Pilgrim Dark Energy in $f(T, T_G)$ cosmology

We work on the reconstruction scenario of pilgrim dark energy" (PDE) in $f(T, T_G)$. In PDE model it is assumed that a repulsive force that is accelerating the Universe is phantom type with $(w_{DE}<-1)$ and it so strong that prevents formation of the black hole. We construct the $f(T, T_G)$ models and correspondingly evaluate equation of state parameter for various choices of scale factor. Also, we assume polynomial form of $f(T, T_G)$ in terms of cosmic time and reconstruct $H$ and $w_{DE}$ in this manner. Through discussion, it is concluded that PDE shows aggressive phantom-like behaviour for$s=-2$ in $f(T, T_G)$ gravity.