Entanglement Entropy of the Early Universe in Generalized Chaplygin Gas Model

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.

Inflation as a Solution to the Early Universe Entropy Problem

“…5) as well as the tree-level inhomogeneous part (Fig. 6) previously observed in [17]. The persistence of the entropy minimum after putting back some of the degrees of freedom suggests that it is a real physical feature and we expect this entropy minimum not be completely erased by higher order corrections.…”

“…In particular, a decrease of tripartite entropy after inflation is shown in [16], which inspires us to consider the evolution of bipartite entropy from quantum entanglement. Indeed, in a recent effort by two of the present authors (PC & YN) [17], it was found that a minimum of the entanglement entropy induced from the entanglement between cosmological perturbations is reached at an early stage of the inflation. The calculation made there, however, was classical.…”

“…This contribution can be calculated using the standard cosmological perturbation techniques [39] [40]. The calculation in this section largely follows [17].…”

“…Detailed treatment and numerical results are summarized in next two sections IV and V, which together consist of the total contribution to entanglement entropy. To make comparison with the previous result in [17], the computation therein is reproduced in section V for completeness. Results in each section are discussed, and possible physical origins of the entropy decrease are presented in section VI.…”

Evolution of entanglement entropy in the early universe

“…In particular, a decrease of tripartite entropy after inflation is shown in [21], which inspires us to consider the evolution of bipartite entropy from quantum entanglement. Indeed, in a recent effort by two of the present authors (PC & YN) [22], it was found that a minimum of the entanglement entropy induced from the entanglement between cosmological perturbations is reached at an early stage of the inflation. The calculation made there, however, was classical.…”