Probing noncommutativity with inflationary gravitational waves

In this Letter we study the behaviour of gravitational wave background (GWB) generated during inflation in the noncommutative field approach. From this approach we derive one additional term, and then we find that the dispersion relation of the gravitational wave would be modified and the primordial gravitational wave would obtain an effective mass. Therefore it breaks local Lorentz symmetry. Moreover, this additional term suppresses the energy spectrum of the GWB greatly at low energy scale where the wave length is near the current horizon. Due to this, a sharp peak is formed in the energy spectrum at the low frequency band. This peak should be a key criterion in detecting the space-time noncommutativity and a critical test for Lorentz symmetry breaking in local field theory.