Holography and Eternal Inflation

TL;DR

The paper investigates whether holographic entropy bounds conflict with eternal inflation, proposing light-cone holography that constrains only the entropy inside an observer's past light cone. It derives that the late-time bound $S_i \lesssim 1/\lambda$ yields $S_i = R_i^3 \Lambda^{1/(1+\kappa)}$ with $R_i \approx \Lambda^{-1/2}(a_f/a_i)^{(3\kappa+1)/2}$, and this bound is independent of the number of past $e$-foldings $N$, implying $\kappa \le 1$ but no restriction on $N$. Consequently, light-cone holography does not bound the amount of past inflation, supporting compatibility between holography and eternal inflation. The discussion also touches on holographic considerations for baby universes and bubble nucleation, noting such constraints require additional high-energy assumptions and are not dictated by current holographic understanding.

Abstract

We show that eternal inflation is compatible with holography. In particular, we emphasize that if a region is asymptotically de Sitter in the future, holographic arguments by themselves place no bound on the number of past e-foldings. We also comment briefly on holographic restrictions on the production of baby universes.

Figures (3)

• Figure 1: Spacetime diagram. The dashed line is the past light cone of a late-time observer.
• Figure 2: A representation of the spacetime of eternal inflation. The shaded triangle corresponds to the region shown in figure \ref{['cap:Spacetime-diagram']}.
• Figure 3: The inflating patch of $\Lambda$-de Sitter space.