One of the main motivations behind formulating the general theory of relativity was to provide a mathematical description to the Mach’s principle. However, soon after its formulation, it was realized that the theory does not follow Mach’s principle. As the theoretical predictions were matching with the observations, Einstein believed that the theory was correct and did not make any farther attempt to reformulate the theory to explain Mach’s principle. Later on, several attempts were made by different researchers to formulate the theory of gravity based on Mach’s principle. However most of these theories remain unsuccessful to explain different physical phenomena.
In this report I have proposed a new theory of gravity which is completely based on the Mach’s principle. The theory can explain the galactic velocity profiles up to a high degree of accuracy, without demanding the existence of any dark matter component in the universe. The theory can also explain the accelerated expansion of the universe without Dark Energy. It is a metric theory and can be derived from the action principle, which guarantees energy or momentum conservation. Modern theories like TeVeS or Modified gravity give some mathematical modification of the Einstein’s equation to explain different observational phenomenon like the galactic velocity profile, accelerated expansion of the universe or CMBR power spectrum. Most of these theories don’t have any underlying logic. However, the new theory explained in this paper, is a mathematical formulation of the Mach’s principle. Therefore, the theory is not just a mathematical jugglery to explain some observed facts, but arises from a deep physical argument.