On the Cardy-Verlinde Formula and the de Sitter/CFT Correspondence

Abstract

We derive the Cardy--Verlinde entropy formula for the field theory that lives on the boundary of an asymptotically de Sitter space with a black hole. The boundary theory which is not conformal has a monotonic $C$--function defined by the Casimir energy. The instability of the space due to Hawking radiation from the black hole corresponds to an RG flow from the IR to the UV during which $C$ increases. The endpoint of black hole evaporation is de Sitter space which is described by a conformal theory at the UV fixed point of the RG flow.

16 pages in phyzzx.tex, the discussion in section 4 clarified, minor corrections, two references added; v3: the relation between time evolution and RG flow made explicit, Comments and references added

References in corpus (12)

• The dS/CFT Correspondence
• Inflation and the dS/CFT Correspondence
• Cardy-Verlinde Formula and Asymptotically de Sitter Spaces
• Some Aspects of the de Sitter/CFT Correspondence
• Conformal anomaly from dS/CFT correspondence
• Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
• Quantum cosmology, inflationary brane-world creation and dS/CFT correspondence
• Gravitational energy, dS/CFT correspondence and cosmic no-hair
• dS/CFT correspondence on a brane
• Holographic Entropy on the Brane in de Sitter Schwarzschild Space
• Universal Counting of Black Hole Entropy by Strings on the Stretched Horizon
• dS/CFT Duality on the Brane with a Topological Twist

Cited by in corpus (11)

• Radiation via Tunneling from a de Sitter Cosmological Horizon
• Entropy and universality of Cardy-Verlinde formula in dark energy universe
• Slow-roll parameters in braneworld cosmologies
• Asymptotics of Quasi-normal Modes for Multi-horizon Black Holes
• Bouncing Cosmologies and Self-Gravitational Corrections
• dS-Holographic C-Functions with a Topological, Dilatonic Twist
• Entropy Bounds in $R\times S^3$ Geometries
• Strings and the Holographic Description of Asymptotically de Sitter Spaces
• Implications of Conformal Symmetry in Quantum Mechanics
• Holographic Inflation
• On Entropy Bounds and Holography