Quantum-gravitational effects on gauge-invariant scalar and tensor
  perturbations during inflation: The slow-roll approximation
  We continue our study on corrections from canonical quantum gravity to the
power spectra of gauge-invariant inflationary scalar and tensor perturbations.
A direct canonical quantization of a perturbed inflationary universe model is
implemented, which leads to a Wheeler-DeWitt equation. For this equation, a
semiclassical approximation is applied in order to obtain a Schroedinger
equation with quantum-gravitational correction terms, from which we calculate
the corrections to the power spectra. We go beyond the de Sitter case discussed
earlier and analyze our model in the first slow-roll approximation, considering
terms linear in the slow-roll parameters. We find that the dominant correction
term from the de Sitter case, which leads to an enhancement of power on the
largest scales, gets modified by terms proportional to the slow-roll
parameters. A correction to the tensor-to-scalar ratio is also found at second
order in the slow-roll parameters. Making use of the available experimental
data, the magnitude of these quantum-gravitational corrections is estimated.
Finally, the effects for the temperature anisotropies in the cosmic microwave
background are qualitatively obtained.
