  One of the interesting open problems in the cosmological framework is
applying quantum physics to the whole universe, consistently. Although
different conceptual aspects of quantum cosmology are still very much alive,
till now, all the attempts of obtaining a unique and well-defined version of
quantum cosmology have been unfeasible. Motivated by what was mentioned above,
in this paper, the quantum tunneling of thick brane is investigated by deriving
the Wheeler-DeWitt equation and corresponding solutions. Besides, the
cosmological analysis of the brane is studied based on two special cases of the
scalar field. Finally, it is found that the constant scalar potential arising
from a time-dependent scalar field is supported by the so-called slow-roll
inflation.

General Relativity and Quantum Cosmology;High Energy Physics - Theory