Study On The Brans-dicke Theory And Analytic Potential Of BD Scalar Field

In recent years, the observations of the Supernovae of type1a, the probing of the cosmicmicrowave background anisotropy and the constraints from the large scale structure (LSS)provide the evidence that the universe is undergoing accelerated expansion. The problem whythe universe is accelerated expansion becomes one of the hot topic of current cosmologicalresearch. For interpreting the accelerated expansion of the universe, one of the explanation isthat the universe contains a special matter, called dark energy, which has a negative pressure.In addition, there are the modified gravity theories to explain the accelerating expansion of theuniverse.The accelerating universe provides a challenge to Standard Cosmology based onEinstein’s general relativity (GR). This require us to search for some replaced or modifiedtheory of GR. Brans-Dicke (BD) theory is one of the alternative theory of general relativity.BD theory as the theory of scalar tensor, it can be divided into two frame, i.e. the Jordanframe and the Einstein frame. In Einstein frame, BD scalar field is not coupled to geometricquantities-Ricci scalar R, but it interacts with the material system. This irregular coupling hasnot corresponding part in Einstein’s gravity, which indicates that the energy momentumtensor of matter and scalar field are not conserved. In Jordan frame, BD scalar field is coupledwith R. In BD theory these two frames can be connected by a conformal transformation. Inthese two frames, we derive the analytical potential of BD scalar field, and compare thedifferences between these BD potential.