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Using the results of a numerical simulation which follows the evolution, metal enrichment and energy deposition of both Population III and II stars, we predict the redshift dependence of the formation rate of black hole remnants of Population III stars with masses  100–500 M ⊙   and of neutron stars (black holes) remnants of Population II stars with masses  8–20 M ⊙ (20–40 M ⊙  ).  We describe the gravitational wave spectrum produced by Population III and II sources adopting the most appropriate signals available in the literature and we compute the stochastic backgrounds resulting from the cumulative emission of these sources throughout the history of the Universe.  With the aim of assessing whether these backgrounds might act as foregrounds for signals generated in the inflationary epoch, we compare their amplitudes with the sensitivity of currently planned and future ground/space‐based interferometers.  The predicted Population III background lies in the sensitivity range of Ultimate‐Decihertz Interferometer Gravitational Wave Observatory (DECIGO), adding as a confusion‐limited noise, with a peak amplitude of  Ω GW  h  2 ≃ 3 × 10 −15   at   f = 2.74 Hz . However, differently to previous claims, we find that the gravitational wave background (GWB) generated in the inflationary epoch may dominate for   f ≤ 2  Hz. At frequencies   f ≥ 10 Hz , the background generated by Population II stellar remnants is much larger than that associated with Population III stars, with peak amplitudes ranging between  10 −12 ≤Ω GW  h  2 ≤ 7 × 10 −10   at frequencies   f ∈ 387–850  Hz: progenitors with masses in the range  20–100 M ⊙   contribute with a nearly monotonically increasing behaviour, whereas for stars with masses  8–25 M ⊙   the resulting background shape depends on the waveforms used to represent the collapse signal.  Finally, we explore a scenario in which Super Massive Stars, formed in protogalactic dark matter haloes out of gas of primordial composition and irradiated by a strong ultraviolet background, collapse to Super Massive Black Holes (SMBHs). Even assuming, as an upper limit to their formation rate, that the mass density of these SMBHs at   z = 10  equals the presently observed value, the resulting GWB is too low to be detected from the space‐based interferometer LISA; it is in the sensitivity range of Ultimate‐DECIGO but in a frequency region seriously limited by the Galactic binary confusion background.

Gravitational wave backgrounds and the cosmic transition from Population III to Population II stars