Dynamical system and statefinder analysis of cosmological models in f(T, B) gravity

Abstract

This study systematically investigates the cosmological dynamics of two well-motivated functional forms in $f(T,B)$ gravity within a flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe. Here $T$ denotes the torsion scalar and $B$ the boundary term, with the special choice $f(T,B) = - T + B$ recovering General Relativity. We focus on a multiplicative power-law model $f(T,B) = c_1 T^\alpha B^\beta$ and an additive mixed power-law model $f(T,B) = c_2 T^\alpha + c_3 B^\beta$. Using dynamical system techniques, we construct autonomous systems and identify de Sitter attractors that naturally explain late-time cosmic acceleration. Analytical stability conditions for these fixed points are derived, and numerical simulations reveal characteristic evolutionary patterns, such as spiral trajectories and damped oscillations in the additive mixed power-law model. Furthermore, statefinder diagnostics are applied to quantitatively distinguish these models from the standard $\Lambda$CDM paradigm and other dark energy scenarios. The results indicate that $f(T,B)$ gravity offers a theoretically consistent and observationally distinguishable geometric framework for explaining cosmic acceleration, presenting a compelling alternative to conventional dark energy models.