  The full set of cosmological observables coming from linear scalar and tensor
perturbations of loop quantum cosmology is computed in the presence of
inverse-volume corrections. Background inflationary solutions are found at
linear order in the quantum corrections; depending on the values of
quantization parameters, they obey an exact or perturbed power-law expansion in
conformal time. The comoving curvature perturbation is shown to be conserved at
large scales, just as in the classical case. Its associated Mukhanov equation
is obtained and solved. Combined with the results for tensor modes, this yields
the scalar and tensor indices, their running, and the tensor-to-scalar ratio,
which are all first order in the quantum correction. The latter could be
sizable in phenomenological scenarios. Contrary to a pure minisuperspace
parametrization, the lattice refinement parametrization is in agreement with
both anomaly cancellation and our results on background solutions and linear
perturbations. The issue of the choice of parametrization is also discussed in
relation with a possible superluminal propagation of perturbative modes, and
conclusions for quantum spacetime structure are drawn.
