Hypothesis of photonic portal in the problem of dark matter and classical nature of gravitation

Within our model of “photonic portal” to the hypothetical hidden sector of the Universe, an option is considered, where the massive sterile bosons, mediating in this sector and described by the antisymmetric-tensor field A_{\mu\nu} (of dimension one), are gauged by a vector field \chi_\mu (of dimension zero). When the Einsteinian gravity is switched on into this model, then it is argued that the metric g_{\mu\nu}(x) of spacetime is proportional to <\chi_\mu(x) \chi_\nu(x)>{vac}, being in this way classical in its nature, not the subject of quantization within an overall quantum theory including gravitation. A Lagrangian density(generally dependent on \chi\mu and its first and second derivatives) is tentatively proposed in such a form, where \chi_\mu appears also outside of A_{\mu\nu}, spoiling the trivial gauge invariance of our earlier model with respect to the gauging field \chi_\mu. If the cosmological constant \lambda is neglected, then the term with \chi_\mu outside of A_{\mu\nu} vanishes.