Scalar Fields For Dark Energy

Present astronomical observations suggest that the expansion of the universe is accelerating, which indicates the existence of dark energy. A dominating cos-mological constant is the simplest candidate for dark energy. The LCDM model mainly contains the cosmological constant withω∧= - 1, cold dark matter, and baryon matters. This simple model agrees with all astronomical observations, such as SnIa (type Ia supernovae), CMB (cosmic microwave background), and LSS (large scale structure). But the LCDM model is burdened with fine tun-ing and coincidence problems, which needs to be explained in any dark energy models.Another well studied candidate of dark energy is a scalar field. In this type of models, the equation of state of dark energy is evolving. As the present ob-servations of dark energy is still not precise enough, there are plenty of possible scalar models. These models can be induced from theoritical physics, such as particle physics, supergravity, string theory, or just be reconstructed from obser-vations. In this paper we will introduce several well studied scalar models, such as Quintessence, Phantom, K-essence, and scalar-tensor theories. In these mod-els, the fine tuning and coincidence problems could always be relaxed to certain extent.In Quintessence models, there are tracking solutions for a class of potentials. In these cases, the evolving of scalar field will converge to a single tracker solu-tion. If the early tracking era is long enough, any residue of initial condition will be washed away and the solution of scalar field today depends only on parameters in the potential. So the coincidence problem can thus be solved. By using the tracker equation, one can get the condition of the existence of tracking solution and study the evolving ofωQ. But the original tracker equation is satisfied only whenΩQ<< 1. To get the attractor ofωQ and study its properties at present dark energy dominated era, we will derive the full tracker equation. We will get {ωQ,ΩQ} relation in the attractor of full tracker equation, both of which are ana- lytical functions of the quintessence potential. If there is a long enough tracking solution at early times,{ωQ,ΩQ} always approach to{ωQ,ΩQ} and their rela-tive relations can be predicted at present era. From the potential and{ωQ,ΩQ} relation, one can induce theωQ～ΩQ relation without solving equations of mo-tion numerically. Vice versa, forms of Quintessence potentials can be constrained directly by conditions on{ωde,Ωde} from astronomical observations.We have also numerically analyzed non-minimally coupled theories of special potentials. Such theories yield equations of stateω<-1 and oscillations of the cosmological expansion, which are favored by the recent analysis of observations. Fitting these theories to the Gold SnIa dataset, we obtain results comparable with other models. A potential of the form Similar results are obtained for potentials of the form In most of these models, dark energy and dark matter can be unified.