[Paper Review] The cosmological singularity problem

Ben Craps|arXiv (Cornell University)|Jan 25, 2010

Black Holes and Theoretical Physics15 references3 citations

TL;DR

This paper investigates the cosmological singularity problem using the AdS/CFT correspondence, proposing that big crunch singularities in asymptotically AdS spacetimes can be studied via dual field theories with unbounded potentials. It demonstrates that quantum instabilities in such field theories—specifically in a deformed ABJM model—signal the onset of singularity formation, and suggests that self-adjoint extensions in the dual theory may allow for a consistent evolution through the singularity, potentially leading to a cosmological bounce.

ABSTRACT

Despite impressive phenomenological successes, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Depending on the model, one would like to understand how appropriate initial conditions were selected at the big bang singularity, or how a pre-existing contracting universe underwent a big crunch/big bang transition, if such transitions are possible at all. In this talk, after an introduction to these questions, an attempt is described to study cosmological singularities using the AdS/CFT correspondence. A specific model in which asymptotically AdS initial data evolve into a big crunch singularity is discussed and a dual field theory description is provided.

Motivation & Objective

• To address the incompleteness of cosmological models due to the unresolved nature of the big bang singularity.
• To explore whether the AdS/CFT correspondence can provide a non-perturbative description of cosmological singularities.
• To investigate whether time evolution can be consistently extended through a big crunch singularity using dual field theory techniques.
• To determine whether a cosmological bounce can emerge from quantum dynamics in the dual field theory, particularly in models with unbounded potentials.

Proposed method

• Utilizes the AdS/CFT correspondence to map gravitational singularities in asymptotically AdS spacetimes to quantum field theories with unbounded potentials.
• Analyzes a deformed ABJM theory with sextic scalar interactions, focusing on renormalization group flow toward UV fixed points.
• Identifies quantum instabilities in the dual field theory—specifically, the runaway of the $\vec{\phi}_2$ field when $\lambda_{222}$ exceeds a critical value $\lambda_c$—as a signal of singularity formation.
• Applies the concept of self-adjoint extensions in quantum mechanics to the dual field theory to explore whether time evolution can be consistently defined across the singularity.
• Studies the behavior of both homogeneous and inhomogeneous modes in the dual theory to assess particle creation and backreaction effects.
• Translates bulk initial states with modified boundary conditions into boundary field theory states, evolves them through the singularity, and seeks a geometric interpretation of the final state.

Experimental results

Research questions

• RQ1 Can the AdS/CFT correspondence be used to describe the big bang singularity in a non-perturbative way?
• RQ2 What happens in the dual field theory when a gravitational system evolves into a big crunch singularity?
• RQ3 Does the presence of an unbounded potential in the dual field theory signal a breakdown of time evolution, and can this be resolved via self-adjoint extensions?
• RQ4 Can a cosmological bounce emerge from quantum dynamics in the dual field theory, and under what conditions?
• RQ5 How do inhomogeneous modes affect particle creation and backreaction during the singularity transition?

Key findings

• The dual field theory of a big crunch spacetime features an unbounded potential, which leads to quantum instabilities as couplings flow toward the UV.
• In the deformed ABJM model, the $\vec{\phi}_2$ field becomes quantum unstable when $\lambda_{222}$ exceeds a critical value $\lambda_c$, signaling the onset of singularity formation.
• The system exhibits a runaway behavior where $\vec{\phi}_1$ rolls to large values, releasing energy and triggering instability in $\vec{\phi}_2$, indicating a transition to a singular regime.
• Self-adjoint extensions in the dual theory may allow for consistent time evolution through the singularity, suggesting a potential mechanism for a cosmological bounce.
• Preliminary results indicate that certain boundary conditions (non-brick wall type) lead to more favorable particle creation and backreaction behavior than others.
• If homogeneous modes dominate, the final state after the singularity may resemble the initial state, hinting at a possible bounce, though inhomogeneous modes could significantly alter this picture.