# Entanglement entropy of Primordial Black Holes after inflation

## TL;DR

This paper investigates how entanglement entropy of scalar fields during inflation can lead to the formation of entangled primordial black holes, highlighting UV-finite contributions and their relation to inflationary parameters.

## Contribution

It introduces a novel analysis of entanglement entropy's role in primordial black hole formation during inflation, emphasizing UV-finite effects and their scaling with inflationary e-folds.

## Key findings

- UV-finite entanglement entropy contributions scale with e-folds
- Entanglement entropy depends logarithmically on the horizon radius
- Entanglement entropy is small compared to Bekenstein entropy of PBHs

## Abstract

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.