Cosmological coupling of nonsingular black holes

Abstract: We show that -- in the framework of general relativity (GR) -- if black holes (BHs) are singularity-free objects, they couple to the large-scale cosmological dynamics. We find that the leading contribution to the resulting growth of the BH mass ($M_{\rm BH}$) as a function of the scale factor $a$ stems from the curvature term, yielding $M_{\rm BH} \propto a^k$, with $k=1$. We demonstrate that such a linear scaling is universal for spherically-symmetric objects, and it is the only contribution in the case of regular BHs. For nonsingular horizonless compact objects we instead obtain an additional subleading model-dependent term. We conclude that GR nonsingular BHs/horizonless compact objects, although cosmologically coupled, are unlikely to be the source of dark energy. We test our prediction with astrophysical data by analysing the redshift dependence of the mass growth of supermassive BHs in a sample of elliptical galaxies at redshift $z=0.8 -0.9$. We also compare our theoretical prediction with higher redshift BH mass measurements obtained with the James Webb Space Telescope (JWST). We find that, while $k=1$ is compatible within $1 \sigma$ with JWST results, the data from elliptical galaxies at $z=0.8 -0.9$ favour values of $k>1$. New samples of BHs covering larger mass and redshift ranges and more precise BH mass measurements are required to settle the issue.