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8.3 Applications

Once available, equations for inhomogeneous systems have the prospect of applications such as the following.
Structure formation:
 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.

Robustness:
 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 undertaken.

New effects:
 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 [70]).
Ansätze:
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.

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