Power solution of the f(R)-gravity with Maxwell term and g-essence

Abstract

In this paper the ݂f(R) model of gravity with a Maxwell term F_μνF^μν and g-essence in four dimensions together with a homogeneous, isotropic and flat Friedman-Robertson-Walker universe is considered. The introduction of the Maxwell term for f(R) gravity allows finding new approaches to solving the problem of the observed accelerated expansion of the Universe. G-essence includes, as a partial case, two important models: k݇-essence and  ݂f-essence. For this model, a system of equations of motion is found. Power solution for the scale factor, scalar and fermion fields was built. An expression for the 4-vector potential is obtained. Scalar and fermion potentials are restored. Energy conditions were investigated and obtained. These conditions impose very simple and independent of the model boundary on the behavior of the energy density and pressure, since they do not require a definite equation of state of matter. For the considered model a zero, weak and dominant energy condition is satisfied and a strong energy condition is not satisfied. The energy density, pressure, parameter of the equation of state ω, the deceleration parameter q and jerk parameter j were found, the value of which corresponds to the accelerated expansion of the universe at λ > 1.