Once available, equations for inhomogeneous systems have the prospect of applications such as the
- There are diverse scenarios for the early universe with a potential for viable
structure formation, which can only be checked with a reliable handle on inhomogeneities.
This applies to inflaton models with loop effects, inflation models without inflaton, and the
generation of structure before a bounce and subsequent propagation through it.
- All results obtained so far have to be regarded as preliminary and their validity in
the presence of perturbative inhomogeneities has to be established. A detailed analysis of their
robustness to quantization freedom such as ambiguities or choosing matter fields is still to be
- Some cosmological issues that have not been addressed in detail so far by loop
quantum gravity, and which most likely require inhomogeneities, are: the initial state of the
inflaton (Gaussianity) or the present acceleration of cosmic expansion. The latter has been
suggested to be a result of small, local quantum corrections adding up to a sizeable effect on
the whole universe . From a technical point of view, closer contact to quantum gravity
phenomenology in a particle physics context should be made (as initially in ), especially
including anomaly freedom and analyzing the status of Lorentz symmetry.
- For the time being, these questions can be addressed preliminarily by choosing suitable
forms of inhomogeneous equations motivated by operators in full loop quantum gravity.