A Framework for the Landscape

TL;DR

Freivogel and Susskind propose an S-matrix–based framework to study the string theory landscape of metastable de Sitter vacua by embedding eternal inflation in a bounce geometry where a Λ=0 bubble sits inside Λ>0, separated by a domain wall. In this setup, de Sitter vacua appear as intermediate resonances in scattering processes, enabling a quantum-mechanical description of transitions across the landscape while preserving asymptotically flat regions for S-matrix data. The authors connect this to horizon complementarity, arguing that information about the multiverse is encoded in the causal patch's radiation and discuss perturbative and nonperturbative aspects, including bubble collisions. While theoretical, the framework lays groundwork for linking the landscape to string theory holography and cosmology, outlining concrete objects (S-branes, bounce background, hats) and open questions about string dynamics in such backgrounds.

Abstract

It seems likely that string theory has a landscape of vacua that includes very many metastable de Sitter spaces. However, as emphasized by Banks, Dine and Gorbatov, no current framework exists for examining these metastable vacua in string theory. In this paper we attempt to correct this situation by introducing an eternally inflating background in which the entire collection of accelerating cosmologies is present as intermediate states. The background is a classical solution which consists of a bubble of zero cosmological constant inside de Sitter space, separated by a domain wall. At early and late times the flat space region becomes infinitely big, so an S-matrix can be defined. Quantum mechanically, the system can tunnel to an intermediate state which is pure de Sitter space. We present evidence that a string theory S-matrix makes sense in this background and contains metastable de Sitter space as an intermediate state.

Figures (18)

• Figure 1: On the left, the Penrose diagram for de Sitter space. On the right, the conformal diagram for $1+1$ dimensional de Sitter space.
• Figure 2: On the left, a bubble of smaller cosmological constant forming inside de Sitter space. On the right, a bubble of flat space forming inside de Sitter space.
• Figure 3: A potential which has a metastable minimum with positive energy and a stable minimum at infinity with zero energy.
• Figure 4: Wick rotation of the Euclidean geometry yields a Lorentzian geometry with this Penrose diagram. The geometry is not geodesically complete and can be analytically continued to yield the full Lorentzian solution.
• Figure 5: On the left, the Penrose diagram for the full Lorentzian geometry. On the right, the value of the scalar field is shown. At the top right of the diagram, the scalar field rolls to its true minimum giving $\Lambda = 0$; at the top left the field is in the false vacuum and $\Lambda > 0$ .