Raphael Bousso

The Holographic Principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at

A covariant entropy conjecture

1.4\ifmmode\times\else\texttimes\fi{}{10}^{69}

Holography in general space-times

bits per square meter. This article reviews the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. This article explains how the bound is tested, and its validity is demonstrated in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. This article surveys some successes and challenges in implementing the holographic principle.

Conformal vacua and entropy in de Sitter space

We conjecture the following entropy bound to be valid in all space-times admitted by Einsteins equation: let A be the area of any two-dimensional surface. Let L be a hypersurface generated by surface-orthogonal null geodesics with non-positive expansion. Let S be the entropy on L. Then S ≤ A/4. We present evidence that the bound can be saturated, but not exceeded, in cosmological solutions and in the interior of black holes. For systems with limited self-gravity it reduces to Bekensteins bound. Because the conjecture is manifestly time reversal invariant, its origin cannot be thermodynamic, but must be statistical. It thus places a fundamental limit on the number of degrees of freedom in nature.

Positive vacuum energy and the N-bound

We provide a background-independent formulation of the holographic principle. It permits the construction of embedded hypersurfaces (screens) on which the entire bulk information can be stored at a density of no more than one bit per Planck area. Screens are constructed explicitly for AdS, Minkowski, and de Sitter spaces with and without black holes, and for cosmological solutions. The properties of screens provide clues about the character of a manifestly holographic theory.

Cosmology and the S-matrix

The de Sitter/conformal field theory (dS/CFT) correspondence is illuminated through an analysis of massive scalar field theory in d-dimensional de Sitter space. We consider a one-parameter family of dS-invariant vacua related by Bogolyubov transformations and compute the corresponding Green functions. It is shown that none of these Green functions correspond to the one obtained by analytic continuation from AdS. Among this family of vacua are in (out) vacua which have no incoming (outgoing) particles on

Holographic Probabilities in Eternal Inflation

{\mathcal{I}}^{\ensuremath{-}}

The holographic principle for general backgrounds

({\mathcal{I}}^{+}).

A paradox in the global description of the multiverse

Surprisingly, it is shown that in odd spacetime dimensions the in and out vacua are the same, implying the absence of particle production for this state. The correlators of the boundary CFT, as defined by the dS/CFT correspondence, are shown to depend on the choice of vacuum state---the correlators with all points on