Entanglement measures for multi-component universe from holography

TL;DR

The paper develops a holographic framework to study time-dependent information measures for a multi-component FLRW universe realized on a brane in RS-II geometry. By deriving the second Israel junction condition and incorporating bulk $p$-brane gas, the authors obtain the brane’s time evolution for universes with no matter, radiation+matter, and radiation+exotic matter. Using the Ryu-Takayanagi prescription and a perturbative expansion, they compute the time-dependent holographic entanglement entropy and holographic subregion complexity, finding that early times are dominated by radiation while late times reflect matter or exotic matter, in line with cosmological history. The results provide analytic expressions linking entanglement and complexity to the evolving brane geometry and offer a robust platform for exploring additional information-theoretic measures in realistic multi-component cosmologies.

Abstract

Recent studies in \cite{Park:2020jio,Paul:2025gpk} have calculated various holographic information theoretic quantities of the four-dimensional FLRW universe for different matter-dominated eras using the braneworld model of cosmology. These studies are done for a single matter component, which is a good toy model for understanding the entanglement properties of the universe. Although for a more realistic model, one should consider a scenario where our universe has coexisting matter components like radiation-dark matter or radiation-exotic matter, etc. In this work, we have presented a systematic way to study various holographic information-theoretic quantities (entanglement entropy and complexity) of the FLRW universe in the presence of coexisting matter components. We have shown that the black brane geometry in the presence of $p$-brane gas indeed supports the existence of a universe with two-component matter sources. The second Israel junction condition, along with the Ryu-Takayanagi formula, is used to compute the time-dependent holographic entanglement entropy of the universe with coexisting radiation-dark matter and radiation-exotic matter. The expression of the time-dependent volume complexity is also evaluated in these scenarios. For both universes, these information-theoretic quantities show a clear radiation dependence in the early time and matter and exotic matter dominance in the late time, which is consistent with the thermal history of the universe.

Figures (1)

• Figure 1: A schematic diagram of the braneworld model along with a circular susystem $A$ and its corresponding RT surface in the bulk.