Neutrinos and long-range weak forces in cosmology

The Lorentz and coordinate covariant calculus of spinors in Riemannian spacetime, which is the mathematical model for the description of the quantum mechanics of elementary particles with spin interacting with the classical gravitation field, is explored. The Dirac equation describing the interaction of neutrinos with the gravitational fields of the Robertson-Walker cosmological world models is separated, and the spectrum of eigenfunctions and eigenvalues for particular choices of the set of quantum numbers is given explicitly for the k = 0 and k = +1 models, although only the radial equations determining the final quantum number are given for the k = -1 model. The mathematical theory of the motion of a perfect fluid whose elements interact via long-range neutrino-exchange forces, as well as gravitationally, is developed. The formalism for calculating, by calculating the Bogoliubov transformation of the Fock space operators that instantaneously diagonalize their quantized field Hamiltonian, the rate of creation of neutrino-antineutrino pairs by the gravitational field of the Bianchi type IX cosmological model is presented