We establish a new covariant phenomenological model, which describes an influence of pseudoscalar (axion) field on spins of test massive particles. The model includes general relativistic equations of particle motion and spin evolution in background pseudoscalar (axion), electromagnetic and gravitational fields. It describes both the direct spin-axion coupling of the gradient type and indirect spin-axion interaction mediated by electromagnetic fields. Special attention is paid to the direct spin-axion coupling caused by the gradient of the pseudoscalar (axion) field. We show that it describes a spin precession, when the pseudoscalar (axion) field is inhomogeneous and/or nonstationary. Applications of the model, which correspond to the three types of four-vectors attributed to the gradient of the pseudoscalar (axion) field (timelike, spacelike, and null), are considered in detail. These are the spin precessions induced by relic cosmological axions, axions distributed around spherically symmetric static objects, and axions in a gravitational wave field, respectively. We discuss features of the obtained exact solutions and some general properties of the axionically induced spin rotation.

We present some exact solutions of the Einstein equations with an anisotropic fluid exploiting the Chaplygin equation of state. The solutions describe space-times with two identical T-regions and an intermediate static spherically symmetric R-region containing a wormhole. The metric in the T-region represents an anisotropic Kantowski-Sachs cosmological model. Its evolution starts from a horizon and develops according to different scenarios including eternal expansion, contraction and also a finite lifetime.

In the framework of the Einstein-aether theory we consider a cosmological model, which describes the evolution of the unit dynamic vector field with activated rotational degree of freedom. We discuss exact solutions of the Einstein-aether theory, for which the space-time is of the Gödel-type, the velocity four-vector of the aether motion is characterized by a non-vanishing vorticity, thus the rotational vectorial modes can be associated with the source of the universe rotation. The main goal of our paper is to study the motion of test relativistic particles with a vectorial internal degree of freedom (spin or polarization), which is coupled to the unit dynamic vector field. The particles are considered as the test ones in the given space-time background of the Gödel-type; the spin (polarization) coupling to the unit dynamic vector field is modeled using exact solutions of three types. The first exact solution describes the aether with arbitrary Jacobson's coupling constants; the second one relates to the case, when the Jacobson's constant responsible for the vorticity is vanishing; the third exact solution is obtained using three constraints for the coupling constants. The analysis of the exact expressions, which are obtained for the particle momentum and for the spin (polarization) four-vector components, shows that the interaction of the spin (polarization) with the unit vector field induces a rotation, which is additional to the geodesic precession of the spin (polarization) associated with the universe rotation as a whole.