We study the mechanism of generating parity-violated gravitational waves from inflation, which are potentially detectable in future gravitational wave interferometers and pulsar timing arrays such as DECIGO, eLISA and SKA.  More precisely, we study the inflationary dynamics with a dilatonic field and an axionic field, both of which are coupled with a SU(2) gauge field. Remarkably, we find that parity-violated tensor modes can be enhanced due to a tachyonic instability of the gauge field, which is controlled by the effective coupling of an axion to gauge field.

 In this talk, we discuss the mechanism that provides chiral tensor spectrum compatible with current CMB observations and potentially observable by future experiments.