Constraining the cosmic merger history of intermediate-mass black holes with gravitational wave detectors

Intermediate-mass black holes (IMBHs) have not been detected beyond any reasonable doubt through either dynamical or accretion signatures. Gravitational waves (GWs) represent an unparalleled opportunity to survey the sky and detect mergers of IMBHs, making it possible for the first time to constrain their formation, growth, and merger history across cosmic time. While the current network LIGO-Virgo-KAGRA is significantly limited in detecting mergers of IMBH binaries, the next generation of ground-based observatories and space-based missions promise to shed light on the IMBH population through the detection of several events per year. Here, we asses this possibility by determining the optimal network of next-generation of GW observatories to reconstruct the IMBH merger history across cosmic time. We show that Voyager, the Einstein Telescope, and Cosmic Explorer will be able to constrain the distribution of the primary masses of merging IMBHs up to $\sim 10^3\ M_\odot$ and with mass ratio $\gtrsim 0.1$, while LISA will complementary do so at higher mass and smaller mass ratios. Therefore, a network of next-generation ground-based and space-based observatories will potentially reconstruct the merger history of IMBHs. Moreover, IMBHs with masses $\lesssim 5\times 10^3\ M_\odot$ could be observed in multiband up to a redshift of $z\approx 4$, ushering in a new of era GW astronomy.