The Boson In The Gravitational Force Of F (R)

Boson stars are constructed with a complex scalar field coupled to gravity. Such scalar particle could cancel out the force of gravity underlaying the Heisen-berg Uncertainty Principle, so that boson stars can be established theoretically. With the discovery of Higgs boson, people are convinced the existence of scalar particle in nature. Therefore, studying boson stars which are constructed with a complex scalar field not only has theoretical significance, but also has the signifi-cance of observation. As we all know, dark matter must exist in the universe, and most of the scalar particle can be considered as dark matter candidates, mean-while, many studies have shown that the mass of boson stars cover much wide scope. Consequently, it is practically important to discuss the the formation and evolution of boson stars and the possibility of boson star being an candidate of dark matter.We study the formation and features of boson stars under f (R) gravity and investigate the existence of boson stars, f (R) gravity is one of the most popular modified theories of gravity to Einstein’s general relativity, which have been used to interpret cosmological inflation, dark energy and other issues in cosmology. Using f(R) gravity, we could provide a more accurate cosmological background to study boson stars. First, we select the most simple f (R) gravity theories, Starobinsky gravity model, which is in good agreement with the observed data of the current inflationary universe. Then, applying the principle of least action, we obtain the Einstein-Klein-Gordon equations which describe the configuration of boson stars, and then, examine the boundary conditions of boson stars. Next, we consider the junction condition with internal stellar and outside space-time. In addition, we discuss the existence of boson star solutions. Applying the series solution, we obtain the mass of boson star, the effective radius and other relevant quantities. We find that series solution requires field equations to start at least four bands, so that boson stars are stable. Finally, we discuss the mass of boson stars using weak gravitational approximation. The results show that the mass of Starobinsky boson star is greater than the one in the models in the context of Einstein gravity and Brans-Dicke gravity.The existence of relativistic stars in f(R) gravity is still a controversial is- sue. In our study, we assume the existence of relativistic stars. Moreover, we only give the series solution of boson star, and discuss its mass under the weak gravitational approximation. Therefore, a better solution of boson star should be calculated their exact solution or numerical solution, which will be an important and difficult issue.