Charged False Vacuum Bubbles and the AdS/CFT Correspondence

TL;DR

This paper investigates cosmology within the AdS/CFT framework by analyzing a charged domain wall separating an exterior RN–AdS spacetime from an interior de Sitter region using Israel junction conditions. It derives the shell dynamics, reducing to an effective potential and mapping turning points via functions $P(r)$ and $N(r)$ to classify possible trajectories, including growing, collapsing, and bouncing solutions in four dimensions. The AdS/CFT interpretation is then used to argue that holography yields a unitary evolution that resolves classical singularities and fixes the interior evolution by relating it to black hole microstates in the dual CFT, with the interior de Sitter region requiring a CFT perturbation that acts as an inflaton. The work discusses how quantum evolution can avoid a problematic past timelike singularity, the potential patching of solutions to smooth initial data, and the speculative possibility of creating an inflating universe in the laboratory under certain initial conditions, while outlining different scenarios for singularity resolution in the CFT framework.

Abstract

We initiate a study of cosmology within the framework of Maldacena's AdS/CFT correspondence. We present a comprehensive analysis of the classical motion of a charged domain wall that separates an external Reissner-Nordstrom region of spacetime (with small or vanishing cosmological constant) from an internal de-Sitter region. The possible associated spacetime diagrams are drawn, although in the classical case, an unambiguous prediction of what occurs at late times in the interior region is not possible, since singularities and Cauchy horizons form. We argue that, when the asymptotic region is anti-de Sitter, the AdS/CFT correspondence gives a prescription for resolving the curvature singularities and evolving solutions across the expected Cauchy horizon. Some of our solutions contain inflating interiors, and we provide evidence these can be patched onto solutions with smooth initial data, circumventing an obstacle found by Farhi and Guth to creating an inflating universe in the laboratory.

Figures (6)

• Figure 1: The separate Penrose diagrams for Reissner-Nordstrø m (left) and de Sitter (right) spacetimes.
• Figure 2: "Growing" trajectories
• Figure 3: "Collapsing" trajectories
• Figure 4: Penrose diagrams describing the trajectory that begins and ends at $r=0$.
• Figure 5: "Bounce" trajectories. Check marks indicate allowed trajectories, crosses indicate forbidden trajectories.