Merging cosmologically coupled black holes: stochastic gravitational wave background and implications for pulsar timing arrays

It has been argued that realistic models of (singularity-free) black holes (BHs) embedded within an expanding Universe are coupled to the large-scale cosmological dynamics, with striking consequences, including pure cosmological growth of BH masses. We examine the consequences of this growth for the stochastic gravitational wave background (SGWB) produced by merging supermassive cosmologically coupled BHs. We show that the predicted SGWB amplitude is enhanced relative to the standard uncoupled case, while maintaining the $\Omega_{\text{gw}} \propto f^{2/3}$ frequency scaling of the spectral energy density. For the case where BH masses grow with scale factor as $M_{\text{bh}} \propto a^3$, thus contributing as a dark energy component to the cosmological dynamics, the enhancement factor can exceed an order of magnitude. This has important consequences for the SGWB signal detected by pulsar timing arrays, whose measured amplitude is slightly larger than most theoretical predictions for the spectrum from binary BH mergers, a discrepancy which can be alleviated by the cosmological mass growth mechanism.