Holographic Multiverse

TL;DR

The paper tackles the measure problem in an eternally inflating multiverse by proposing a holographic dual: the dynamics are encoded on the future boundary in a Euclidean boundary theory with a Wilsonian UV cutoff. This boundary measure naturally corresponds to the bulk scale-factor cutoff, providing a finite framework to compute probabilistic predictions from boundary data. The authors introduce a concrete picture where the eternal set projected onto a fiducial surface forms a 3D sponge, with boundary degrees of freedom on the holes representing terminal bubbles, and they discuss how Weyl rescalings and RG flow encode bulk evolution. If borne out, this boundary formulation offers a tractable route to predict cosmological observables while avoiding common measure-pathologies.

Abstract

We explore the idea that the dynamics of the inflationary multiverse is encoded in its future boundary, where it is described by a lower dimensional theory which is conformally invariant in the UV. We propose that a measure for the multiverse, which is needed in order to extract quantitative probabilistic predictions, can be derived in terms of the boundary theory by imposing a UV cutoff. In the inflationary bulk, this is closely related (though not identical) to the so-called scale factor cutoff measure.

Figures (4)

• Figure 1: Causal diagram of the inflationary multiverse. The vertical direction represents time, and the horizontal direction is space. Bubbles of different types nucleate and start expanding close to the speed of light. Bubbles with positive vacuum energy (dS bubbles) inflate eternally. Inflation stops in bubbles with vanishing or negative vacuum energy (Minkowsi and AdS bubbles, respectively).
• Figure 2: We assign co-moving coordinates to the points in the eternal set $E$, by introducing a fiducial hypersurface $\Sigma_3$ and a congruence of geodesics orthogonal to it. The metric $g_{ij}({\bf x})$ on $\Sigma_3$ can be used in order to assign co-moving distances amongst the points in $E$.
• Figure 3: The future boundary of a Minkowski bubble is a "hat", consisting of the union of future null infinity $\mathscr{I}^+$ and time-like infinity $i^+$. The worldline of a "census taker" ending at $i^+$ is also represented.
• Figure 4: For given co-moving resolution $\xi$, the eternal set $E$ can be mapped into the fiducial hypersurface $\Sigma_3$, and looks like a 3 dimensional space with holes in it. The holes correspond to geodesics in the congruence which have fallen inside of terminal bubbles. The bulk dynamics of these bubbles is described in terms of degrees of freedom which live at the boundary of the holes. The images of bubbles of inflating vacua look like sponges, whose pores are occuppied by other inflating vacua, or by holes.