Implication of island for inflation and primordial perturbations

TL;DR

This paper explores how the island rule affects the bounds on inflation's efolds number, suggesting that the traditional entropy limit may not apply and that primordial perturbations could exhibit a Page curve-like behavior.

Contribution

It introduces a novel perspective on inflation and primordial perturbations by applying the island rule, challenging the conventional entropy bound and proposing a connection to black hole physics.

Findings

Efolds bound may be absent due to island rule effects.

Primordial perturbations follow a Page curve, indicating a new entropy behavior.

Large-scale perturbation spectrum shows a Page-like suppression.

Abstract

It is usually thought that the efolds number of inflation must be bounded by its de Sitter entropy, otherwise we will have an information paradox. However, in light of the island rule for computing the entanglement entropy, we show that such a bound might be nonexistent, while the information flux of primordial perturbation modes the observer after inflation is able to detect follows a Page curve. In corresponding eternally inflating spacetime, it seems that our slow-roll inflation patch is accompanied with a neighbourly collapsed patch (eventually developing into a black hole) so that its Hawking radiation might be just our primordial perturbations. Accordingly, the perturbation spectrum we observed will present a ``Page-like" suppression at large scale.