These corrections are responsible for a surprising variety of phenomena, which all improve the
behavior in classical cosmology. Nevertheless, they were not motivated by phenomenology but were
derived through background-independent quantization. In most models and applications the
corrected equations introduce different geometrical effects separately, rather than proceeding with
complete effective equations including all quantum corrections. In this sense, such studies are
phenomenological since they isolate specific effects. While some situations have already been supported
by the rigorous effective equations discussed in Section 6, such a justification remains to be
worked out in general; see [110] for a general discussion. Once all corrections are included, one
has complete effective equations in a strict sense. This has been achieved so far only in one
class of models; see Section 6.3. Most currently available models are incomplete but provide a
wide range of perturbative calculations and have passed several non-trivial tests for consistent
behavior.
Details of the derivation in cosmological models and of their technical origin will now be reviewed in Section 5, before we come to precise effective equations in Section 6 and a discussion of the link to the full theory in Section 7.
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