Inflation in modified quantum gravity with a fermion field

Viable inflation of modified nonuniform isotropic F(R) gravity with a fermionic field of f-essence is investigated using the quantum approach. The action of which is S=\int [], where R is the curvature scalar, and Lm is the matter Lagrangian. In this case, we consider a non-minimally coupled fermionic field f-essence, the Lagrangian of which is denoted by K(Y,u) by a function depending on Y-kinetic and u potential arguments. The equations of motion of this model are obtained for the homogeneous and isotropic Friedman-Robertson-Walker space-time. As F(R) we consider the generalized Horava-Lifshitz quantum gravity function. In 2009, Horava proposed a new approach to studying membranes in the theory of quantum gravity, known as the Horava-Lifshitz gravity.The peculiarity of Horava-Lifshitz gravity is that it is renormalizable. Further, the particular case of K(Y,u)=lnY+u is investigated in detail. The parameters of describing the current accelerated expansion of the Universe are obtained and the explicit form of the connection of matter with space-time h(u) is determined. The inflationary period of the evolution of this model is also investigated. To describe the inflationary period, the form of the Hubble parameter and the slow roll-off parameter, as well as other inflationary parameters, were determined. The presented results are compared with the observation results. The analysis of the results coincides with the observation data at certain values of the integral constants in the solutions.