Eternal Inflation: The Inside Story

TL;DR

The paper develops a causal-patch, local description of eternal inflation, arguing that a global semiclassical geometry behind an observer's horizon cannot be reliably predicted because large-scale spacetime is governed by quantum fluctuations and decoherence. It distinguishes slow-roll eternal inflation (SREI) from false vacuum eternal inflation (FVEI) and derives that, for any given worldline, inflation ends in a terminal vacuum, with negative $\\Lambda$ yielding a crunch and zero or positive $\\Lambda$ leading to open FRW regions or further inflation depending on the exit mechanism. By analyzing both SREI and FVEI from a local perspective, the authors show that the usual global measure problems arise from attempting to ascribe a single geometry to causally disconnected regions, while a local approach yields well-defined end states and universal features such as bubble-collision solutions that preserve open FRW asymptotics. The work provides exact results for bubble collisions, demonstrates how entropy considerations constrain horizon-area evolution during inflation, and offers a framework for understanding observer-specific outcomes in a richly structured vacuum landscape with potential cosmological consequences for predictions in the multiverse context.

Abstract

Motivated by the lessons of black hole complementarity, we develop a causal patch description of eternal inflation. We argue that an observer cannot ascribe a semiclassical geometry to regions outside his horizon, because the large-scale metric is governed by the fluctuations of quantum fields. In order to identify what is within the horizon, it is necessary to understand the late time asymptotics. Any given worldline will eventually exit from eternal inflation into a terminal vacuum. If the cosmological constant is negative, the universe crunches. If it is zero, then we find that the observer's fate depends on the mechanism of eternal inflation. Worldlines emerging from an eternal inflation phase driven by thermal fluctuations end in a singularity. By contrast, if eternal inflation ends by bubble nucleation, the observer can emerge into an asymptotic, locally flat region. As evidence that bubble collisions preserve this property, we present an exact solution describing the collision of two bubbles.

Figures (12)

• Figure 1: A conformal diagram for the global geometry in FVEI. The hats represent the future infinity of open FRW universes with vanishing cosmological constant. Regions with negative cosmological constant end in a big crunch singularity (squiggly lines). The part of the universe which remains in the inflationary phase has zero comoving volume but infinite physical volume. The thick diamond shows an example of a causally connected region accessible to a single observer. The local description developed here is confined to such regions.
• Figure 2: On the left, a spin is measured after the apparatus has entered a black hole, leaving the outside observer ignorant of the outcome. On the right, the measurement takes place outside the black hole, beyond the causal past of an infalling observer. Either way, the observer cannot ascribe a definite outcome to the measurement. If the geometry depends on this outcome, it cannot be treated semiclassically, since it would involve a quantum superposition of macroscopically distinct metrics.
• Figure 3: Examples of causal horizons in cosmology: A closed FRW universe (left) and de Sitter space (right). The observer is on the left edge of each diagram. She cannot access the result of the measurement in the (white) region outside her causal past.
• Figure 4: The slow-roll potential $V=\frac{1}{2}m^2\phi^2$. The SREI regime is $\phi>m^{-1/2}$.
• Figure 5: A potential with a plateau supporting eternal inflation and a relatively short-lived classical slow roll.