  The inflationary and pre-inflationary evolution of scalar modes of
cosmological perturbations in a closed universe is analyzed for a loop quantum
cosmology model with an inflationary regime consistent with the constraints on
inflation derived from observations of the cosmic microwave background. The
effective background dynamics includes a bounce induced by quantum gravity
effects. Initial conditions for the perturbations are set before the bounce,
and the perturbations are numerically evolved until the end of inflation,
allowing the determination of the primordial power spectrum for comoving
curvature perturbations. The power spectrum includes corrections due to the
presence of spatial curvature and excitations produced before the onset of
slow-roll inflation. The deviations from the usual power-law spectrum can be
significant for observable modes even for spatial curvatures much smaller than
the observational limit obtained without considering the pre-inflationary
evolution of the perturbations.
