Bianchi type-I cosmology with scalar and spinor fields

Abstract

We consider a self-consistent system of interacting spinor and scalar fields within the framework of a Bianchi type-I (BI) cosmological model filled with perfect fluid. The interacting term in the Lagrangian is chosen in the form of derivative coupling, i.e., ${\mathcal{L}}_{\mathrm{int}}=(\ensuremath{\lambda}/2){\ensuremath{\varphi}}_{,\ensuremath{\alpha}}{\ensuremath{\varphi}}^{,\ensuremath{\alpha}}F.$ Here F is a power or trigonometric function of the invariants I and/or J constructed from bilinear spinor forms $S=\overline{\ensuremath{\psi}}\ensuremath{\psi}$ and $P=i\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}^{5}\ensuremath{\psi}.$ Self-consistent solutions to the spinor, scalar, and BI gravitational field equations are obtained. The problems of an initial singularity and the asymptotically isotropization process of the initially anisotropic space-time are studied. The role of the cosmological constant $(\ensuremath{\Lambda}$ term) in the evolution of a BI Universe is studied. It is shown that a positive $\ensuremath{\Lambda}$ generates an oscillatory mode of expansion of the BI model, whereas if F in ${\mathcal{L}}_{\mathrm{int}}$ is chosen to be a trigonometric function of its arguments, there exists a nonexponential mode of evolution even with a negative $\ensuremath{\Lambda}.$ It is shown also that for a suitable choice of problem parameters the present model allows regular solutions without a broken dominant energy condition.