Noether Symmetry Approach in multiple scalar fields Scenario

In this Letter, we find suitable potentials in the multiple scalar fields scenario by using the Noether symmetry approach. We discussed three models with multiple scalar fields: N-quintessence with positive kinetic terms, N-phantom with negative kinetic terms and N-quintom with both positive and negative kinetic terms. In the N-quintessence case, the exponential potential which could be derived from several theoretic models is obtained from the Noether conditions. In the N-phantom case, the potential $\frac{V_{0}}{2}(1-\cos(\sqrt{\frac{3N}{2}}\frac{\phi}{m_{pl}}))$, which could be derived from the Pseudo Nambu-Goldstone boson model, is chosen as the Noether conditions required. In the N-quintom case, we derive a relation $DV'_{\phi q}=-\tilde{D}V'_{\phi p}$ between the potential forms for the quintessence-like fields and the phantom-like fields by using the Noether symmetry.