  Quantum gravitational effects in loop quantum cosmology lead to a resolution
of the initial singularity and have the potential to solve the horizon problem
and generate a quasi scale-invariant spectrum of density fluctuations. We
consider loop modifications to the behavior of the inverse scale factor below a
critical scale in closed models and assume a purely thermal origin for the
fluctuations. We show that the no-go results for scale invariance in classical
thermal models can be evaded even if we just consider modifications to the
background (zeroth order) gravitational dynamics. Since a complete and
systematic treatment of the perturbed Einstein equations in loop cosmology is
still lacking, we simply parameterize their expected modifications. These
change quantitatively, but not qualitatively, our conclusions. We thus urge the
community to more fully work out this complex aspect of loop cosmology, since
the full picture would not only fix the free parameters of the theory, but also
provide a model for a non-inflationary, thermal origin for the structures of
the Universe.
