A Quintessence with Tiny Dark Energy Induced by Inflation

Abstract

We propose a postulate $\dot{q} =MH$ concerning temporal variation of quintessence field $q$ where $H$ is Hubble parameter ($=\dot{a}/a$) and $M$ is the scale characterizing the field. Using the postulate we uniquely determines a dynamical model of the field. The potential of the field satisfies the tracking condition. The minimum of the total energy density of matter and the field is located at $a=\infty$. We show that the present tiny dark energy is caused by early inflation, while the energy is comparable to Planck scale before the inflation. Since the model is reduced to $\Lambda$CDM model in the limit $M\to 0$, it is a natural generalization of $\Lambda$CDM model.