Reflected entropy and islands in a braneworld cosmology

Abstract: This work investigates the nature of mixed state entanglement and correlation in a braneworld cosmological model, where the bulk geometry is described by an eternal BTZ black hole truncated by an end-of-the-world brane representing a Friedmann-Robertson-Walker (FRW) cosmology. We explore the holographic reflected entropy for both adjacent and disjoint subsystems using the island prescription and the defect extremal surface prescription. In the large central charge limit, we demonstrate that both prescriptions yield an exact agreement. Additionally, we analyze the time evolution of reflected entropy and holographic mutual information, along with an analysis of the geometric Markov gap. Our study provides new insights into the role of quantum extremal surfaces in probing black hole interiors and cosmological spacetimes, with implications for understanding mixed state entanglement and quantum information dynamics in holographic cosmological models.