Boundary definition of a multiverse measure

TL;DR

This paper introduces a boundary-based measure for eternal inflation by relating bulk cut-offs to boundary volumes, resulting in a consistent, holographically motivated approach that aligns with previous proposals and simplifies the measure problem.

Contribution

It proposes an intrinsic boundary volume definition in a conformal frame, resolving geometric ambiguities and providing a new, consistent measure for eternal inflation.

Findings

Boundary boundary becomes a round three-sphere in FRW approximation

The proposed measure matches previous bulk projection methods

It offers a holographically motivated, phenomenologically successful measure

Abstract

We propose to regulate the infinities of eternal inflation by relating a late time cut-off in the bulk to a short distance cut-off on the future boundary. The light-cone time of an event is defined in terms of the volume of its future light-cone on the boundary. We seek an intrinsic definition of boundary volumes that makes no reference to bulk structures. This requires taming the fractal geometry of the future boundary, and lifting the ambiguity of the conformal factor. We propose to work in the conformal frame in which the boundary Ricci scalar is constant. We explore this proposal in the FRW approximation for bubble universes. Remarkably, we find that the future boundary becomes a round three-sphere, with smooth metric on all scales. Our cut-off yields the same relative probabilities as a previous proposal that defined boundary volumes by projection into the bulk along timelike geodesics. Moreover, it is equivalent to an ensemble of causal patches defined without reference to bulk geodesics. It thus yields a holographically motivated and phenomenologically successful measure for eternal inflation.