[Paper Review] Further Holographic Investigations of Big Bang Singularities

Netta Engelhardt, Thomas Hertog+1 more|arXiv (Cornell University)|Mar 30, 2015

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates quantum field theory signatures of cosmological singularities in anisotropic Kasner-AdS spacetimes using gauge/gravity duality. By computing two-point correlators via spacelike geodesics in the bulk, it finds a universal pole at horizon scale for separations along directions with negative Kasner exponent p < 0, which signals a non-normalizable state in the dual Yang-Mills theory and indicates the geodesic approximation breaks down near the singularity.

ABSTRACT

We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves N=4 super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. We find evidence that the pole is absent at finite coupling in the dual field theory, indicating the singularity is resolved.

Motivation & Objective

• To understand how cosmological singularities in asymptotically AdS spacetimes manifest in the dual conformal field theory via gauge/gravity duality.
• To determine whether bulk geodesics probing high-curvature regions near singularities can yield observable signatures in the boundary CFT.
• To investigate the validity and limitations of the geodesic approximation in computing two-point correlators in the presence of singularities.
• To clarify whether the dual field theory remains well-defined and normalizable when the bulk contains a cosmological singularity.
• To explore alternative observables such as entanglement entropy and Wilson loops for probing singularity physics beyond geodesics.

Proposed method

• Use the AdS/CFT correspondence to map the bulk evolution in anisotropic Kasner-AdS spacetimes to N=4 super Yang-Mills theory on a contracting anisotropic de Sitter space.
• Compute two-point correlators of high-dimension operators in the boundary CFT using the geodesic approximation, where the correlator is proportional to the regulated length of spacelike geodesics anchored on the boundary.
• Analyze geodesics that bend toward the singularity in directions with negative Kasner exponent p < 0, particularly focusing on their behavior as boundary separation approaches the horizon scale.
• Identify the divergence in geodesic length at horizon separation as the origin of a pole in the two-point function, which corresponds to approximately null geodesics.
• Apply regularization techniques to extract finite, pole-like behavior in the correlator and interpret it as a signature of non-normalizable states in the dual field theory.
• Compare results with known constraints from causality and the domain of influence, and assess the applicability of the Ryu-Takayanagi formula for entanglement entropy in time-dependent geometries with p < 0.

Experimental results

Research questions

• RQ1 Does the geodesic approximation in AdS/CFT yield a well-defined, normalizable state in the dual CFT when the bulk contains a cosmological singularity?
• RQ2 What is the origin of the pole in the two-point correlator at horizon scale for separations along directions with p < 0?
• RQ3 How does the presence of a bulk singularity affect the validity of the geodesic approximation for computing boundary correlators?
• RQ4 Can entanglement entropy or Wilson loops provide alternative probes of the singularity when geodesics fail?
• RQ5 What is the physical interpretation of the non-normalizable state selected by the geodesic approximation in the context of the dual field theory?

Key findings

• A universal pole appears in the two-point correlator at horizon scale for any boundary separation along a direction with negative Kasner exponent p < 0, regardless of spacetime dimension.
• This pole arises from the divergence in the length of spacelike geodesics that approach an approximately null trajectory near the boundary, which is a direct consequence of the bulk singularity.
• The pole indicates that the geodesic approximation selects a non-normalizable state in the dual N=4 super Yang-Mills theory, implying a breakdown of the standard interpretation of the approximation.
• The singularity-related pole persists even in the presence of two additional subtle singularities in the model, and can be eliminated in slightly more refined AdS cosmologies.
• The failure of the geodesic approximation to yield a normalizable state suggests that the standard 1/N expansion may not have a continuous limit in the presence of such singularities.
• Finite-N corrections may smooth the pole into a finite bump, suggesting the geodesic result could approximate a key feature of the exact answer in a non-perturbative regime.