The Holographic Principle in a Cosmological Setting

We study the holographic principle in a cosmological context. First, entropy bounds are derived from the holographic principle and applied within a Anti-de Sitter spacetime. Next, the compatibility of the holographic principle and de Sitter spacetime is considered. The holographic principle is a general feature of any theory of quantum gravity. Hence, it should be compatible with any cosmological model that strives to describe our universe. By studying this compatibility, the feasibility of different cosmological models can thus be assesed. For Anti-de Sitter spacetime a satisfactory implementation of the holographic principle has been obtained in the AdS/CFT correspondence. Also, there has been significant progress recently in describing the holographic principle in a flat background. A logical next step would then be to consider positively curved space, or de Sitter space. After reviewing recent work we propose a novel perspective on de Sitter space which may facilitate implementing the holographic principle in de Sitter spacetime

CFT and Entropy on the Brane

We consider a brane-universe in the background of an Anti-de Sitter/ Schwarschild geometry. We show that the induced geometry of the brane is exactly given by that of a standard radiation dominated FRW-universe. The radiation is represented by a strongly coupled CFT with an AdS-dual description. We show that when the brane crosses the horizon of the AdS-black hole the entropy and temperature are simply expressed in the Hubble constant and its time derivative. We present formulas for the entropy of the CFT which are generally valid, and which at the horizon coincide with the FRW equations. These results shed new light on recently proposed entropy bounds in the context of cosmology.Comment: 10 pages, 2 figures, axodraw; v2: minor corrections and references added; v3: reference added, published versio

Elliptic de Sitter Space: dS/Z_2

We propose that for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an ``elliptic'' $Z_2$-identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analog of an S-matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter-invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hilbert space can be finite-dimensional and still have positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type IIB* string theory.Comment: LaTeX, 31 pages; v2: some points clarified, expanded section on string realization, minor corrections, references adde