# de Sitter and Scaling solutions in a higher-order modified teleparallel theory

## TL;DR

This paper investigates the existence, stability, and behavior of de Sitter, ideal gas, and scaling solutions in a higher-order modified teleparallel gravity theory, linking it to General Relativity with a noncanonical scalar field.

## Contribution

It introduces a higher-order modified teleparallel theory, analyzes exact solutions, stability conditions, and demonstrates how it can reproduce the Hubble function of $\\Lambda$-cosmology.

## Key findings

- De Sitter solutions exist and are stable under certain conditions.
- The theory can reproduce the Hubble function of $\\Lambda$-cosmology.
- Scaling solutions are characterized in the presence of matter.

## Abstract

The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent with that of General Relativity with a minimally coupled noncanonical field. The conditions for the existence of de Sitter solutions and ideal gas solutions in the case of vacuum are studied as also the stability criteria. Furthermore, in the presence of matter the behaviour of scaling solutions is given. Finally, we discuss the degrees of freedom of the field equations and we reduce the field equations in an algebraic equation, where in order to demonstrate our result we show how this noncanonical scalar field can reproduce the Hubble function of $\Lambda$-cosmology.