Integrable modified gravity cosmological models with an additional scalar field

TL;DR

This paper explores modified gravity cosmological models with an extra scalar field, transforming them into two-field models, and analyzes their solutions and evolution in different frames.

Contribution

It introduces a method to transform modified gravity models into two-field chiral models and derives general solutions for specific cases.

Findings

General solutions for $R^2$ gravity with scalar field in flat FLRW

Analysis of cosmic time solutions and Hubble parameter evolution

Comparison between Einstein and Jordan frame dynamics

Abstract

We consider modified gravity cosmological models that can be transformed into two-field chiral cosmological models by the conformal metric transformation. For the $R^2$ gravity model with an additional scalar field and the corresponding two-field model with the cosmological constant and nonstandard kinetic part of the action, the general solutions have been obtained in the spatially flat FLRW metric. We analyze the correspondence of the cosmic time solutions obtained and different possible evolutions of the Hubble parameters in the Einstein and Jordan frames.