Multiscalar field cosmological model and possible solutions using Noether symmetry approach

TL;DR

This paper develops a multiscalar field cosmological model with mixed kinetic terms, using Noether symmetry to determine coupling and potential functions, leading to simplified solutions and cosmological insights.

Contribution

It introduces a method to determine coupling and potential functions in a multiscalar cosmological model via Noether symmetry, avoiding phenomenological assumptions.

Findings

Derived exact solutions for the cosmological model.

Identified conditions for cyclic variables simplifying equations.

Analyzed cosmological implications of the solutions.

Abstract

In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on one of the scalar fields. Instead of choosing these functions phenomenologically here, they are evaluated assuming the existence of Noether symmetry. By appropriate choice of a point transformation in the augmented space, one of the variables in the Lagrangian becomes cyclic and the evolution equations become much simpler to have solutions. Finally, the solutions are analyzed from cosmological view point.