Abstract
In expanding universes, the entanglement entropy must be time-dependent because the background geometry changes with time. For understanding time evolution of quantum correlations, we take into account two distinct holographic models, the dS boundary model and the braneworld model. In this work, we focus on two-dimensional expanding universes for analytic calculation and comparison. Although two holographic models realize expanding universes in totally different ways, we show that they result in the qualitatively same time-dependence for eternal inflation. We further investigate the time-dependent correlations in the radiation-dominated era of the braneworld model. Intriguingly, the holographic result reveals that a thermal system in the expanding universe is dethermalized after a critical time characterized by the subsystem size.
Highlights
In order to study the power-law expansion, we take into account another holographic model called the braneworld model [17–21], where we consider a moving brane in an asymptotic AdS geometry
The two holographic models, the dS boundary and braneworld models, describe the expanding universes in totally different ways. We show that these two holographic models yield a similar time-dependent entanglement entropy for an inflationary universe
Let us take into account the holographic entanglement entropy described by the Hubeny– Rangamanni–Takayanagi (HRT) formula
Summary
We take into account a two-dimensional inflationary universe. In the holographic setup, there are two distinct models realizing an inflationary universe. Which is the metric of a two-dimensional dS space with a Hubble constant H = /R2. If we introduce a new time coordinate τ with τ = τ − log (H R) /H , the boundary metric further reduces to a simple FLRW metric dsB2 = −dτ 2 + e2Hτ d x2,. This is the well-known dS metric representing eternal inflation. It is worth noting that the bulk metric is invariant under the constant shift of time and rescaling of x τ → τ = τ + a and x → x = e−Ha x. The metric (2.5), without loss of generality, reduces to (2.6) by redefining the spatial coordinate x
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