On the Quantum Resolution of Cosmological Singularities using AdS/CFT

TL;DR

The paper leverages AdS/CFT to translate cosmological singularities into boundary quantum dynamics with an unstable double-trace deformation. By imposing self-adjoint extensions for the boundary theory, it shows the homogeneous boundary mode can bounce from infinity, corresponding to a quantum crunch-to-bang transition in the bulk. However, detailed semiclassical analysis reveals substantial particle production across the bounce, driven by the running boundary coupling, which typically backreacts and prevents the wave packet from returning to its initial state. Consequently, in this five-dimensional AdS/CFT setup, a quantum transition from big crunch to big bang is unlikely, although the framework provides a clear route to study such transitions and their possible realizations in related models.

Abstract

The AdS/CFT correspondence allows us to map a dynamical cosmology to a dual quantum field theory living on the boundary of spacetime. Specifically, we study a five-dimensional model cosmology in type IIB supergravity, where the dual theory is an unstable deformation of $\N=4$ supersymmetric SU(N) gauge theory on $\Rbar\times S^3$. A one-loop computation shows that the coupling governing the instability is asymptotically free, so quantum corrections cannot turn the potential around. The big crunch singularity in the bulk occurs when a boundary scalar field runs to infinity, in finite time. Consistent quantum evolution requires that we impose boundary conditions at infinite scalar field, i.e. a self-adjoint extension of the system. We find that quantum spreading of the homogeneous mode of the boundary scalar leads to a natural UV cutoff in particle production as the wavefunction for the homogeneous mode bounces back from infinity. However a perturbative calculation indicates that despite this, the logarithmic running of the boundary coupling governing the instability generally leads to significant particle production across the bounce. This prevents the wave packet of the homogeneous boundary scalar to return close to its initial form. Translating back to the bulk theory, we conclude that a quantum transition from a big crunch to a big bang is an improbable outcome of cosmological evolution in this class of five-dimensional models.

Figures (20)

• Figure 1: The Penrose diagram of a large black hole in anti-de Sitter space is identical to that of an anti-de Sitter cosmology. In a black hole spacetime, however, time at infinity continues forever whereas in an AdS cosmology the singularity hits the boundary in finite time.
• Figure 2: The dual description of AdS cosmologies involves a wave packet rolling down an unstable direction of the field theory potential (left) whereas the formation of large black holes in AdS is described as a thermalization process in a dual theory that has a ground state (right).
• Figure 3: Regular initial data $\varphi (r)$ that evolve to a big crunch singularity for boundary conditions with $f =0.1$.
• Figure 4: Anti-de Sitter cosmology. To predict what happens at the singularities one must turn to the dual field theory description.
• Figure 5: The singular hypersurface $\Sigma$, assumed spacelike, upon which $\phi$ is infinite and $\chi$ is zero.