  We study the contribution of binary black hole (BH-BH) mergers from the
first, metal-free stars in the Universe (Pop III) to gravitational wave
detection rates. Our study combines initial conditions for the formation of Pop
III stars based on N-body simulations of binary formation (including rates,
binary fraction, initial mass function, orbital separation and eccentricity
distributions) with an updated model of stellar evolution specific for Pop III
stars. We find that the merger rate of these Pop III BH-BH systems is
relatively small (< 0.1 Gpc^-3 yr^-1) at low redshifts (z<2), where it can be
compared with the LIGO empirical estimate of 9-240 Gpc^-3 yr^-1 (Abbott et al.
2016). The predicted rates are even smaller for Pop III double neutron star and
black hole neutron star mergers. Our rates are compatible with those of Hartwig
et al. (2016), but significantly smaller than those found in previous work
(Bond & Carr 1984; Belczynski et al. 2004; Kinugawa et al. 2014, 2016). We
explain the reasons for this discrepancy by means of detailed model comparisons
and point out that (i) identification of Pop III BH-BH mergers may not be
possible by advanced LIGO, and (ii) the level of stochastic gravitational wave
background from Pop III mergers may be lower than recently estimated (Kowalska
et al. 2012; Inayoshi et al. 2016; Dvorkin et al. 2016). We further estimate
gravitational wave detection rates for third-generation interferometric
detectors. Our calculations are relevant for low to moderately rotating Pop III
stars. We can now exclude significant (> 1 per cent) contribution of these
stars to low-redshift BH-BH mergers. However, it remains to be tested whether
(and at what level) rapidly spinning Pop III stars (homogeneous evolution) can
contribute to BH-BH mergers in the local Universe.
