Probing crunching AdS cosmologies

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 factorã max . Radial geodesics connecting antipodal points necessarily have de Sitter energy E ã max , while geodesics with E >ã 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 byã max which corresponds to the lowest quasinormal frequency.

Quasinormal modes and holographic correlators in a crunching AdS geometry

“…In two related works [26,38] in the case of three specific microscopic models with d = 3 and 4 we find that the exponent γ = 1/d. In this article we will focus our attention on the AdS 4 deformation (discussed in [26]) which happens to be analytically tractable. Certain qualitative features of this model, however, appear to be generic.…”

“…The theory in question is the large-N limit of the CFT on M2-branes [3,31] which is intrinsically strongly coupled, placed in three dimensional de Sitter space and deformed by a relevant operator with conformal dimension ∆ = 1 at the conformal fixed point. The resulting gravity dual has several attractive features worthy of detailed exploration, some of which were already pointed out in [26]. One of the properties of this system, which also happens to be a general feature of these types of crunching AdS models, is that geodesic probes which compute boundary correlators (of high dimension operators) stay away from, and therefore do not probe the bulk singularity 2 [32][33][34][35].…”

“…1 Generally speaking, analytically tractable models of deformed CFTs are difficult to come by, and this is particularly important if the questions of interest involve analytic properties of correlation functions. In recent work [26] we pointed out that a particular, single scalar truncation of N = 8 supergravity in four dimensions, with a known Euclidean solution [27][28][29][30], provides (upon appropriate analytic continuation) an analytically tractable example of a gravity dual of a strongly coupled QFT in de Sitter spacetime. The theory in question is the large-N limit of the CFT on M2-branes [3,31] which is intrinsically strongly coupled, placed in three dimensional de Sitter space and deformed by a relevant operator with conformal dimension ∆ = 1 at the conformal fixed point.…”

“…The isometries of the de Sitter slices allow a natural separation of variables. Following the line of reasoning adopted in [16,26], we may expand the (probe) bulk field ϕ in terms of temporal de Sitter harmonics T (ω, t), and spatial spherical harmonics on S d−1 :…”

Holographic entanglement entropy for massive flavours in dS 4

“…• It is known that holographic field theories in de Sitter have the property that twopoint correlators, in the geodesic limit, for superhorizon sized separations, are sensitive to the FRW geometry behind the bulk horizon, see e.g., [31], and also see e.g. [32], for the analogous situation involving thermal field theories dual to AdS black holes.…”