In this paper, we consider three types of k-essence. These k-essence models were presented in the parametric forms. The exact analytical solutions of the corresponding equations of motion are found. It is shown that these k-essence models for the presented solutions can give rise to cosmic acceleration.

The presence of spinor fields is considered in the framework of some extensions of teleparallel gravity, where the Weitzenböck connection is assumed. Some well-known models as the Chaplygin gas and its generalizations are reconstructed in terms of a spinor field in the framework of teleparallel gravity. In addition, the ΛCDM model is also realized with the presence of a spinor field where a simple self-interacting term is considered and the corresponding action is reconstructed. Other cosmological solutions and the reconstruction of the gravitational action in terms of the scalar torsion are studied.

We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass ℘(t), σ(t) and ζ(t) functions with two periods being infinite. If the universe can evolve periodically, a non-singular universe can be realized. Furthermore, we examine the cosmological evolution and nature of the equation of state (EoS) of dark energy in the Friedmann-Lemaître-Robertson-Walker cosmology. It is explicitly illustrated that there exist three type models in which the universe always stays in the non-phantom (quintessence) phase, whereas it always evolves in the phantom phase, or the crossing of the phantom divide can be realized. The scalar fields and the corresponding potentials are also analyzed for different types of models.

We study the g-essence model with Yukawa interactions between a scalar field φ and a Dirac field ψ. For the homogeneous, isotropic and flat Friedmann-Robertson-Walker universe filled with the such g-essence, the exact solution of the model is found. Moreover, we reconstruct the corresponding scalar and fermionic potentials which describe the coupled dynamics of the scalar and fermionic fields. It is shown that some particular g-essence models with Yukawa interactions correspond to the usual and generalized Chaplygin gas unified models of dark energy and dark matter. Also we present some scalar-fermionic Dirac-Born-Infeld models corresponding g-essence models with Yukawa interactions which again describe the unified dark energy-dark matter system.

In this paper, we study the model of the late universe with the homogeneous, isotropic and flat Friedmann–Robertson–Walker metric, where the source of the gravitational field is based on the fermion and boson fields, with the Maxwell term [Formula: see text] in four dimensions. The actuation of the Maxwell term for the Einstein gravity makes it possible to find new approaches to solve the problem of the observed accelerated expansion of the universe. Energy conditions have been obtained and studied. These conditions impose very simple and model-independent restrictions on the behavior of energy density and pressure since they do not require a specific equation-of-state of matter. To consider the model, the energy conditions NEC, WEC, DEC are realized, and the SEC condition is violated. The boson and fermion fields are responsible for the accelerated regime at early times, but since the total pressure tends toward zero for large times, a transition to a decelerated regime occurs. Maxwell field is crucial only in the early times.