Noether symmetries in Gauss-Bonnet-teleparallel cosmology

Area of Science:

• Cosmology
• Theoretical Physics
• Gravitation

Background:

• Teleparallel gravity offers an alternative to General Relativity, focusing on torsion rather than curvature.
• The Gauss-Bonnet topological invariant is crucial in higher-order gravity theories.
• Noether symmetry provides a powerful tool for finding exact solutions in dynamical systems.

Purpose of the Study:

• To investigate a generalized teleparallel cosmological model incorporating the torsion scalar (T) and the teleparallel Gauss-Bonnet invariant (G).
• To utilize the Noether symmetry approach to constrain the model's functional form.
• To derive exact cosmological solutions within this framework.

Main Methods:

• The study employs the Noether symmetry approach within the context of teleparallel gravity.
• The analysis focuses on a specific cosmological model defined by the torsion scalar and the teleparallel Gauss-Bonnet invariant.
• Mathematical techniques are used to identify symmetries and derive solutions.

Main Results:

• The Noether symmetry approach successfully fixes the functional form of the teleparallel cosmological model.
• Exact cosmological solutions were derived, providing insights into the model's behavior.
• The study demonstrates the efficacy of Noether symmetries in teleparallel cosmology.

Conclusions:

• The Noether symmetry approach is a viable method for studying teleparallel cosmological models.
• The derived solutions offer potential avenues for understanding cosmic acceleration and dark energy.
• This research contributes to the theoretical framework of modified gravity theories.