  Together with holonomy corrections, inverse volume terms should be taken into
account when studying the primordial universe in loop quantum cosmology. We
investigate how the tensor power spectrum is modified with respect to the
standard general relativistic prediction by those semiclassical corrections.
Depending on the values of the free parameters of the model, it is shown that
the spectrum can exhibit a very large deviation from its usual shape, in
particular with a very red slope and a strong running in the infrared limit.
