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 and subsequent propagation through a bounce.
- 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 so far from 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 could be a result of
small, local quantum corrections adding up to a sizeable effect on the whole universe. From
a technical point of view, contact to quantum gravity phenomenology in a particle physics
context can be made (as initially in ).
- For the time being, those questions can be addressed preliminaryly by choosing suitable
forms of inhomogeneous equations motivated by operators in full loop quantum gravity.