How the Cosmic Tree Gives Birth to Two Kinds of Black Holes ✛ ✎ ✦

Original: "Compaction function in stochastic inflation: a \texttt{FOREST} of type I and II primordial black holes"
arXiv:2606.30087 · 2026-06-29 · arXiv non-exclusive · independent analysis · 1 min
Scientists came up with a branching model of the early universe and found that primordial black holes come in two types: ordinary and exotic.

Immediately after the Big Bang, space grew like a branching tree. Alan Guth proposed the idea of inflation — a super-fast expansion that made the cosmic microwave background so smooth. In this inflating world, each microscopic branch doubled and split, while random quantum fluctuations made some branches slightly denser. Branches heavy enough collapsed into primordial black holes.

These holes turned out to be of two types. The first is ordinary: a branch shrinks into a superdense point. The second is exotic: due to strong spacetime curvature, something like a knot forms. Outside, it's a black hole, but inside — endless inflation with the birth of new branches. Although Hawking and Penrose predicted the inevitability of holes, the second type turned out to be far stranger. In the eternal inflation regime, it dominates.

These holes are ideal candidates for dark matter, the invisible mass that holds galaxies together. Their collisions produce gravitational waves with a distinctive pattern. Computer simulations analyzing billions of branching structures confirmed: the exotic type will change the hunt for signals from the early universe.

In some scenarios, exotic black holes outnumber all the stars in the observable universe.

C_{l,\ b_L} = 2z(w) \left[ 1 - \log_2\!\left( \frac{V_{b_R}}{V_{c_R}} \right) \right]
The linear compaction function C_l at node b_L is determined by the ratio of volumes arising from its two 'side' branches: the right neighbor by parent (b_R) and its own right descendant (c_R). Here z(w) = 3(1+w)/(5+3w) is a factor depending on the equation of state w.
C_c = \frac{1}{2}
If the compaction function value C_l at a node exceeds 1/2, the corresponding region of space collapses into a black hole.
Scientists
Stephen HawkingJacob BekensteinAlan GuthJames PeeblesAndrei LindeBarry Barish
Concepts
primordial black hole stochastic inflation mass inflation black hole memory burden Bekenstein-Hawking entropy barrow entropy logarithmic correction initial mass function partition function effective spin inflationary cosmology topological charge quantum cosmological inhomogeneities inflationary gravitational waves critical collapse ringdown accretion disk wind wald entropy black hole mass stochastic fluctuations