General anisotropic cosmological solutions and physical viability in f(T, B) gravity

An anisotropic Bianchi type-I cosmological model is examined in the framework of modified teleparallel gravity described by a general function f ( T , B ) of the torsion scalar and the boundary term. We consider the general cosmological solutions of the field equations obtained without imposing symmetry conditions at the level of the action. These solutions are employed to analyze the associated Noether symmetries and the structure of the corresponding symmetry algebras. In particular, we identify distinct classes of solutions admitting higher-dimensional Noether vector fields, whose dimensionality reflects enhanced geometrical invariance and leads to qualitatively different anisotropic cosmological behaviors. For representative cases, we investigate the geometrical evolution of the scale factors, relevant cosmological parameters, and the behavior of the effective energy density and anisotropic pressures. Our analysis shows that physically acceptable cosmological evolution arises only for restricted classes of solutions, thereby providing viability constraints on anisotropic dynamics in f ( T , B ) gravity.