  In this paper we study the survival of entanglement of a scalar field state
created during inflation. We find that there exist UV-finite subdominant
contributions to the entanglement entropy per momentum mode that scale with the
number of e-folds between horizon exit and the end of inflation, and depend on
the logarithm of the radius of the entangling surface, which can be taken to be
the horizon sphere. We argue that this entanglement entropy allows for the
formation of entangled Primordial Black Holes (PBH). We find that the entropy
arising from the entanglement between PBH is small compared with their
Bekenstein entropy.
