The dS/CFT correspondence

Abstract

A holographic duality is proposed relating quantum gravity on dS D (D-dimensional de Sitter space) to conformal field theory on a single S D−1 ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I + (the future boundary of dS D ) are mapped to the antipodal points on S D−1 relative to those on I − . For the case of dS 3 , which is analyzed in some detail, the central charge of the CFT 2 is computed in an analysis of the asymptotic symmetry group at I ± . This dS/CFT proposal is supported by the computation of correlation functions of a massive scalar field. In general the dual CFT may be non-unitary and (if for example there are sufficently massive stable scalars) contain complex conformal weights. We also consider the physical region O − of dS 3 corresponding to the causal past of a timelike observer, whose holographic dual lives on a plane rather than a sphere. O − can be foliated by asymptotically flat spacelike slices. Time evolution along these slices is generated by L 0 +L 0 , and is dual to scale transformations in the boundary CFT 2 .

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“…Firstly, observations of high-redshift supernovae suggest that the universe may possess a small, positive cosmological constant [1]. Theoretically, there has been much interest in the adS/CFT (conformal field theory) cor-respondence (see [2] for a review) and its more recent relative the dS/CFT correspondence (see, for example, [3]). Finally, a negative cosmological constant is a key ingredient of "brane world" scenarios (see, for example, [4]).…”

Inflation and the dS/CFT Correspondence

“…In recent theoretical work [4], it was conjectured that a fully quantum theory, including gravity, in pure de Sitter space with a fixed cosmological constant has a certain dual representation as a conformally invariant Euclidean field theory on the boundary of de Sitter space. 1 The purpose of this short note is to extend this "dS/CFT correspondence" so as to potentially include our own universe.…”

“…We begin with a brief synopsis of the relevant portions of [4] for the case of four dimensional de Sitter space, dS 4 . 2 We assume that all observables can be generated from the complete set of quantum correlation functions whose arguments lie on the asymptotic boundary of dS 4 .…”

Braneworld cosmology in (anti)-de Sitter Einstein-Gauss-Bonnet-Maxwell gravity

“…Let us first investigate this analogy in Einstein gravity for the usual (n + 1)-dimensional FRW Universe with a metric 1) where the n-dimensional spatial hypersurfaces with negative, zero or positive curvature are parametrized by k = −1, 0, 1, respectively 6 . We limit our discussion mainly to that of the closed universe (k = 1), with a spatial volume defined by V = a n d n x √ g. The standard FRW equations may then be written as 2) where …”