Noether symmetries in f(T, TG) cosmology

Abstract

AbstractAll degrees of freedom related to the torsion scalar can be explored by analysing, thef(T,TG) gravity formalism where,Tis a torsion scalar andTGis 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 inf(T,TG) gravity formalism with three different forms off(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. C76, 629. for the formf(T,TG)=b0TGk+t0Tmand 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.