Auto-localization in de-Sitter space

TL;DR

The work addresses how gravity localizes in de-Sitter spaces and how dS entropy can be understood when compactifications and branes are involved. By presenting de-Sitter space as a warped product with a localized graviton on a $(d-1)$-dimensional slicing and a KK continuum, the author derives a direct relation between the $d$- and $(d-1)$-dimensional Planck scales and shows that the entropy computed from the localized graviton matches the full de-Sitter entropy, despite a residual KK spectrum; KK modes induce a mass gap of order $1/L$ and prevent true lower-dimensional Newtonian gravity, yet the horizon-area bound on accessible degrees of freedom remains applicable. Extending to domain walls, the author computes the brane-localized entropy $4S= A_{d-2} M_{Pl,d}^{d-3} V L_{d-1}^{d-3}$ and shows it is strictly less than the bulk $dS$ entropy, reflecting the finite, observer-accessible degrees on the brane. The results offer a semiclassical holographic perspective on de-Sitter holography, discuss potential dS/dCFT-type duals, and clarify the limits of reducing gravity to lower dimensions on brane worlds in de-Sitter backgrounds.

Abstract

We point out that gravity on dS_n gives rise to a localized graviton on dS_{n-1}. This way one can derive a recursion relation for the entropy of dS spaces, which might have interesting implications for dS holography. In the same spirit we study domain walls interpolating between dS spaces with different cosmological constant. Our observation gives an easy way to calculate what fraction of the total entropy can be accessed by an observer stuck on the bubble wall.

Figures (6)

• Figure 1: Warpfactor for the de Sitter slicing of de Sitter space. Even without any brane or defect we get a localized, normalizable zero mode. Including a brane as usual pastes together two regions of pure de Sitter.
• Figure 2: Volcano potential for the dS slicing of pure dS. This (and the other potentials shown) is plotted for $d=5$ and $L=1$.
• Figure 3: Embedding of the dS slicing in dS. The brane cuts out the shaded region in the diagram on the right.
• Figure 4: Volcano potential for $z_0=1$ at $L=1$, $d=5$.
• Figure 5: Volcano potential for $z_0=7$ at $L=1$, $d=5$.