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We discuss spacetime instability for effective field theories of quantumgravity. The effective action of gravity introduces infinite higher derivativecurvature terms $R^{2}, { R }_{ \mu \nu }{ R }^{ \mu \nu },R_{\mu\nu\kappa\lambda} R^{\mu\nu\kappa\lambda}\dots$. Although these higherderivative curvature terms are indispensable to construct the self-consistentrenormalizable theory of quantum gravity, they lead to several pathologies. Weclearly show that even if they are written as the Planck-suppressed operatorsthey lead to serious consequences and and de Sitter or radiation-dominatedUniverse is highly unstable. We show that the couplings of these higherderivative curvatures must satisfy $\left|a_{1,2,3}\right|\gtrsim 10^{118}$ tobe consistent with the cosmological observations. Thus, the standard effectivefield theories of quantum gravity fail to describe the observed Universe unlessintroducing a specific technique dealing with the higher derivative curvatureterms.

Spacetime Instability and Quantum Gravity as Low Energy Effective Field Theory