Entanglement Entropy of the Early Universe in Generalized Chaplygin Gas Model

TL;DR

This paper calculates the evolution of cosmic entanglement entropy in the early universe using the generalized Chaplygin gas model, revealing how different contributions change during inflation and radiation eras.

Contribution

It provides an explicit quantum cosmological calculation of entanglement entropy evolution in the early universe within the GCG framework, considering both background and perturbation effects.

Findings

Homogeneous entropy grows exponentially at inflation start

Perturbation entropy decreases then increases after a minimum

Total entropy reaches a minimum early in inflation and then rises

Abstract

We provide an explicit calculation of the evolution of the cosmic entanglement entropy in the early universe before the matter dominant era. This is made possible by invoking the generalized Chaplygin gas (GCG) model, which has the advantage of preserving unitarity and providing a smooth transition between the inflation epoch and the radiation dominant era. The dynamics of the universe is described by the quantization in the minisuperspace of the GCG model, following the prescription proposed by Wheeler and DeWitt. Two sources of contribution to the cosmic entanglement entropy are considered: one from the homogeneous background where the observable and the unobservable regions of the universe are entangled and the other from the inhomogeneous cosmological perturbations where different modes are entangled. We find that the homogeneous contribution grows exponentially at the very beginning of the inflation, but decreases during the radiation dominant era. Conversely, that from the cosmological perturbation is found to decrease at first and then increase after reaching a minimum value. The net result is that the total entanglement entropy reaches a minimum at an early stage of the inflation and then increases throughout most of the inflation and the entire radiation dominant era.