  We do not observe quantum effects on cosmological scales. Thus, if loop
quantum cosmology (LQC) is to provide an accurate depiction of the real world,
it must allow for quantum states of spacetime geometry which are semi-classical
in two respects: they must be sharply peaked around a single, classical
geometry, and they must have small quantum fluctuations. It is generally
assumed that Gaussian states exhibit both of these properties. After all, they
do in ordinary quantum mechanics. In this paper, we derive exact closed-form
expressions for the fluctuations of Gaussian states in LQC and their lower
bound given by the Robertson-Schr\"odinger inequality. We demonstrate that,
contrary to ordinary quantum mechanics, fluctuations for Gaussian states in
spatially flat, homogeneous and isotropic LQC diverge as the state variance
increases (as well as in related cosmological models with the same kinematic
Hilbert space and canonical observables). However, when the holonomy length is
made to scale with a volume regularization parameter, these fluctuations may be
arbitrarily suppressed by taking the fiducial volume to be large, providing
analytic control over their divergence. Finally, we show that, despite this,
Gaussian states in LQC generally do not minimize uncertainty. Moreover, it is
conjectured that no such minimal-uncertainty states exist. Throughout this
work, it becomes clear how important the often-assumed condition of holonomy
length volume-scaling is; we show that when this condition is violated, the
resulting theory exhibits operator closure pathologies and other exotic
algebraic features.
