Primordial black holes from supercooled phase transitions

Cosmological first-order phase transitions (1stOPTs) are said to be strongly supercooled when the nucleation temperature is much smaller than the critical temperature. These are often encountered in theories that admit a nearly scale-invariant potential, for which the bounce action decreases only logarithmically with temperature. During supercooled 1stOPTs the equation of state of the universe undergoes a rapid and drastic change, transitioning from vacuum domination to radiation domination. The statistical variations in bubble nucleation histories imply that distinct causal patches percolate at slightly different times. Patches which percolate the latest undergo the longest vacuum-domination stage and as a consequence develop large overdensities triggering their collapse into primordial black holes (PBHs). We derive an analytical approximation for the probability of a patch to collapse into a PBH as a function of the 1stOPT duration, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>β</a:mi><a:mrow><a:mo>−</a:mo><a:mn>1</a:mn></a:mrow></a:msup></a:math>, and deduce the expected PBH abundance. We find that 1stOPTs which take more than 15% of a Hubble time to complete (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>β</c:mi><c:mo>/</c:mo><c:mi>H</c:mi><c:mo>≲</c:mo><c:mn>7</c:mn></c:math>) produce observable PBHs. Their abundance is independent of the duration of the supercooling phase, in agreement with the de Sitter no hair conjecture. Published by the American Physical Society 2024