Why are the effective equations of loop quantum cosmology so accurate?

Understand

We point out that the relative Heisenberg uncertainty relations vanish for non-compact 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 back-reaction 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.