Quantum Spacetime Instability and Breakdown of Semiclassical Gravity
  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.
