Eur. Phys. J. C (2016) 76: 542
https://doi.org/10.1140/epjc/s10052-016-4389-x

Regular Article - Theoretical Physics

Criticality in Einstein–Gauss–Bonnet gravity: gravity without graviton

¹ Center for High Energy Physics, Peking University, No. 5 Yiheyuan Rd, Beijing, 100871, People’s Republic of China
² Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, No. 5 Yiheyuan Rd, Beijing, 100871, People’s Republic of China
³ Collaborative Innovation Center of Quantum Matter, No. 5 Yiheyuan Rd, Beijing, 100871, People’s Republic of China
⁴ Department of Physics, Center for Advanced Quantum Studies, Beijing Normal University, Beijing, 100875, China

^* e-mail: fanzhy@pku.edu.cn

Received: 13 September 2016
Accepted: 19 September 2016
Published online: 5 October 2016

Abstract

General Einstein–Gauss–Bonnet gravity with a cosmological constant allows two (A)dS spacetimes as its vacuum solutions. We find a critical point in the parameter space where the two (A)dS spacetimes coalesce into one and the linearized perturbations lack any bilinear kinetic terms. The vacuum perturbations hence lose their interpretation as linear graviton modes at the critical point. Nevertheless, the critical theory admits black hole solutions due to the nonlinear effect. We also consider Einstein gravity extended with general quadratic curvature invariants and obtain critical points where the theory has no bilinear kinetic terms for either the scalar trace mode or the transverse modes. Such critical phenomena are expected to occur frequently in general higher-derivative gravities.