Cosmological Dynamics and Stability Analysis in f(T, B) Gravity with Interacting Scalar Field

We explore the dynamical behavior of two f(T, B) gravity models with a scalar field: 1. \(f(T,B)=T-\gamma log\bigg [\frac{\psi B_{0}}{B}\bigg ]\) and 2. \(f(T,B)=\eta T+\frac{\zeta }{B^{n}}\), using the potential \(V(\phi )=V_{0}(\alpha +e^{-\beta \phi })^{-\delta }\) and an interaction term \(\bar{Q} = \epsilon H \dot{\phi }^2\). A phase space analysis reveals four fixed points in Model 3.1 (three stable, one saddle) and five in Model 3.2 (four stable), indicating transitions from matter to dark energy dominance. With interaction, Model 3.2 exhibits seven fixed points, including five stable, one unstable (stiff matter era) and one saddle point. Evolution of the deceleration parameter q and the total EoS parameter \(\omega _{tot}\) confirms sustained cosmic acceleration, with present values \(q_{0} = -1.005\) and \(\omega _{0} = -0.556\) (Model 3.1) and \(q_{0} = -1.245\) and \(\omega _{0}=-1.0404\) (Model 3.2). Comparisons of our observationally constrained parameters with \(\Lambda \)CDM show strong consistency, supporting the viability of these models in describing the late-time accelerated expansion of the Universe.