Infrared Screening of the Cosmological Constant

Abstract

The observed cosmological constant is set by the deepest infrared scale of the present universe rather than by the microscopic scales that contribute to the vacuum energy. We show that this emerges as the quantum fluctuations of the gravitational field are progressively taken into account. Considering the Einstein-Hilbert+$R^2$ truncation of gravity, we find that in a wide region of the parameter space the theory develops instabilities that give rise to large amplitude quantum fluctuations which govern the renormalization group flow. Once the flow enters this region, it remains there all the way towards the infrared and progressively loses memory of its boundary conditions. The running cosmological constant $Λ_k$ ($k$ is the running scale) is driven towards the universal infrared scaling $Λ_k\sim λ_{_{\rm IR}}\,k^2$, with $λ_{_{\rm IR}}= \frac{1}{2(π-2)}$. At the deepest infrared scale $k\sim H_0$ (the current Hubble scale), the cosmological constant is then screened to its observed value $Λ_{_{\rm IR}}\sim H_0^2$.