Holographic multiverse and the measure problem

TL;DR

This paper explores a holographic duality between the multiverse wave function and a boundary theory, proposing a new measure based on constant comoving apparent horizon surfaces to address the measure problem.

Contribution

It introduces the CAH+ measure prescription, linking boundary cutoff scales to bulk hypersurfaces, and offers a novel approach to the multiverse measure problem.

Findings

Proposes the CAH+ measure as a non-pathological solution.

Links boundary UV cutoff to bulk hypersurface choice.

Shows consistency with constant CAH cutoff in slow H regions.

Abstract

We discuss the duality, conjectured in earlier work, between the wave function of the multiverse and a 3D Euclidean theory on the future boundary of spacetime. In particular, we discuss the choice of the boundary metric and the relation between the UV cutoff scale xi on the boundary and the hypersurfaces Sigma on which the wave function is defined in the bulk. We propose that in the limit of xi going to 0 these hypersurfaces should be used as cutoff surfaces in the multiverse measure. Furthermore, we argue that in the inflating regions of spacetime with a slowly varying Hubble rate H the hypersurfaces Sigma are surfaces of constant comoving apparent horizon (CAH). Finally, we introduce a measure prescription (called CAH+) which appears to have no pathological features and coincides with the constant CAH cutoff in regions of slowly varying H.