Classical and quantum cosmological solutions in teleparallel dark energy with anisotropic background geometry

We investigate exact and analytic solutions for the field equations in teleparallel dark energy model where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like Lagrangian exist for the description of the field equations and variational symmetries are applied for the construction of invariant functions and conservation laws. The later are used for the derivation of new analytic solutions for the classical field equations and exact function forms for the wavefunction in the quantum limit.