Spacetime Instability and the Problems with Low Energy Quantum Gravity

In this paper we discuss spacetime instability problems in effective field theories of the quantum gravity (QG). The effective action of the gravity requires higher-derivative curvature terms $R^{2}, { R }_{ \mu \nu }{ R }^{ \mu \nu }, R_{\mu\nu\kappa\lambda} R^{\mu\nu\kappa\lambda}\dots$ and they are leading quantum gravitational corrections. Although these higher-curvature terms are indispensable for the construction of the semiclassical or quantum gravity, they lead to several pathologies. We clearly show that even if they are Planck-suppressed operators they lead to serious consequences of the spacetime stability and, de Sitter or radiation dominated Universe are highly unstable for the Hubble perturbation. Furthermore, these curvature terms also violate the null energy condition (NEC) which is required for the self-consistent theories or system. The standard effective field theory of the gravity might fail to describe the observed Universe.Comment: 20 pages, 8 figures, Minor corrections and updated list of reference