  Quantum fluctuations or other moments of a state contribute to energy
expectation values and can imply interesting physical effects. In quantum
cosmology, they turn out to be important for a discussion of density bounds and
instabilities of initial-value problems in the presence of signature change in
loop-quantized models. This article provides an effective description of these
issues, accompanied by a comparison with existing numerical results and an
extension to squeezed states. The comparison confirms that canonical effective
methods are well-suited for computations of properties of physical states. As a
side product, an example is found for a simple state in which quantum
fluctuations can cancel holonomy modifications of loop quantum cosmology.
