We point out that the relative Heisenberg uncertainty relations vanish for noncompact spaces in homogeneous loop quantum cosmology. As a consequence, for sharply peaked states quantum fluctuations in the scale factor never become important, even near the bounce point. This shows why quantum backreaction effects remain negligible and explains the surprising accuracy of the effective equations in describing the dynamics of sharply peaked wave packets. This also underlines the fact that minisuperspace models—where it is global variables that are quantized—do not capture the local quantum fluctuations of the geometry.

• Received 24 April 2014

DOI:https://doi.org/10.1103/PhysRevD.90.023538