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How well do we know the primordial black hole abundance? The crucial role of nonlinearities when approaching the horizon. (arXiv:2307.13633v2 [astro-ph.CO] UPDATED)

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We discuss the non-linear corrections entering in the calculation of the
primordial black hole abundance from the non-linear radiation transfer function
and the determination of the true physical horizon crossing. We show that the
current standard techniques to calculate the abundance of primordial black
holes suffer from uncertainties and argue that the primordial black hole
abundance may be much smaller than what routinely considered. This would imply,
among other consequences, that the interpretation of the recent pulsar timing
arrays data from scalar-induced gravitational waves may not be ruled out
because of an overproduction of primordial black holes.

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