We focus on a viable teleparallel cosmological model with a scalar field in a flat Friedman-Robertson-Walker universe. The Lagrangian and equations of motion are obtained. The case of an inhomogeneous viscous dark energy is considered and the cosmological parameters associated with the viscosity parameter are determined. It is shown that when considering constant viscosity and state parameter, the Universe expands exponentially

In this paper, we study the generalized Heisenberg ferromagnet equation, namely, the M-CVI equation. This equation is integrable. The integrable motion of the space curves induced by the M-CVI equation is presented. Using this result, the Lakshmanan (geometrical) equivalence between the M-CVI equation and the two-component Camassa-Holm equation is established.

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In this paper, we consider a cosmological model of the flat and homogeneous universe for the Starobinsky model F (R) = αR+βR 2 , which is non-minimally coupled with f -essence. For this model we obtained the field equations and considered particular solutions of the coupling and fermionic field functions. It is shown that the fermionic field can describe a nature of the universe.

In this paper, we investigate the dynamics of the universe on the background of f-essence when a non-minimal coupling with gravity. Field equations are obtained and using the Noether theorem, explicit forms of the coupling function and the Lagrange function of the f-essence were obtained. Accordingly, for this model, the cosmological parameters that describe the accelerated expansion of the universe are determined.