Constraining f(T,B,TG,BG) gravity by dynamical system analysis

In this paper, we have studied the different phases of the evolution of the Universe through the dynamical system analysis. Here we explored the f(T,B,TG,BG) gravity, where T, B, TG, and BG respectively represent torsion, boundary term, teleparallel Gauss–Bonnet term, and Gauss–Bonnet boundary term. The transformation f(T,B,TG,BG)=−T+F(T,B,TG,BG) has been incorporated to get the deviation from the Teleparallel Equivalent of General Relativity. Two well motivated cosmological models (i) F(T,B,TG,BG)=f0TmBnTGk and (ii) F(T,B,TG,BG)=b0B+g0TGk have been studied. The critical points representing different phases of evolution have been studied in details. Further with the help of the eigenvalues and phase space diagrams, the stability and attractor nature of the accelerating solutions have been explored. The evolution plots have been analysed for the corresponding cosmology. The compatibility of the evolution plots has been checked with standard density parameters at present time.