  We calculate the full spectrum, as observed today, of the cosmological
gravitational waves generated within a model based on loop quantum cosmology.
It is assumed that the universe, after the transition to the classical regime,
undergoes a period of inflation driven by a scalar field with a chaotic-type
potential. Our analysis shows that, for certain conditions, loop quantum
effects leave a clear signature on the spectrum, namely, an over-production of
low-frequency gravitational waves. One of the aims of our work is to show that
loop quantum cosmology models can be tested and that, more generally,
pre-inflationary physical processes, contrary to what is usually assumed, leave
their imprint in those spectra and can also be tested.
