Entanglement measures for multi-component universe from holography

TL;DR

This paper extends holographic entanglement measures to a multi-component universe, analyzing how coexisting matter types like radiation and dark matter influence entanglement entropy and complexity over cosmic time.

Contribution

It introduces a systematic approach to compute holographic entanglement and complexity in a universe with multiple matter components using braneworld models.

Findings

Entanglement entropy shows radiation dominance at early times.

Complexity reflects matter and exotic matter dominance at late times.

Results align with the universe's thermal history.

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.