Bianchi I quantum cosmology in the Bergmann-Wagoner theory (Q5947427)

The paper is dedicated to Bianchi-type-I quantum cosmology in the Bergmann-Wagoner scalar-tensor theory of gravity. The latter theory is of growing interest for current cosmology since (i) it embraces scalar-tensor theories like the Brans-Dicke theory as special cases, (ii) higher-order and higher-dimensional theories of gravity may be expressed in a scalar-tensor form, and (iii) in a wide class of scalar-tensor cosmologies, there exist inflationary cosmological models. The author starts with the Bergmann-Wagoner action for a homogeneous anisotropic space-time of the Bianchi-type I (where, to the reviewer's mind, it is mathematically a bit risky to regard special symmetries like the Bianchi symmetry already in the action integral), transits to the canonical formalism and arrives at the corresponding Wheeler-DeWitt equation. Exact solutions of these equations are found for two self-interacting potentials and arbitrary coupling constants. The WKB wave functions are obtained for both cases.