Constraints on Cosmological Coupling from the Accretion History of Supermassive Black Holes

Abstract

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 × 106 M ⊙ 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 × 106 M ⊙ 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.