Minisuperspace Quantization of $f\left(T,B\right) $ Cosmology

Abstract

We discuss the quantization in the minisuperspace for the generalized fourth-order teleparallel cosmological theory known as $f\left( T,B\right) $. Specifically we focus on the case where the theory is linear on the torsion scalar, in that consideration we are able to write the cosmological field equations with the use of a scalar field different from the scalar tensor theories, but with the same dynamical constraints as that of scalar tensor theories. We use the minisuperspace description to write for the first time the Wheeler-DeWitt equation. With the use of the theory of similarity transformations we are able to find exact solutions for the Wheeler-DeWitt equations as also to investigate the classical and semiclassical limit in the de Broglie -Bohm representation of quantum mechanics.