Stability of de Sitter Spacetime against Infrared Quantum Scalar Field Fluctuations

We study the backreaction of superhorizon fluctuations of a light quantum scalar field on a classical de Sitter geometry by means of the Wilsonian renormalization group. This allows us to treat the gravitationally amplified fluctuations in a nonperturbative manner and to analytically follow the induced renormalization flow of the spacetime curvature as long wavelength modes are progressively integrated out. Unbounded loop corrections in the deep infrared are eventually screened by nonperturbative effects which stabilize the geometry.

Figure 1

Flow of the spacetime curvature $H_{\kappa }^2$ with parameters $\alpha =0.1$, $\beta =1$, and $\lambda =0.1$. Also shown are the one- and two-loop perturbative results, which correctly describe the flow at sufficiently large $\kappa$. For lower $\kappa$, all loop orders contribute equally and perturbation theory breaks down. The flow eventually saturates as a nonperturbative mass is dynamically generated. The long-dashed curve shows the approximate expression (17).