Noether Symmetry Approach in multiple scalar fields Scenario

TL;DR

This paper employs the Noether symmetry approach to identify suitable potentials in models with multiple scalar fields, including quintessence, phantom, and quintom, revealing specific potential forms consistent with symmetry conditions.

Contribution

It introduces a systematic method to derive scalar field potentials in multi-field cosmological models using Noether symmetries, providing explicit potential forms for different scenarios.

Findings

Derived exponential potential for N-quintessence.

Identified pseudo Nambu-Goldstone potential for N-phantom.

Established a relation between potentials in N-quintom model.

Abstract

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.