Quantum Spacetime Instability and Breakdown of Semiclassical Gravity

Abstract: The semiclassical gravity describes gravitational back-reactions of the classical spacetime interacting with quantum matter fields but the quantum effects on the background is formally defined as higher derivative curvatures. These induce catastrophic instabilities and classic solutions become unstable under small perturbations or their evolutions. In this paper we discuss validity of the semiclassical gravity from the perspective of the spacetime instabilities and consider cosmological dynamics of the Universe in this theory. We clearly show that the homogenous and isotropic flat Universe is unstable and the solutions either grow exponentially or oscillate even in Planckian time $t_{\rm I}=(\alpha_{ 1 }G_N)^{1/2}\approx \alpha_{ 1 }10^{-43}\ {\rm sec}$. The subsequent curvature evolution leads to Planck-scale spacetime curvature in a short time and causes a catastrophe of the Universe unless one takes extremely large values of the gravitational couplings. Furthermore, we confirm the above suggestion by comparing the semiclassical solutions and $\Lambda$CDM with the Planck data and it is found that the semiclassical solutions are not consistent with the cosmological observations. Thus, the standard semiclassical gravity using quantum energy momentum tensor $\left< { T }_{ \mu \nu } \right>$ is not appropriate to describe our Universe.