Phenomenology with fluctuating quantum geometries in loop quantum
  cosmology
  The goal of this paper is to probe phenomenological implications of large
fluctuations of quantum geometry in the Planck era, using cosmology of the
early universe. For the background (Friedmann, Lema\^{i}tre, Robertson, Walker)
\emph{quantum} geometry, we allow `widely spread' states in which the
\emph{relative} dispersions are as large as $168\%$ in the Planck regime. By
introducing suitable methods to overcome the ensuing conceptual and
computational issues, we calculate the power spectrum $P_{\mathcal{R}}(k)$ and
the spectral index $n_s(k)$ of primordial curvature perturbations. These
results generalize the previous work in loop quantum cosmology which focused on
those states which were known to remain sharply peaked throughout the Planck
regime. Surprisingly, even though the fluctuations we now consider are large,
their presence does not add new features to the final $P_{\mathcal{R}}(k)$ and
$n_s(k)$: Within observational error bars, their effect is degenerate with a
different freedom in the theory, namely the number of \emph{pre-inflationary}
e-folds $N_{{\rm B}\,\star}$ between the bounce and the onset of inflation.
Therefore, with regard to observational consequences, one can simulate the
freedom in the choice of states with large fluctuations in the Planck era using
the simpler, sharply peaked states, simply by allowing for different values of
$N_{{\rm B}\,\star}$.
