Probing crunching AdS cosmologies

TL;DR

This paper investigates the behavior of two-point correlators in holographic models of crunching AdS cosmologies, revealing late-time factorization, non-analyticities, and the connection to quasinormal modes near the singularity.

Contribution

It provides an analytical study of geodesics and wave equations in crunching AdS backgrounds, linking correlator behavior to maximal expansion and quasinormal frequencies.

Findings

Late-time correlators factorize and show non-analyticity at a_{max}.

Geodesics with energy exceeding a_{max} terminate at the crunch.

The scalar wave equation reveals a branch point linked to the lowest quasinormal frequency.

Abstract

Holographic gravity duals of deformations of CFTs formulated on de Sitter spacetime contain FRW geometries behind a horizon, with cosmological big crunch singularities. Using a specific analytically tractable solution within a particular single scalar truncation of N=8 supergravity on AdS_4, we first probe such crunching cosmologies with spacelike radial geodesics that compute spatially antipodal correlators of large dimension boundary operators. At late times, the geodesics lie on the FRW slice of maximal expansion behind the horizon. The late time two-point functions factorise, and when transformed to the Einstein static universe, they exhibit a temporal non-analyticity determined by the maximal value of the scale factor a_{max} . Radial geodesics connecting antipodal points necessarily have de Sitter energy E \leq a_{max}, while geodesics with E > a_{max} terminate at the crunch, the two categories of geodesics being separated by the maximal expansion slice. The spacelike crunch singularity is curved "outward" in the Penrose diagram for the deformed AdS backgrounds, and thus geodesic limits of the antipodal correlators do not directly probe the crunch. Beyond the geodesic limit, we point out that the scalar wave equation, analytically continued into the FRW patch, has a potential which is singular at the crunch along with complex WKB turning points in the vicinity of the FRW crunch. We then argue that the frequency space Green's function has a branch point determined by a_{max} which corresponds to the lowest quasinormal frequency.