Primordial gravitational waves: the seeds within the primal seed (the fingerprints of GOd???) - from the Quora poster "Huang China". This is a possibl efascinating application of GW detection, although I believe LIGo is not able to detect ultra low frequencies.
Till now our knowledge of the early universe is from the cosmic microwave background(CMB). However, the early universe is filled with plasma, which is opaque to electromagnetic radiation. So the CMB only tells us what happened 378 thousand years after the big bang. However, the gravitational waves can travel freely through the plasma, so it provides an insight into extremely early universe events such as inflation. Such gravitational wave is called primordial gravitational wave.
The BICEP II last year announced the discovery of the primordial gravitational waves, but it was soon falsificated by the datas from the Planck. Now many teams, including BICEP III are competing for the discovery of primordial gravitational wave. If it is verified, it will greatly promote the development of cosmology and possibly the quantum gravity.