  Within a perturbative cosmological regime of loop quantum gravity corrections
to effective constraints are computed. This takes into account all
inhomogeneous degrees of freedom relevant for scalar metric modes around flat
space and results in explicit expressions for modified coefficients and of
higher order terms. It also illustrates the role of different scales
determining the relative magnitude of corrections. Our results demonstrate that
loop quantum gravity has the correct classical limit, at least in its sector of
cosmological perturbations around flat space, in the sense of perturbative
effective theory.
