Stochastic background of gravitational waves generated by pre-galactic black holes

In this work, we consider the stochastic background of gravitational waves (SBGWs) produced by pre-galactic stars, which form black holes in scenarios of structure formation. The calculation is performed in the framework of hierarchical structure formation using a Press-Schechter-like formalism. Our model reproduces the observed star formation rate at redshifts z less than or similar to 6.5. The signal predicted in this work is below the sensitivity of the first generation of detectors but could be detectable by the next generation of ground-based interferometers. Specifically, correlating two coincident advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors (LIGO III interferometers), the expected signal-to-noise ratio (S/N) could be as high as 90 (10) for stars forming at redshift z similar or equal to 20 with a Salpeter initial mass function with slope x = 0.35 (1.35), and if the efficiency of generation of gravitational waves, namely, epsilon(GW) is close to the maximum value similar to 7 x 10(-4). However, the sensitivity of the future third generation of detectors as, for example, the European antenna EGO could be high enough to produce S/N > 3 same with epsilon(GW) similar to 2 x 10(-5). We also discuss what astrophysical information could be derived from a positive (or even negative) detection of the SBGWs investigated here.