A Model of Vanishing Cosmological Constant

We propose a model in which there exists a real scalar field $q$ satisfying a condition $\dot{q} =MH$ and its energy density is given by $(1/2)\dot{q}^2+V(q)$, where $H$ is the Hubble parameter ($H=\dot{a}/a$) and $M$ is a mass scale characterizing the field. We show that the potential $V(q)$ of the field is uniquely determined by the condition. The potential depends on the energy densities of background matters. We find that the vacuum energy of the matters is cancelled by the potential of the field. As a result, the minimum of the total energy density of the matters and the field vanishes and is located at the infinite scale factor $a=\infty$. This remarkable property results without a supersymmetry. We show that the present tiny dark energy is caused by early inflation, while the energy is comparable to Planck scale before the inflation. As our model is reduced to the $\Lambda$CDM model in the limit $M\to 0$, it is a natural generalization of the $\Lambda$CDM model.