Cosmologies, singularities and quantum extremal surfaces

TL;DR

This work investigates how quantum extremal surfaces probe cosmological Big-Ccrunch/Big-Bang singularities by employing two-dimensional dilaton gravity reductions of higher-dimensional holographic cosmologies. By extremizing the generalized entropy $S_{gen}=S_{cl}+S_{bulk}$ and using a spatial regulator, the authors show that in AdS Kasner backgrounds the QES lags behind the observer and island-like regions are not realized, with similar behavior extending to other holographic cosmologies. In null Kasner cases the QES can approach the near-singularity region while $S_{gen}$ remains singular, highlighting reliability limits near singularities. De Sitter and FRW reductions reveal timelike QES with imaginary entropy in some cases and regulator-dependent spacelike QES in others, suggesting islands are not generic in these closed cosmologies. Overall, the results indicate that entanglement-based probes via QES in cosmologies with singularities largely exclude the near-singularity region and that two-dimensional models capture key qualitative features, guiding future investigations into more realistic bulk states and broader cosmological backgrounds.

Abstract

Following arXiv:2012.07351 [hep-th], we study quantum extremal surfaces in various families of cosmologies with Big-Crunch singularities, by extremizing the generalized entropy in 2-dimensional backgrounds which can be thought of as arising from dimensional reduction. Focussing first on the isotropic $AdS$ Kasner case, introducing a spatial regulator enables relating the locations in time of the quantum extremal surface and the observer. This shows that the quantum extremal surface lags behind the observer location. A potential island-like region, upon analysing more closely near the island boundary, turns out to be inconsistent. Similar results arise for other holographic cosmologies. We then study certain families of null Kasner singularities where we find that the quantum extremal surface can reach the near singularity region although the on-shell generalized entropy is generically singular. We also study other cosmologies including de Sitter (Poincare slicing) and FRW cosmologies under certain conditions.

Figures (3)

• Figure 1: Cartoon of extremal surfaces in $AdS$ Kasner spacetime, anchored on a boundary time slice $t_0$ (extended as the grey horizontal plane in the bulk). The extremal surface (red) bends away from the singularity at $t=0$ (dotted line), i.e.$t_*>t_0$, with $(t_*,r_*)$ the turning point.
• Figure 2: Cartoon of the 2-dim $AdS$ Kasner geometry (singularity at $t=0$), the holographic boundary at $r=0$ and the QES at $(t_*,r_*)$, with a time-independent $AdS$ space appended for $t>t_K$. The boundary observer $(t_0,0)$ moves in time from the time-independent region to the $AdS$ Kasner region. The QES lags behind in time, i.e.$t_*>t_0$, when $t_0$ is in the Kasner region.
• Figure 3: Cartoon of the 2-dim geometry with the null singularity at $x^+=0$, the worldline $(x^+_0,x^-_0)$ of a timelike observer (vertical trajectory, representing for simplicity a fixed spatial location), and the quantum extremal surface at $(x^+_*,x^-_*)$. As can be seen, the QES is spacelike separated from the observer ($\Delta^2>0$) if $\Delta x^+>0$ and $\Delta x^-\sim-\infty$, and lies towards the singularity in terms of $x^+$-slices. The entanglement wedge defined by the QES is shown as the blue wedge.