Classification of Teleparallel Horndeski Cosmology via Noether Symmetries

TL;DR

This paper classifies Teleparallel Horndeski cosmological models using Noether symmetries, enabling the identification of specific models and derivation of exact solutions in scalar-tensor theories.

Contribution

It introduces a novel classification method for Teleparallel Horndeski models based on Noether symmetries, facilitating model selection and solution derivation.

Findings

Identified specific models within Teleparallel Horndeski theories.

Derived exact cosmological solutions from symmetry-selected models.

Provided new cosmological systems for further study.

Abstract

Teleparallel Horndeski theory offers an avenue through which to circumvent the speed constraint of gravitational waves in an efficient manner. However, this provides an even larger plethora of models due to the increase in action terms. In this work we explore these models in the context of cosmological systems. Using Noether point symmetries, we classify the dynamical systems that emerge from Teleparallel Horndeski cosmologies. This approach is very effective at selecting specific models in the general class of second-order Teleparallel scalar-tensor theories, as well as for deriving exact solutions within a cosmological context. By iterating through the Lagrangians selected through the Noether symmetries, we solve for a number of cosmological systems which provides new cosmological systems to be studied.