Conformally-coupled dark spinor and FRW universe

We study conformal coupling of dark spinor fields to gravity and calculate the energy density and the pressure of the spinor in FRW spacetime. We consider the renormalizable potential of the spinor field. In the cases where the field is proportional to some power of the cosmic scale factor $a(t)$, we determine the Hubble parameter as a function of the scale factor and find analytic solutions for $a(t)$ when the spinor field matter dilutes as the universe expands. We discuss the possibility that both matter- and dark energy-dominated eras of our universe can be described by the dark spinor.Comment: 4 pages, Revised argument in section III, results unchanged. To be published in PR

Scalar Non-Luminous Matter in Galaxies

As a candidate for dark matter in galaxies, we study an SU(3) triplet of complex scalar fields which are non-minimally coupled to gravity. In the spherically symmetric static spacetime where the flat rotational velocity curves of stars in galaxies can be explained, we find simple solutions of scalar fields with SU(3) global symmetry broken to U(1) X U(1), in an exponential scalar potential, which will be useful in a quintessence model of the late-time acceleration of the Universe.Comment: 6 pages, no figure, LaTex. Submitted to IJMP

Isospin particle on S2S^{2} with arbitrary number of supersymmetries

We study the supersymmetric quantum mechanics of an isospin particle in the background of spherically symmetric Yang-Mills gauge field. We show that on $S^{2}$ the number of supersymmetries can be made arbitrarily large for a specific choice of the spherically symmetric SU(2) gauge field. However, the symmetry algebra containing the supercharges becomes nonlinear if the number of fermions is greater than two. We present the exact energy spectra and eigenfunctions, which can be written as the product of monopole harmonics and a certain isospin state. We also find that the supersymmetry is spontaneously broken if the number of supersymmetries is even.Comment: 6 page