Integrable cosmological models in the Einstein and in the Jordan frames and Bianchi-I cosmology

TL;DR

This paper explores integrable cosmological models within Bianchi I metrics, examining scalar fields with minimal and non-minimal coupling, and demonstrates solution correspondence between Einstein and Jordan frames.

Contribution

It provides a method to derive general solutions in the Jordan frame from minimally coupled models, enhancing understanding of frame transformations in integrable cosmologies.

Findings

Established correspondence between solutions in Einstein and Jordan frames.

Derived general solutions for scalar field models in Bianchi I cosmology.

Illustrated the approach with a model having a constant potential.

Abstract

We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a constant potential as an example, we demonstrate how to obtain the general solutions of the corresponding models in the Jordan frame.