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I've read the recent news about non-Kerr black holes coupling to the universe's expansion rate, and it looks like an excellent fit to the data. From the paper, I understand that these black holes grow with the universe's expansion rate to the third power in the absence of accretion, as observed, and that they predict a cosmological constant of about \Omega_V = 0.7, which is also spot on.

What I don't understand is the model. The black holes don't contain singularities, but are "filled with vacuum energy." Following the references back, I didn't understand the original theory papers, apart from the statement that these black holes can't spin, which I think is in contradiction with gravitational wave detections.

Does anyone here understand the model well enough to explain to general physicists, or better yet, undergraduate or high school level? "Filled with vacuum energy" isn't helpful, since all of space is filled with vacuum energy. What's special about black holes in this model?

Jim Pivarski
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They proposes that all small-scale inhomogeneity should contribute to the pressure term in the Friedmann equations, including the pressure within the cores of compact objects. Let us write the perfect fluid equation of state (EOS) as

$$ P = \omega \rho \,,$$

where $P, \rho$ stands for pressure and density while $\omega$ is a const. They hypothesize that black holes are not really black holes, but instead, some compact objects with their interior having an EOS with $\omega = -1$ (e.g., Gravastars - black hole mimickers with de-Sitter interior). As a result, these objects would contribute to the cosmological EOS.

With this assumption, they then further assume that if their mass $m$ follows the trend (where $a$ is the cosmic scale factor and $t_i$ the cosmic time when the black hole was born)

$$ m(t) = m(t_i) \left( \frac{a(t)}{a(t_i)} \right)^3 \,,$$

hence deserving the name "cosmological coupling", then to respect the principle of stress-energy conservation, it becomes necessary that they contribute to the cosmological pressure, which will be equal to the negative of their energy density. This pressure will have a similar effect on the universe's expansion, akin to the influence of dark energy.

They then show that with a standard population of stellar mass black holes alone, one can reproduce the accelerated expansion effect along with the value of $\Omega_\Lambda$.

Interestingly, in this paper, they then show observational evidence for their proposed mass growth trend by looking at supermassive black holes residing at the centers of elliptical galaxies. They, therefore, conclude that "black holes" are the source of accelerated expansion.

However, up till now, there has been severe criticism of their claim on many accounts.

S.G
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