  An approach to compute quantum-gravity corrections to the scalar and
tensorial power spectra of the inflationary perturbations is presented. The
analysis of the Wheeler-DeWitt equation is performed by a decomposition of the
wave function into its infinite set of moments, which must obey certain system
of (first-class) constraints. Considering a semiclassical approximation, the
system is truncated at second order in moments and an appropriate gauge-fixing
condition is introduced, which allows us to interpret the scale factor of the
universe as an internal time. The evolution of the different fluctuations and
correlations is then explicitly considered for a de Sitter universe. An
approximate analytical solution is obtained for the corrections of the power
spectra, which produces an enhancement of power for large scales. Remarkably,
the result is in agreement with previous studies in the literature that made
use of very different semiclassical approximations. Finally, the numerical
implementation of the system is also considered to verify the validity of the
analytical solution.
