Entropy, Entanglement and Swampland Bounds in DS/dS

TL;DR

This work analyzes entanglement entropy in the DS/dS holographic framework, revealing a surprising one-parameter family of bulk minimal surfaces that all reproduce the de Sitter entropy. It identifies a clear distinction between entanglement across the two CFTs (left-right) and horizon entanglement, and shows that, in general warped geometries with extra matter, the L/R entanglement can exceed the dS entropy, prompting swampland-type considerations. The authors derive both numerical and analytical descriptions of the interpolating surfaces, examine general warp factors, and connect their results to energy conditions, ultimately offering interpretations about entropy bounds and the viability of DS/dS in quantum gravity. The findings highlight rich entanglement structures in de Sitter holography and spotlight potential constraints on matter content from holographic entropy principles.

Abstract

We calculate the entanglement entropy of the de-Sitter (dS) static patch in the context of the DS/dS correspondence. Interestingly, we find that there exists a one parameter family of bulk minimal surfaces that all have the same area. Two of them have appeared earlier in the literature. All of them correctly calculate the dS entropy. One surface yields the entanglement between the two different CFTs that provide the holographic dual of the bulk DS geometry. The second surface describes the entanglement across the horizon in the boundary static patch. The other surfaces describe a mixture of these two concepts. We also show that in the presence of extra matter fields the former entanglement entropy always exceeds the dS entropy. We interpret this result in the context of entropy bounds in de Sitter space and the swampland program.

Figures (3)

• Figure 1: Solution for $\rho(r)$ in dependence of $r^\star$.
• Figure 2: Geometric Interpretation of the analytical solution eq. \ref{['analyticsolution']}.
• Figure 3: Left: Warp factor $A(r)$ in presence of a linear scalar. The warp factor $A$ diverges at $r_\text{min}$ and $r_\text{max}$. Right: The blue line depicts the reconstructed potential of the scalar field. The dashed red line depicts the fit with an 10th order polynomial $\text{exp}(-60.19+V(\phi))=1.00 -8.12\, \phi^2 + 75.53\, \phi^4 - 367.12\, \phi^6 + 940.42\, \phi^8 - 1016.03\, \phi^{10}$ .