A note on the scalar products in sLQC

Solvable loop quantum cosmology provides a simple model of spatially flat, homogeneous, and isotropic quantum cosmology where the initial singularity is resolved. A close inspection of the literature reveals that there exist two different proposals for a scalar product that are usually assumed to be identical, but agree only in the large volume limit. The small volume limit, and thus the reported difference, turns out to be important for questions such as coarse graining fundamental quantum states in full theory embeddings of these cosmological models.