Constraints On The F(R)-gravity Theories From A Time-varying Gravitational Constant

The observational results of SNIa indicate that the Universe is in the state of accelerated expansion at present time. It has been later on more precisely confirmed by other observational probes such as the formation of the large scale structure and anisotropies in the cosmic microwave background radiation. There are mainly three types of explanations for the acceleration: Introducing an exotic dark energy in the frame of general relativity; The General Relativity may not be the universal theory of the gravity; The existence of the higher dimensions.Under the aborative guidance of Prof. Jun Luo, the feasibility researches which use the f(R) theory to explain the cosmic acceleration are carried out in this paper: (1). Based on the observational results of the relative variation of the Newtonian gravitational constant, new criterions on the feasibility of an acceptable f(R) theory both in the metric formulation and in the Palatini formalism are developed. Our criterions overcome the difficulties of the data from the cosmological observations which can only constrain some simple models. Relative to the usual constraint methods, the developed criterions provide an extremely simple method to investigate the feasibility of f(R) model. These criterions are used to various of f(R)-gravity models that have been suggested to explain the current acceleration of the cosmic expansion, and we find that most of them conflict with the criterions and therefore unacceptable. Theories satisfied with the constraint conditions either have not significant difference from the ACDM model, or their parameters are correlative to each other. (2). Based on the criterions, we suggest a new modified gravity to explain the current acceleration of the Universe without resorting to the exotic dark energy, and the defects appeared in other models are overcome. The numerical simulation shows that the resulting effective parameter of equation of state of our model displays a phantomlike behavior at present time which can explain the tiny deviation of the state parameter from -1, and it consistent with the present observations. We also investigate the local behavior of the model and find that this model can pass the tests carried out in the solar system.There also exists a flaw in our research. On the cosmological large scale and over 10 billion years from the early Universe to the present time, big bang nucleosynthesis and anisotropies in the cosmic microwave background radiation yield upper limits on thelong-term averaged variation . The assumption which the average isused as the present value requires a further experimental verification. However, investigators have not found the evidence of a time-varying gravitational constant, we believe the adopted assumption is reasonable.