Mach’s principle and modified gravity

It was after the discussion about the nature of matter and space among scientists and philosophers,meanwhile Newton presented more accurate theories based on his equations. Newton believed that time and space are absolute, and he based his principles upon this belief.After him many scientists presented sometimes complementary or different theories.Mach was one of the famous scientists who had another ideas different from Newton, that later used and considered by Einstein as the completion of general relativity and named it Mach's principle. Although later Einstein rejected some subjects of this principle such as the reference frame. He succeeded to explain the relation between space and time according to the field equation which extracted from his theory and pull over the Newton’s absolute space In fact Mach's theories and thoughts had such a significant impact on change the point of view of scientists towards substance in universe. Today we dare to say that students are less aware of his attempts in evolution and revolutions that happened in physics early by Newton and then by Einstein.In recent years and probably less than half a century, scientists that proved general relativity theory due to the experiments (about the investigation of substance's nature and space and the influence of gravity on them) decided to create a unified theory between the four main forces in nature.Therefore, gravity was always the main reason that left all the efforts unfinished.This was the reason that scientists decided to modify the gravity which clearly affects the Einstein field equation,which maybe can create a new approach to unify the gravity force with other main forces in nature.In this thesis I tried to investigate one of these efforts for modified gravity and show its role in couple of matter and space in a format by using several theories and hypotheses (such as f(R) gravity,Pressuron etc.) raised in recent years. Although there is still a long way to reach the main answer