Holographic multiverse and the measure problem

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.

A minor change: the discussion of unitarity on p.9 is clarified

References in corpus (8)

• Setting the boundary free in AdS/CFT
• The cosmic microwave background temperature bispectrum from scalar perturbations induced by primordial magnetic fields
• Holographic Multiverse
• Complementarity in the Multiverse
• Vacuum decay into Anti de Sitter space
• Stationary Measure in the Multiverse
• Crunches, Hats, and a Conjecture
• Geometric origin of coincidences and hierarchies in the landscape

Cited by in corpus (18)

• Holographic No-Boundary Measure
• Cycles in the Multiverse
• How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem
• Watchers of the multiverse
• TASI lectures on complex structures
• $\delta N$ formalism from superpotential and holography
• Multi-field inflation from holography
• Vacuum Structure and the Arrow of Time
• Bubble collisions and measures of the multiverse
• Holographic inflation and the conservation of $\zeta$
• The CMB and the measure of the multiverse
• Tensor modes on the string theory landscape
• Dynamical systems of eternal inflation: A possible solution to the problems of entropy, measure, observables and initial conditions
• Phenomenology of the CAH+ measure
• New Local Duals in Eternal Inflation
• SuperCool Inflation: A Graceful Exit from Eternal Inflation at LHC Scales and Below
• Multiverse rate equation including bubble collisions
• Effects of high-order operators in non-relativistic Lifshitz holography