Classically Integrable Cosmological Models with a Scalar Field

TL;DR

This paper introduces new integrable cosmological models involving scalar fields, including models with exponential and Sine-Gordon potentials, solved through analytic continuation of Toda field theory, expanding the set of exactly solvable cosmological scenarios.

Contribution

It presents novel classes of integrable scalar field cosmological models by exploiting freedom in defining time and fields, including models with exponential and Sine-Gordon potentials.

Findings

Models with exponential potentials are integrable.

Sine-Gordon potential model solvable via Toda field theory.

Expanded the set of exactly solvable cosmological models.

Abstract

New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial metric are shown to be integrable. The model with the Sine-Gordon potential can be solved in terms of analytic continuation of the non-periodic Toda field theory.