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Abstract
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We quantize a homogeneous and isotropic universe
for two models of modified teleparallel gravity: one
wherein an arbitrary function of the boundary term, namely
B, is present in the action, and in the other model, a scalar field
that is non-minimally coupled to both the torsion and boundary
term. In this regard, we study exact solutions of both
the classical and quantum frameworks by utilizing the corresponding
Wheeler–DeWitt (WDW) equations of the models.
To correspond to the comprehensive classical and quantum
levels, in the second model, we propose an appropriate initial
condition for the wave packets and observe that they
closely adhere to the classical trajectories and reach their
peak.We quantify this correspondence using the de Broglie–
Bohm interpretation of quantum mechanics. According to
this proposal, the classical and Bohmian trajectories coincide
when the quantum potential vanishes along theBohmian
paths. Furthermore, we apply the de-parameterization technique
to our model in the realm of the problem of time in
quantum cosmological models based on theWDWequation,
utilizing the global internal time denoted as χ, which represents
a scalar field.
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