Abstract
There are two modification methods that describe the accelerated expansion of the Universe: it is necessary either to modify the geometry or matter. Until now, many modified models have been proposed, one of which is common f(R) gravity. In f(R) gravity, in the well-known Einstein-Hilbert action, we replace the curvature tensor with its generalized function f(R), and the geometry changes. The unification of general relativity and quantum physics has become one of the most important issues of our time. In 1942, Lifshitz proposed a model based on high-energy anisotropic scaling that combines gravity and quantum physics, and in 2009 the Japanese scientist Peter Khorava proposed its unitary, renormalized version of gravity. In the studies of recent years, the name has spread - the gravity of Horava-Lifshits. In 2010, Masud Chaichyan, Shinichi Nojiri, Sergei D. Odintsov, Markku Oksanen, and Anka Tureanu jointly proposed a generalized form of this theory - f(R) gravity. In this work, the generalized gravity of Horava-Lifshitz will be studied for an inhomogeneous viscous fluid in space-time, based on this kind of gravity. At constant viscosity, with increasing time, the density and pressure of light and baryonic matter decrease. If we consider the state of dark energy, that is, the case when , then the density and pressure tend to infinity. Therefore, if we consider the viscosity constant, for the case in a vacuum, the universe will expand infinitely.