Quantum entanglement in cosmology

TL;DR

This review surveys how quantum information concepts illuminate cosmology and gravity, focusing on entanglement generation during spacetime dynamics, entanglement harvesting, and the spatial structure of entanglement near horizons. It combines momentum-space and position-space techniques to quantify entanglement from gravitational particle production, inflationary perturbations, and black hole thermodynamics, including the area-law behavior and the Page curve via island prescriptions. Key contributions include explicit analyses of scalar and Dirac fields under FRW expansion and torsionful spacetimes, relativistic detector-based harvesting, and the realization that entanglement entropy and related measures encode background geometry and horizon information. The work highlights conceptual advances toward a quantum-gravitational understanding of classical cosmological perturbations and black hole evaporation, with implications for both fundamental physics and potential analogue experiments.

Abstract

We discuss recent progress in the study of entanglement within cosmological frameworks, focusing on both momentum and position-space approaches and also reviewing the possibility to directly extract entanglement from quantum fields. Entanglement generation in expanding spacetimes can be traced back to the phenomenon of gravitational particle production, according to which the background gravitational field may transfer energy and momentum to quantum fields. The corresponding entanglement amount and its mode dependence are both sensitive to the field statistics and to the details of spacetime expansion, thus encoding information about the background. Gravitational production processes also play a key role in addressing the quantum-to-classical transition of cosmological perturbations. In order to directly extract entanglement from quantum fields, local interactions with additional quantum systems, working as detectors, have been suggested, leading to the formulation of the entanglement harvesting protocol. Despite harvesting procedures are currently unfeasible from an experimental point of view, various proposals for implementation exist and a proper modeling of detectors and local interactions is crucial to address entanglement extraction via realistic setups. In the final part of the work, we address entanglement characterization in position space, primarily focusing on black hole spacetimes. We first investigate a possible interpretation of Bekenstein-Hawking black hole entropy in terms of the entanglement entropy arising in discrete quantum field theories, on account of the area law. Then, we discuss the resolution of the black hole information paradox via the gravitational fine-grained entropy formula, which provides a new way to compute the entropy of Hawking radiation and allows to preserve unitarity in black hole evaporation processes.

Figures (15)

• Figure 1: Penrose diagram of a black hole formed by gravitational collapse. On the right, the near-horizon region has been enlarged, showing the trajectory of a uniformly accelerated observer. Figure adapted from RevModPhys.93.035002.
• Figure 2: Entanglement entropy for the KG field in a $(1+1)$-dimensional FRW spacetime described by Eq. \ref{['dunctoy_scal']}, with $\epsilon_S=1$ and $\sigma=1, \dots, 100$ GeV. On the left, the entropy is plotted for $m=1$ GeV as function of the momentum $k$, while on the right it is plotted for $k=1$ GeV and varying mass. Figure adapted from Fuentes:2010dt.
• Figure 3: Entanglement entropy for the Dirac field in a (1+1)-dimensional FRW spacetime described by Eq. \ref{['dunctoy_dir']}, with $\epsilon_S=1$ and $\sigma=1, \dots, 100$ GeV. On the left, the entropy is plotted for $m=1$ GeV as function of the momentum $k$, while on the right it is plotted for $k=1$ GeV and varying mass. Figure adapted from Fuentes:2010dt.
• Figure 4: Density plot of the anisotropic subsystem entropy $S$ of a conformally coupled scalar field (left) and a minimally coupled Dirac field (right), as function of the field momentum $k \equiv \lvert {\bf k} \rvert$ and $\phi$. The other parameters are: $\rho=10$, $\epsilon=0.1$, $\theta=\pi/2$. Figure adapted from Pierini:2018wki.
• Figure 5: Entanglement entropy $S\left( \rho_{k_1} \right)$ of a KG field, as function of the particle momentum $k_1$, with $A=3$, $B=2$, $\sigma=1$ GeV, $M=10^{-5}$ GeV, $r_{\text{min}}=5$ GeV$^{-1}$, $\tau_i=-10^4$ GeV$^{-1}$ and $\Delta \tau \equiv \tau_f- \tau_i=100$ GeV$^{-1}$. On the left, the entropy is plotted for a massive field with $m=0.01$ GeV, while on the right a massless field is considered. Figure adapted from Belfiglio:2022cnd.