, properties of dynamical coherent states are available [70, 69]. Thus, cosmological applications, which take into account the evolution of a full quantum state, rather than just classical variables subject to equations with quantum corrections, become possible. Quite surprisingly at first sight, state properties can change significantly in cosmological transitions, especially at the Big Bang, and play an important role for potential conclusions drawn from observations [72, 74]. This highlights the role of dynamical coherent states, which illustrate effects not visible for kinematical coherent states.
- Matter systems:
- Matter systems provide a rich source of diverse scenarios, but a full analysis is yet to be done. This includes adding different kinds of fluids [244], fermions or anisotropy parameters (shear term).

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