The status of quantum cosmologies as testable models of the early universe is
assessed in the context of inflation. While traditional Wheeler-DeWitt
quantization is unable to produce sizable effects in the cosmic microwave
background, the more recent loop quantum cosmology can generate potentially
detectable departures from the standard cosmic spectrum. Thus, present
observations constrain the parameter space of the model, which could be made
falsifiable by near-future experiments.Comment: 16 pages, 3 figures. Invited review article also containing original
material. v2: new section on holonomy corrections, introduction extended,
references added, typos corrected; v3: includes corrections of eqs. (3), (62)
and (64c) of the erratu
