The Newest Research On Nontopological Solitons And Dark Matter

The dark matter problem is one of the most important problems in particle physics and astrophysics.Researchers try their best to understand what dark matter,which makes up about 26%of the universe's energy density,really is.This thesis mainly focuses on a kind of candidates of dark matter—Q-balls.We mainly study several types of Q-balls:Coleman Q-balls,Q-balls in thermal logarithmic potential,Q-balls in one-loop motivated effective potential and U(1)gauged Q-balls,and calculate their radius,conserved charge,energy,stability.Besides their internal properties,we also study the influence of Q-balls on spacetime.We choose a kind of simple Q-balls,namely Q-balls with Signum-Gordon potential,to study their astrophysical effect—strong gravitational lensing.Chapter 1 introduces some background knowledge and research progress.The first part is the introduction of dark matter,including,quantity of dark matter,organization of dark matter in galaxies and clusters of galaxies,properties of dark matter.The second part is about the research situation and typical applications of nontopological solitons,and a kind of representative nontopological soliton model.In the third part,we focus on a type of nontopological soliton—Q-balls:what Q-balls are,how they generate and evolve,what the relation between Q-balls and dark matter;gauged Q-balls are also introduced.We also describe an analytical method of studying Q-balls.The last part is about strong gravitational lensing.In chapter 2,we study Q-balls dominated by the thermal logarithmic potential analytically instead of estimating their characters numerically.Firstly,we derive the virial relation of this kind of Q-balls.Then,with the help of large and small Q-ball models,the analytical expressions for radius and energy of this kind of Q-ball are obtained.According to these explicit expressions we demonstrate strictly that the large Q-balls enlarge and the small ones become smaller in the background with lower temperature.The energy per unit charge could be calculated,and it will not be divergent if the charge is enormous.We find that the lower temperature will lead the energy per unit charge of Q-ball smaller.We also prove rigorously the necessary conditions that the model parameters should satisfy to keep the stability of the Q-balls.When one of model parameters of Q-balls,K,is positive,the Q-balls will not form or survive unless the temperature is high enough.In the case of negative K,the Q-balls are stable no matter the temperature is high or low.In chapter 3,the analytical description on the Friedberg-Lee-Sirlin type Q-balls is performed.The two-field Q-balls are also discussed under the one-loop motivated effective potential.According to the calculation of the energy per unit charge,it is proven that the Q-balls can exist stably and there exist the conditions to support them.If the energy density is low enough by choosing appropriate values of model parameters,the Q-balls can become candidates of dark matter.The two-field Q-balls can be generated in the first-order phase transition and survive while they are affected by the expansion of the universe.The phase transition happens while the temperature of the universe is less than some critical temperature,which could be calculated by the condition which guarantees the energy would not diverge.In chapter 4,we discuss the U(1)gauged Q-balls with N-power potential to examine their properties analytically.We demonstrate strictly some new limitations that the stable U(1)gauged Q-balls should accept instead of estimating those with only some specific values of model variables numerically.Having derived the explicit expressions of radius,the Noether charge and energy of the gauged Q-balls,we find that these models under the potential of matter field with general power and the boundary conditions will exist instead of dispersing and decaying.The Noether charge of the large gauged Q-balls must be limited.The mass parameter of the model can not be tiny.Chapter 5 mainly focuses on a kind of astrophysical effect of Q-balls with Signum-Gordon potential—strong gravitational lensing.First,we deduce the Einstein equation of the gravitational field produced by this type of Q-balls.Then we substitute the series solutions of the spacetime metric and the field quantity into the equation to determine the expansion coefficients.Finally we calculate the Q-balls' radius of photon sphere and deflection angle and so on.We obtain the conclusion:there exists a range of model parameter ?,in which as ?decreases,the radius of photon sphere and the deflection angle of the light ray would increase,then the strong gravitational lensing appears.This result is interesting,because the Q-balls with small value of ? is stable,and could be the candidate of dark matter.Therefore,the Q-balls with small value of? could become candidate of dark matter,meanwhile,they could produce the strong gravitational lensing.