# On higher derivative gravity, c-theorems and cosmology

@article{Sinha2011OnHD, title={On higher derivative gravity, c-theorems and cosmology}, author={Aninda Sinha}, journal={Classical and Quantum Gravity}, year={2011}, volume={28}, pages={085002} }

We consider higher derivative gravity lagrangians in three and four 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…

## 38 Citations

New massive gravity and AdS(4) counterterms.

- Physics, MedicinePhysical review letters
- 2011

This theory is rewritten in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory and the parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS(3) gravity and two-dimensional conformal field theory.

Consistent truncations of IIB Supergravity and a Holographic c-theorem for Higher Derivative Gravity.

- Physics
- 2015

We prove a holographic c-theorem for the a central charge in AdS/CFT where the bulk is described by a gravitational action built out of an arbitrary function f(Rcd) of the Riemann tensor coupled to…

Holographic c-theorems and higher derivative gravity

- Physics
- 2012

In AdS/CFT, the holographic Weyl anomaly computation relates the $a$-anomaly coefficient to the properties of the bulk action at the UV fixed point. This universal behavior suggests the possibility…

Short-cut to new anomalies in gravity duals to logarithmic conformal field theories

- Physics
- 2011

Various massive gravity theories in three dimensions are conjecturally dual to logarithmic conformal field theories (LCFTs). We summarise the status of these conjectures. LCFTs are characterised by…

Entropy functionals and c-theorems from the second law

- Physics
- 2016

We show that for a general four derivative theory of gravity, only the holographic entanglement entropy functionals obey the second law at linearized order in perturbations. We also derive bounds on…

Extremal Black Holes and Holographic C-Theorem

- Physics
- 2013

Abstract We found Bogomolʼnyi type of the first order differential equations in three-dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting…

Energy Density Bounds in Cubic Quasi-Topological Cosmology

- Physics
- 2013

We investigate the thermodynamical and causal consistency of cosmological models of the cubic Quasi-Topological Gravity (QTG) in four dimensions, as well as their phenomenological consequences.…

A holographic c-theorem for higher derivative gravity

- Physics
- 2011

We prove a holographic c-theorem for the a central charge in AdS/CFT where the bulk is described by a gravitational action built out of an arbitrary function f(R^{ab}_{cd}) of the Riemann tensor…

c-theorems in arbitrary dimensions

- Physics
- 2012

The dilaton action in 3 + 1 dimensions plays a crucial role in the proof of the a-theorem. This action arises using Wess-Zumino consistency conditions and crucially relies on the existence of the…

Counterterms, critical gravity and holography

- Physics
- 2012

We consider counterterms for odd dimensional holographic conformal field theories (CFTs). These counterterms are derived by demanding cutoff independence of the CFT partition function on S-d and S-1…

## References

SHOWING 1-10 OF 97 REFERENCES

New massive gravity extended with an arbitrary number of curvature corrections

- Physics
- 2010

We consider new massive gravity (NMG) type models in the context of AdS/CFT. By demanding the existence of a holographic c theorem, we construct an infinite family of three-dimensional quantum…

On the new massive gravity and AdS/CFT

- Physics
- 2010

Demanding the existence of a simple holographic c-theorem, it is shown that a general (parity preserving) theory of gravity in 2+1 dimensions involving upto four derivative curvature invariants…

Massive Higher Derivative Gravity in D-dimensional Anti-de Sitter Spacetimes

- Physics
- 2009

We find the propagator and calculate the tree level scattering amplitude between two covariantly conserved sources in an anti-de Sitter background for the most general D-dimensional quadratic,…

Superstring Modifications of Einstein's Equations

- Physics
- 1986

The modifications of the classical equations of motion of the gravitational field in type II string theory are derived by studying tree-level gravitational scattering amplitudes. The effective…

c-functions in the Born-Infeld extended new massive gravity

- Physics
- 2010

We derive and study the equations of motion of the Born-Infeld extension of new massive gravity for globally and asymptotically (anti-)de Sitter spaces, and show that the assumptions of the…

AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound

- Physics
- 2010

We study the relation between the causality and positivity of energy bounds for Gauss-Bonnet gravity in an AdS7 background. Requiring the group velocity of metastable states to be bounded by the…

Conserved charges for gravity with locally anti-de sitter asymptotics

- Physics, MedicinePhysical review letters
- 2000

It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor.

Black holes in quasi-topological gravity

- Physics
- 2010

We construct a new gravitational action which includes cubic curvature interactions and which provides a useful toy model for the holographic study of a three parameter family of four- and…

A new cubic theory of gravity in five dimensions: black hole, Birkhoff's theorem and C-function

- Physics
- 2010

We present a new cubic theory of gravity in five dimensions which has second-order traced field equations, analogous to BHT new massive gravity in three dimensions. Moreover, for static spherically…

Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions

- Physics
- 2010

We classify all the six-derivative Lagrangians of gravity, whose traced field equations are of second or third order, in arbitrary dimensions. In the former case, the Lagrangian in dimensions greater…