Instability of De Sitter Spacetime induced by Quantum Conformal Anomaly

Abstract

The instability of (quasi) de Sitter spacetime from quantum gravitational effects has been discussed in many works. Especially, the gravitational backreaction from quantum energy momentum tensor is crucial for understanding the low-energy description of quantum gravity and sometimes destabilize the spacetime. In this paper we discuss the (quasi) de Sitter instability from gravitational backreaction involving quantum conformal anomaly. The conformal or trace anomaly corresponds to the quantum gravitational contributions of the massless conformal fields and affects the spacetime homogeneously. First, we derive the conformal anomaly using the adiabatic (WKB) approximation and discuss the renormalization of the quantum energy momentum tensor. Then, we consider the dynamics of the Hubble parameter based on the semiclassical Einstein's equations including the cosmological constant, the conformal anomaly and the higher-derivative terms. We have clearly shown that the classical de Sitter attractor $H_{\mathrm{C}} \simeq \sqrt{{\Lambda}/{3}}$ are generally unstable from the viewpoint of the semiclassical gravity and the inflation is destabilized except for the specific conditions. Unless the fine-tuning of the conformal anomaly and the higher derivative terms, the inflation finally becomes the Planckian inflation with the Hubble scale $H \approx M_{\rm P}\equiv \sqrt{1/8\pi G_{N}}$ or terminates $H(t) \rightarrow 0$. The latter case suggests that the cosmic inflation could not last long and the eternal inflation scenarios are strongly constrained.