Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

TL;DR

This paper explores analytical solutions in a higher-order modified teleparallel cosmology using Cartan symmetries, demonstrating their relevance to supernova data, dark matter modeling, and Bianchi I universe solutions through a global dynamical systems approach.

Contribution

It introduces a novel application of Cartan symmetries to find integrable models and analytical solutions in higher-order teleparallel cosmology, including a toy model fitting supernova data.

Findings

Derived specific potential forms for scalar fields ensuring integrability.

Constructed analytical solutions fitting supernova observations and dark matter components.

Performed a comprehensive global dynamical analysis of the cosmological field equations.

Abstract

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization.