Research Related To The Screened Modified Gravity

General relativity(GR)has been tested by various experiments since it is pro-posed.Although GR passed all experimental tests,some people are not satisfied with the dark energy and dark matter introduced in the Standard Cosmology.Moreover,in GR,there must be singularities inside the black hole,and the theory will break down there.For these reasons,various modified gravitational theories have been proposed.Brans and Dicke proposed the so-called Brans-Dicke theory based on the Mach princi-ple.This theory adds a scalar gravitational field and a free parameter.Later Bergmann generalized this theory and got the general scalar-tensor theory.There are two arbitrary functions in the general scalar-tensor theory.In order to pass the constraints of the solar system observation and cosmological observation at the same time,people have intro-duced a screening mechanism in the scalar-tensor theory,which suppresses the scalar force generated by the scalar field in a high-density environment.This is the research object of this thesis-screened modified gravity(SMG).The first chapter introduces the development history of scalar-tensor theory and various observation methods for testing gravitational theory.The second chapter calculates the waveform emitted by an inspiral binary system in GR and discusses the principle of gravitational wave detection.The third and fourth chapters are our research results.The third chapter derives the wave-form of an inspiral binary system in SMG.We found that the gravitational wave in SMG contains four polarizations-two tensor polarizations(h+and h×)and two scalar polar-izations(breathing mode hb,and longitudinal mode hL).Since both scalar polarizations are generated by the scalar field,there is a linear relationship between them.Using the stationary phase approximation,we also calculated the waveform in the frequency domain.Comparing the waveforms in SMG with the waveforms in the frequency do0 main of GR,we obtain the parametrized post-Einsteinian(PPE)parameters of SMG.The PPE parameters of a metric theory characterize the correction of the phase and am-plitude of the gravitational wave waveform radiated by the binary system relative to the waveform in the GR.Then,we predicted the constraint imposed by Einstein Telescope on SMG through observing the gravitational wave emitted by neutron star-black hole binary systems.In this chapter,we also calculate the metrics of the Sun in SMG,and obtain the post-Newtonian parameters of SMG.Since f(R)gravity can be rewritten as a scalar-tensor theory,we applied the previous results to f(R)gravitation in Chapter 4.And got various constraints on f(R)gravity.