2024ApJ...961L..33L

Coupling of black hole mass to the cosmic expansion has been suggested as a possible path to understanding the dark energy content of the Universe. We test this hypothesis by comparing the supermassive black hole (SMBH) mass density at z = 0 to the total mass accreted in active galactic nuclei (AGN) since z = 6, to constrain how much of the SMBH mass density can arise from cosmologically coupled growth, as opposed to growth by accretion. Using an estimate of the local SMBH mass density of ≈1.0 × 10⁶M_⊙ Mpc^–1, a radiative accretion efficiency, η, in the range 0.05 < η < 0.3, and the observed AGN luminosity density at z ≈ 4, we constrain the value of the coupling constant between the scale size of the Universe and the black hole mass, k, to lie in the range 0 < k ≲ 2, below the value of k = 3 needed for black holes to be the source term for dark energy. Initial estimates of the gravitational-wave background (GWB) using pulsar timing arrays, however, favor a higher SMBH mass density at z = 0. We show that if we adopt such a mass density at z = 0 of ≈7.4 × 10⁶M_⊙ Mpc^–1, this makes k = 3 viable even for low radiative efficiencies, and may exclude nonzero cosmological coupling. We conclude that, although current estimates of the SMBH mass density based on the black hole mass-bulge mass relation probably exclude k = 3, the possibility remains open that, if the GWB is due to SMBH mergers, k > 2 is preferred.