Effects of a Quantum or Classical Scalar Field on the Entanglement Entropy of a Pair of Universes

TL;DR

This paper investigates how treating a scalar field as quantum or classical affects the entanglement entropy between pairs of universes in different cosmological models, revealing varied impacts depending on the universe type.

Contribution

It compares the effects of quantum versus classical scalar fields on entanglement entropy across multiple universe models using third quantization formalism.

Findings

Entanglement entropy remains unchanged for de-Sitter universes.

It is zero for flat stiff matter dominated universes.

It depends on the scalar field treatment for closed universes.

Abstract

Using the formalism of the third quantization in canonical quantum gravity, the entropy of entanglement of a pair of universes created in the multiverse from the vacuum has lately been calculated. Here, we examine the differences between considering a scalar field as quantum or classical on the entanglement entropy of three different pairs: de-Sitter universes, flat stiff matter dominated universes, and closed universes with a scalar field. We find that the entanglement entropy is unchanged, zero, or dependent on the treatment of the scalar field, respectively.