Testing super heavy dark matter from primordial black holes with gravitational waves

Ultra-light primordial black holes with masses M_BH < 10⁹ g evaporate before big-bang nucleosynthesis producing all matter fields, including dark matter, in particular super-heavy dark matter: M_DM ≳ 10¹⁰ GeV. If the dark matter gets its mass via U(1) symmetry-breaking, the phase transition that gives a mass to the dark matter also produces cosmic strings which radiate gravitational waves. Because the symmetry-breaking scale Λ_CS is of the same order as M_DM, the gravitational waves radiated by the cosmic strings have a large enough amplitude to be detectable across all frequencies accessible with current and planned experimental facilities. Moreover, an epoch of early primordial black hole domination introduces a unique spectral break in the gravitational wave spectrum whose frequency is related to the super-heavy dark matter mass. Hence, the features of a stochastic background of primordial gravitational waves could indicate that super-heavy dark matter originated from primordial black holes. In this perspective, the recent finding of a stochastic common-spectrum process across many pulsars by two nano-frequency pulsar timing arrays would fix the dark matter mass to be 3 × 10¹³ GeV ≲ M_DM ≲ 10¹⁴ GeV. The (non-)detection of a spectral break at 0.2 Hz ≲ f_* ≲ 0.4 Hz would (exclude) substantiate this interpretation of the signal.