Abstract
To understand the time-dependent quantum correlation in expanding universes, we study the time-dependent entanglement entropy in the braneworld model. If we take into account a generalized string cloud geometry caused by uniformly distributed open strings, cosmologies on the braneworld result in the standard Friedmann-Lema\^{i}tre-Robertson-Walker cosmologies with various matter contents. On the dual field theory side, open strings are reinterpreted as a fundamental matter, while the black hole mass corresponds to the excitation energy of massless gauge bosons. In this work, we show how the string cloud geometry is matched to various braneworld cosmologie,s for example, eternal inflation, radiation-, and matter-dominated universes. Then, we investigate how the entanglement entropy evolves in those expanding universes.
Highlights
Quantum entanglement has become one of the main research areas for understanding quantum features of various physical systems in both high energy physics and condensed matter physics
There was fascinating conjecture in string theory. This is called holography or the AdS=conformal field theory (CFT) correspondence, which claims that a strongly interacting quantum field theory has a one-to-one map to a classical gravity theory defined in one-dimensional higher anti–de Sitter (AdS) space [1,2,3,4]
It was shown that the holographic calculation in three-dimensional AdS space, which is dual to a twodimensional CFT, can reproduce the same results obtained in CFT [7,8]
Summary
Quantum entanglement has become one of the main research areas for understanding quantum features of various physical systems in both high energy physics and condensed matter physics. It was argued that, even in time-dependent geometries, the RT formula can provide the leading contribution to the HRT formula at a given time, at least in the UV regime [24] Following this argument, the leading behavior of the timedependent entanglement entropy has been studied in the eternally inflating universe. When we regard the previous bulk matters in the dual gravity theory, intriguingly, the braneworld model leads to the same power-law behaviors in the braneworld cosmology. Another remarkable point of the braneworld model is that it is possible to calculate the time-dependent entanglement entropy of various expanding universes.
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