A minimal self tuning model to solve the cosmological constant problem

Abstract

The expansion of the Universe is observed to be accelerating, with the simplest solution being a classical cosmological constant. However, this receives contributions from the quantum vacuum, which are predicted to be many orders of magnitude larger than observations, and suffers from radiative instabilities requiring repeated fine tuning. In this paper we present a minimal, self tuning scalar field model that can dynamically cancel a large quantum vacuum energy, avoiding Weinberg's No Go Theorem, and produce accelerated de Sitter expansion at a lower energy scale as a solution to the problem. Our minimal model, which contains a non canonical kinetic energy and a linear potential, belongs to the Kinetic Gravity Braiding subclass of Horndeski theory which is not observationally excluded, and lies outside of the known Fab Four or Well Tempered models. We find analytic solutions in the limits of slow roll and fast roll, and numerically solve the equations of motion to illustrate our model. We show that the model allows for a matter dominated era, and that the attractor solution is stable under a phase transition in the vacuum energy density. We also consider the energy scales required to match observations. Our model shows the existence of a wider class of successful self tuning models than previously assumed.