Einsteinian cubic gravity

Abstract

We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives with respect to one of those parameters. We use our method to construct a D-dimensional cubic theory of gravity which satisfies the following properties: 1) it shares the spectrum of Einstein gravity, i.e., it only propagates a transverse and massless graviton on a maximally symmetric background; 2) the relative coefficients of the different curvature invariants involved are the same in all dimensions; 3) it is neither trivial nor topological in four dimensions. Up to cubic order in curvature, the only previously known theories satisfying the first two requirements are the Lovelock ones: Einstein gravity, Gauss-Bonnet and cubic-Lovelock. Of course, the last two theories fail to satisfy requirement 3 as they are, respectively, topological and trivial in four dimensions. We show that, up to cubic order, there exists only one additional theory satisfying requirements 1 and 2. Interestingly, this theory is, along with Einstein gravity, the only theory which also satisfies 3.

6 pages

References in corpus (11)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Massive Gravity in Three Dimensions
• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Critical Gravity in Four Dimensions
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Universality of corner entanglement in conformal field theories
• Critical Points of D-Dimensional Extended Gravities
• Entanglement entropy across a deformed sphere
• Energy and Angular Momentum in Generic F(Riemann) Theories
• Black holes in five-dimensional Palatini $f(R)$ gravity and implications for the AdS/CFT correspondence

Cited by in corpus (7)

• Four-dimensional black holes in Einsteinian cubic gravity
• Aspects of general higher-order gravities
• Bounce Universe and Black Holes from Critical Einsteinian Cubic Gravity
• Causality and a-theorem Constraints on Ricci Polynomial and Riemann Cubic Gravities
• Generalized Pure Lovelock Gravity
• Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality
• Higher order gravities and the Strong Equivalence Principle