Mach Principle and a new theory of gravitation

Einstein was highly fascinated by Ernest Mach's work and by formulating the general theory of relativity (GR) he tried to provide a mathematical description to the Mach's principle. However, soon after its formulation, it was realized that GR does not follow Mach's principle. As it accurately explained many observational results, Einstein 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 a theory of gravity based on Mach's principle. However, all these theories have their own merits and drawbacks. In this paper a new theory of gravity is proposed that is completely based on the Mach's principle. It is a metric theory and can be derived from action principle, which guarantees to follow all the conservation laws. We present few examples to show that the theory can explain the galactic rotation curves very accurately. It also explains the discrepancy between dynamic mass and the photo-metric mass of the galaxy clusters without any exotic dark matter. The bullet cluster weak lensing phenomenon that is considered to be a strong evidence for dark matter can also be explained using this new gravitational theory. Hence, the theory provides a viable alternative to standard gravity theory.