Validity of the minisuperspace approximation: An example from interacting quantum field theory

We examine the question of the validity of the minisuperspace approximation using the example of an interacting (λΦ⁴) scalar field in a closed Robertson-Walker universe, where the scale factor and the homogeneous mode of the scalar field model the minisuperspace degrees of freedom. We explicitly compute the back reaction of the inhomogeneous modes on the minisuperspace sector using a coarse-grained effective action and show that the minisuperspace approximation is valid only when this back reaction is small.