Observational constraint on the dark energy scalar field

In the present paper, we investigate three scalar fields, \qu field, phantom field and tachyon field, to explore the source of dark energy, using the Gaussian processes method from the background data and perturbation growth rate data. The corresponding reconstructions all suggest that the dark energy should be dynamical. Moreover, the quintom field, a combination between \qu field and phantom field, is powerfully favored by the data within 68\% confidence level. Using the mean values of scalar field $\phi$ and potential $V$, we fit the function $V(\phi)$ in different fields. The fitted results imply that potential $V(\phi)$ in each scalar field may be a double exponential function or Gaussian function. The Gaussian processes reconstructions also indicate that the tachyon scalar field cannot be convincingly favored by the data and is at a disadvantage to describe the dark energy.