The recent discovery of the gravitational wave source GW150914 has revealed a coalescing binary black hole ( BBH ) with masses of \sim 30 ~ { } { M } _ { \odot } .
Previous proposals for the origin of such a massive binary include Population III ( PopIII ) stars .
PopIII stars are efficient producers of BBHs and of a gravitational wave background ( GWB ) in the 10 - 100 Hz band , and also of ionizing radiation in the early Universe .
We quantify the relation between the amplitude of the GWB ( \Omega _ { gw } ) and the electron scattering optical depth ( \tau _ { e } ) , produced by PopIII stars , assuming that f _ { esc } \approx 10 \% of their ionizing radiation escapes into the intergalactic medium .
We find that PopIII stars would produce a GWB that is detectable by the future O5 LIGO/Virgo if \tau _ { e } \ga 0.07 , consistent with the recent Planck measurement of \tau _ { e } = 0.055 \pm 0.09 .
Moreover , the spectral index of the background from PopIII BBHs becomes as small as { d } \ln \Omega _ { gw } / { d } \ln f \la 0.3 at f \ga 30 Hz , which is significantly flatter than the value \sim 2 / 3 generically produced by lower-redshift and less-massive BBHs .
A detection of the unique flattening at such low frequencies by the O5 LIGO/Virgo will indicate the existence of a high-chirp mass , high-redshift BBH population , which is consistent with the PopIII origin .
A precise characterization of the spectral shape near 30 - 50 Hz by the Einstein Telescope could also constrain the PopIII initial mass function and star formation rate .