# Spacetime Instability and Quantum Gravity as Low Energy Effective Field Theory

## TL;DR

This paper examines how higher derivative curvature terms in effective quantum gravity theories cause spacetime instabilities, challenging their viability in describing our universe without special techniques.

## Contribution

It demonstrates that standard effective field theories of quantum gravity lead to instabilities unless couplings are fine-tuned to extremely large values.

## Key findings

- Higher derivative terms induce spacetime instabilities.
- Couplings must be extremely large to match cosmological data.
- Standard EFTs of quantum gravity are insufficient without special techniques.

## Abstract

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