Two scalar field cosmology: Conservation laws and exact solutions

TL;DR

This paper explores two scalar field cosmology in flat FRW spacetime, using Noether symmetries to find exact solutions and generalize to N scalar fields with interactions in potential and kinetic terms.

Contribution

It introduces a method using Noether point symmetries to derive exact solutions and extends the analysis to multiple interacting scalar fields.

Findings

Lagrangian with at least three Noether symmetries describes linear Newtonian systems.

Exact solutions of the field equations are obtained using conservation laws.

Results are generalized to N scalar fields with interactions.

Abstract

We consider the two scalar field cosmology in a FRW spatially flat spacetime where the scalar fields interact both in the kinetic part and the potential. We apply the Noether point symmetries in order to define the interaction of the scalar fields. We use the point symmetries in order to write the field equations in the normal coordinates and we find that the Lagrangian of the field equations which admits at least three Noether point symmetries describes linear Newtonian systems. Furthermore, by using the corresponding conservation laws we find exact solutions of the field equations. Finally, we generalize our results to the case of N scalar fields interacting both in their potential and their kinematic part in a flat FRW background.