9.4 Homogeneous models
There are still several open areas in homogeneous models, which can later be extended to
- 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.
- Even in isotropic models, effective equations have only been derived
completely in one special class of models . A general scheme exists, shown to be analogous
to standard effective-action techniques , but it remains to be applied in detail to quantum
cosmology, as done for an interacting scalar in . 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
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 provide a rich source of diverse scenarios, but a full analysis
is yet to be done. This includes adding different kinds of fluids , fermions or anisotropy
parameters (shear term).