(Potentially too broad, but all my questions are related to the paper in question.)

Recently there was an article published in Astrophysical Journal Letters that claims black holes "contribute cosmologically as vacuum energy". The article was covered in the popular media, e.g. here and here.

I'm trying to understand this result. As far as I can tell from the paper, what is actually argued is that black holes gain mass at a rate proportional to $a^k$, where $a$ is the scale factor of cosmology and $k$ is some constant. The paper claims that $k \sim 3$. Since in cosmology all matter dilutes as $a^{-3}$ as the universe expands, if black holes gain mass at $a^3$, then the two factors cancel out and there is an approximately constant energy density that looks like dark energy. This is in section 3.1 of the paper:

Equation (1) implies that a population of $k \sim 3$ BHs will gain mass proportional to $a^3$. Within an RW [Robertson-Walker] cosmology, however, all objects dilute in number density proportional to $a^{−3}$. When accretion becomes subdominant to growth by cosmological coupling, this population of BHs will contribute in aggregate as a nearly cosmologically constant energy density. From conservation of stress-energy, this is only possible if the BHs also contribute cosmological pressure equal to the negative of their energy density, making $k \sim 3$ BHs a cosmological dark energy species.

However, I don't see why this constant energy density would mimic dark energy. Dark energy drives expansion of the universe, while black holes would presumably act as (gravitationally attractive) matter. Why wouldn't lots of very massive black holes slow down expansion?


  1. Given that black holes of all sizes can at most be 26.8% of the universe's energy content, how can they possibly account for all of dark energy, which has 68.3% of the universe's energy content?
  2. If there are black holes of several million solar masses in the galaxy outskirts (necessary to account for dark matter), why wouldn't that be immediately noticeable, e.g. by capturing stars into orbit?
  • 1
    $\begingroup$ Given that black holes of all sizes can at most be 26.8% of the universe's energy content… that is model dependent. In the paper's model black hole are (discrete) sources of dark energy so they would count toward $\rho_\Lambda$. $\endgroup$
    – A.V.S.
    Commented Feb 21, 2023 at 18:08

1 Answer 1


There is a nice rebuttal to the hype written up on Ask Ethan.

This is what I call a swing. The alternative explanation....is that this method is 100% unsound. It’s possible that $k = 0$, that there is no coupling, and that what’s actually happening is that these black holes are growing by purely astrophysical processes: the infall and accretion of matter over time, as well as from mergers and acts of galactic cannibalism.

That said, it is worth looking into further, it is just highly unlikely that there turns out to be a connection with the interior of black holes and cosmic expansion.

Not least because when black holes cross the cosmic event horizon, they take their entropy (and dark energy in this idea) with them...(noting there is also a currently-minority view that questions expansion, and thus the existence of a cosmic event horizon).


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