#### Date of Award

8-1-1993

#### Document Type

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Physics & Astrophysics

#### Abstract

Boson stars consist of a system of self gravitating scalar fields (bosons) which form a macroscopic quantum state and is one of several dark matter candidates. When considering cosmological models based on the Brans-Dicke gravitational theories, one question that must be addressed is whether certain types of dark matter candidates, possibly boson stars, can exist in the Brans-Dicke gravitational theories. We show in this paper that at least one type of dark matter - boson stars— can exist in these gravitational theories.

For purposes of comparison, we introduce a boson star model in general relativity with a quartic coupling interaction in the boson field and give some of the solutions to the equations of motion.

To derive the equations of motion of the Brans-Dicke model which also contains a quartic coupling interaction in the boson scalar field, we introduce an action similar to that of general relativity with the exception of the introduction of the Brans-Dicke scalar field. Once we have the equations of motion, we then solve them using a Runge- Kutta method. We consider only nonsingular, finite-mass, zero-node solutions to the equations of motion for u = 6.

When we obtain the solutions from the Brans-Dicke model for different values of the coupling interaction strength A, we notice a slight decrease in the maximum mass of the star which is due to the Brans-Dicke scalar field interaction with the matter density of the universe. We also consider the equations of motion in the limit of large values of A, and when the solutions of these equations are compared with their general relativistic counterparts, we again notice a slight decrease in the maximum mass. We also note that the maximum mass of the solution to these equations, which have a A^ dependency, tend to agree fairly well with values for large A, which is expected from the type of modification used. We also note that the maximum mass decreases as u decreases.

By finding solutions to this model, we have shown that boson stars can exist as a form of dark matter in the Brans-Dicke gravitational theories with a slight decrease in the maximum allowed mass of the star.

#### Recommended Citation

Gunderson, Mark, "Boson Stars in the Brans-Dicke Gravitational Theories" (1993). *Theses and Dissertations*. 3243.

https://commons.und.edu/theses/3243