The influence of the kinetic scalar of torsion on the cosmological solutions of F(T) gravity

This work considers power-law inflation within the modified teleparallel gravity with higher-derivative torsion terms of the kind F(T,(∇T)2). The Hubble parameter is expressed as H=m/t, where m>1. The equations of cosmological dynamics are analyzed for private values of ω(T) with the following choice of the function F: F=T+ω(T)∇μT∇μT. It is shown that the energy and pressure of the dark sector, arising due to higher derivatives, weaken over large times. At the early stage of the Universe's evolution, they support power-law inflation, and the dependence of the potential V(ϕ) on the scalar field ϕ is justified from a physical point of view.