Classical Test Of Modified Gravitational Theories

This thesis is a study of solar system tests of pure R~2gravity and R~?gravity as two special examples of f(R)theories.In the preface of Chapter 1,we recall the history and original motivation of modified gravitational theories.With the development of observational cosmology,it becomes more and more important for considering modifications of the theory.For one of the simplest modifications to General Relativity(GR),f(R)theories have some merits,for instant,some models of f(R)theories could provide a scalar field?with a slowly varying potential to be a candidate for inflation.However,f(R)theories have problems such as,for all those with complicated gravitaltional actions,the models need to satisfy not only the cosmological but also local gravity constraints in local regions whose densities are much larger than the homogeneous cosmological density.For this reason,the only way to become the physical law for descrbing our universe is to pass the classical tests.We divide the following content into two parts.First part,in the Chapter 2,using the trajectory equation derived from the geodesic equation of standard form metric,we calculate the light bending and perihelion precession by one of spherically symmetric static solutions of pure R~2gravity which obtains in vacuum and vanishing scalar curvature conditions,and explain the results by the way of assuming that there is a”thin shell”on the surface of central celestial body.At the next part,Chapter 3,we deduce the formula of the perihelion precession of Mercury in post-Newtonion approximation with Clif ton-Barrow metric in isotropis form.Comparing with observations,the expression could provide the val-ue of?that approximate to the first and second order respectively.We summarize this article in Chapter 4.