Asymptotic behavior of $N$-fields Chiral Cosmology

TL;DR

This paper analyzes the long-term behavior of multi-scalar field Chiral cosmology models, deriving a theorem for N-fields and identifying that only up to two fields yield physically interesting solutions.

Contribution

It provides a comprehensive asymptotic analysis for multi-field Chiral models and introduces a theorem characterizing their behavior for any number of fields.

Findings

Maximum of two scalar fields yields physically interesting solutions.

For N>2, stationary points are mathematically interesting but not physically distinct.

Derived conserved quantities and a general theorem for N-fields.

Abstract

We perform a detailed analysis for the asymptotic behaviour for the multi-scalar field Chiral cosmological scenario. We present the asymptotic behaviour for the one-field, two-fields and three-fields Chiral models. From these results, and deriving conserved quantities, we present a Theorem for the $N$-fields model for the Chiral model with $N$--fields. We find that the maximum number of scalar fields which provide interesting physical results is two-fields, while for $N>2$ the new stationary points are only of mathematical interest since they do not describe new exact solutions different from those recovered for $N=2$.