Generating function techniques for loop quantum cosmology

Abstract Loop quantum cosmology leads to a difference equation for the wave function of a universe. In the semiclassical limit, small-scale oscillations must be suppressed by choosing parameters of general solutions appropriately. For anisotropic models this is not possible to do numerically by trial and error; instead, it is shown here for the Bianchi I LRS model how this can be done analytically, using generating function techniques. Those techniques can also be applied to more complicated models, and the results gained allow conclusions about initial value problems and possible large quantum gravity effects.