Natural phantom dark energy, wiggling Hubble parameter H(z) and direct H(z) data

Recent direct H(z) data indicate that the parameter H( z) may wiggle with respect to z. On the other hand, the luminosity distance data of supernovae flatten the wiggles of H( z) because of the integration effect. It is expected that the fitting results can be different in a model permitting a wiggling H( z) because the data of supernovae are degenerate in such a model. As an example the natural phantom dark energy is investigated in this paper. The dynamical property of this model is studied. The model is fitted by the direct H( z) dataset and the SNLS dataset, respectively. The results are rather different, as expected. The quantum stability of this model is also briefly discussed. We find that it is a viable model if we treat it as an effective theory truncated by an upper bound.