# Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term

## TL;DR

This paper explores extended teleparallel gravity theories with a Gauss-Bonnet term, demonstrating their ability to reproduce standard cosmological solutions and mimic the LCDM model without a cosmological constant.

## Contribution

It introduces new Lagrangians in extended teleparallel gravity that can replicate known cosmological behaviors, including the LCDM model, without requiring a cosmological constant.

## Key findings

- Reconstructed analytical solutions for the scale factor and Hubble parameter.
- Found Lagrangians that mimic LCDM without a cosmological constant.
- Potential for new phenomenological implications in extended gravity theories.

## Abstract

In the context of extended Teleparallel gravity theories with a 3+1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological solutions. In particular when applied to a Friedmann-Lema\^itre-Robertson-Walker geometry in four-dimensional spacetime with standard fluids exclusively. We study different types of gravitational Lagrangians and reconstruct solutions provided by analytical expressions for either the cosmological scale factor or the Hubble parameter. We also show that it is possible to find Lagrangians of this type without a cosmological constant such that the behaviour of the LCDM model is precisely mimicked. The new Lagrangians may also lead to other phenomenological consequences opening up the possibility for new theories to compete directly with other extensions of General Relativity.