Noether symmetries in f(T,TG) cosmology

Abstract

All degrees of freedom related to the torsion scalar can be explored by analysing, the f (T, TG) gravity formalism where, T is a torsion scalar and TG is the teleparallel counterpart of the Gauss-Bonnet topological invariant term. The well-known Noether symmetry approach is a useful tool for selecting models that are motivated at a fundamental level and determining the exact solution to a given Lagrangian, hence we explore Noether symmetry approach in f (T, TG) gravity formalism with three different forms of f (T, TG) and study how to establish nontrivial Noether vector form for each one of them. We extend the analysis made in S Capozziello, M De Laurentis, and K F Dialektopoulos 2016, “Noether symmetries in gauss–bonnet-teleparallel cosmology,” Eur. Phys. J. C 76, 629. for the form f T T bT tT , G G k m ( ) = + 0 0 and discussed the symmetry for this model with linear teleparallel equivalent of the Gauss-Bonnet term, followed by the study of two models containing exponential form of the teleparallel equivalent of the Gauss-Bonnet term. We have shown that all three cases will allow us to obtain non-trivial Noether vector which will play an important role to obtain the exact solutions for the cosmological equations.