  Finding signatures of quantum gravity in cosmological observations is now
actively pursued both from the theoretical and the experimental side. Recent
work has concentrated on finding signatures of light-cone fluctuations in the
CMB. Because in inflationary scenarios a Gravitational Wave Background (GWB) is
always emitted much before the CMB, we can ask, in the hypothesis where this
GWB could be observed, what is the imprint of light cone fluctuations on this
GWB. We show that due to the flat nature of the GWB spectrum, the effect of
lightcone fluctuations are negligible.
