On higher derivative gravity, c-theorems and cosmology

Abstract

We consider higher derivative gravity lagrangians in 3 and 4 dimensions, which admit simple c-theorems, including upto six derivative curvature invariants. Following a suggestion by Myers, these lagrangians are restricted such that the fluctuations around (anti) de Sitter spaces have second order linearized equations of motion. We study c-theorems both in the context of AdS/CFT and cosmology. In the context of cosmology, the monotonic function is the entropy defined on the apparent horizon through Wald's formula. Exact black hole solutions which are asymptotically (anti) de Sitter are presented. An interesting lower bound for entropy is found in de Sitter space. Some aspects of cosmology in both D=3 and D=4 are discussed.

23 pages, v3: clarifications added, references added

References in corpus (54)

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• Holographic c-theorems in arbitrary dimensions
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• AdS Black Hole Solutions in the Extended New Massive Gravity
• Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity
• Warped black holes in 3D general massive gravity
• On the Entropy Function and the Attractor Mechanism for Spherically Symmetric Extremal Black Holes
• Entropy function and higher derivative corrections to entropies in (anti-)de Sitter space
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Cited by in corpus (35)

• Towards a derivation of holographic entanglement entropy
• A refinement of entanglement entropy and the number of degrees of freedom
• On entanglement spreading in chaotic systems
• Comments on Holographic Entanglement Entropy and RG Flows
• On generalized gravitational entropy, squashed cones and holography
• Entanglement entropy in higher derivative holography
• On entanglement entropy functionals in higher derivative gravity theories
• All unitary cubic curvature gravities in D dimensions
• The instabilities and (anti)-evaporation of Schwarzschild-de Sitter black holes in modified gravity
• Strong Subadditivity, Null Energy Condition and Charged Black Holes
• Holographic Superconductors and Higher Curvature Corrections
• New Massive Gravity and AdS_4 counterterms
• Holographic stress tensor at finite coupling
• Holographic c-theorems and higher derivative gravity
• Holographic phase space: $c$-functions and black holes as renormalization group flows
• Higher-curvature Gravities from Braneworlds and the Holographic c-theorem
• Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity
• Higher derivative corrections in holographic Zamolodchikov-Polchinski theorem
• Counterterms, critical gravity and holography
• Holographic p-wave Superconductors in Quasi-topological Gravity
• On c-theorems in arbitrary dimensions
• Entropy functionals and c-theorems from the second law
• Generalised massive gravity one-loop partition function and AdS/(L)CFT
• Hyperscaling-violating Lifshitz Solutions in Cubic Gravity
• A holographic c-theorem for higher derivative gravity
• Scale Factor Duality for Conformal Cyclic Cosmologies
• Extremal Black Holes and Holographic C-Theorem
• On the dual flow of slow-roll Inflation
• Thermodynamics of Quasi-Topological Cosmology
• $c$-functions in Higher-derivative Flows Across Dimensions
• Domain Walls in Extended Lovelock Gravity
• Universal corner contributions to entanglement negativity
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
• Aspects of three-dimensional higher-curvature gravities
• Exact Solutions in Weyl-Cubed Gravity