Noether Symmetries in $f(T,T_G)$ Cosmology

S. A. Kadam; B. Mishra; Jackson Levi Said

doi:10.1088/1402-4896/acc0ac

paper

Noether Symmetries in $f (T, T_{G})$ Cosmology

arXiv:2210.06166 · doi:10.1088/1402-4896/acc0ac

Abstract

All degrees of freedom related to the torsion scalar can be explored by analysing, the $f (T, T_{G})$ gravity formalism where, $T$ is a torsion scalar and $T_{G}$ 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 $f (T, T_{G})$ gravity formalism with three different forms of $f (T, T_{G})$ and study how to establish nontrivial Noether vector form for each one of them. We extend the analysis made in \cite{capozziello2016noether} for the form $f (T, T_{G}) = b_{0} T_{G}^{k} + t_{0} T^{m}$ 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.

arXiv comment12 pages

Noether Symmetries in $f (T, T_{G})$ Cosmology

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Noether Symmetries in f(T,TG​) Cosmology

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Noether Symmetries in $f (T, T_{G})$ Cosmology