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UNIVERSITY of CALIFORNIA Los Angeles Exotic UNIVERSITY OF CALIFORNIA Los Angeles Exotic Dark Matter Candidates Generated from Scalar Field Condensation in the Early Universe A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Eric Welch Cotner 2018 c Copyright by Eric Welch Cotner 2018 ABSTRACT OF THE DISSERTATION Exotic Dark Matter Candidates Generated from Scalar Field Condensation in the Early Universe by Eric Welch Cotner Doctor of Philosophy in Physics University of California, Los Angeles, 2018 Professor Alexander Kusenko, Chair Scalar fields, though simple conceptually and mathematically, can be responsible for a wide array of emergent phenomena, such as spontaneous symmetry breaking, superconductivity, and the production of solitons. These fields may be responsible for the creation of, or even the identity of, dark matter. This manuscript details the production of dark matter from scalar fields in the form of Q-balls, boson stars, and primordial black holes, and explores the consequences of the existence of such objects and their interactions. ii The dissertation of Eric Welch Cotner is approved. E T Tomboulis Roberto Peccei Graciela B Gelmini Alexander Kusenko, Committee Chair University of California, Los Angeles 2018 iii To my mother, who I hope would have been very proud. To my father, who somehow managed to bring me up right. To my cats, for their unwavering support and insightful discussions. iv TABLE OF CONTENTS 1 Background :::::::::::::::::::::::::::::::::::::: 1 1.1 History . .1 1.2 Exotic Dark Matter Candidates . .3 1.2.1 Q-balls . .3 1.2.2 Boson Stars . .5 1.2.3 Primordial Black Holes . .6 2 Boson Star Collisions :::::::::::::::::::::::::::::::: 7 2.1 Introduction . .7 2.2 Existence and stability of boson stars in the non-relativistic limit . .9 2.3 Binary interactions . 15 2.4 Numerical Simulation . 23 2.4.1 N1 = N2, ξ 1, α = 0, v0 = 0 ...................... 26 2.4.2 N1 = N2, ξ 1, α = 0, v0 = 0 ...................... 27 6 2.4.3 N1 = N2, ξ 1, α = π, v0 = 0 ...................... 27 2.4.4 N1 = N2, ξ 1, α = π, v0 = 0 ...................... 28 2.4.5 N1 N2, ξ 1, α = π, v0 = 0 ..................... 29 2.4.6 N1 N2, ξ 1, α = 0, v0 = 0 ..................... 29 2.4.7 Behavior of unstable soliton with ξ < 1 ................ 30 − 2.5 Discussion . 31 2.5.1 Results of this paper . 31 2.5.2 Implications for dark matter . 34 2.6 Conclusion . 35 v 2.7 Acknowledgment . 35 3 Infection of Neutron Stars by Baryonic Q-balls :::::::::::::::: 36 3.1 Introduction . 36 3.2 Stable Q-ball states . 38 3.2.1 Flat direction Q-balls . 39 3.2.2 Curved direction Q-balls . 40 3.3 The decay rate . 41 3.3.1 Mathematical background . 42 3.3.2 Mass eigenstates and phonons . 44 3.3.3 Calculation of the matrix element . 45 3.3.4 Calculation of the decay rate . 49 3.4 Interactions between Q-balls and neutron stars . 52 3.4.1 Surface conversion of neutron flux . 53 3.4.2 Hydrodynamic considerations due to pion production . 53 3.5 Baryon number evolution in an infected neutron star . 54 3.6 Limits on baryon-violating (and conserving) operators . 56 3.6.1 From decay of Q-balls in free space . 57 3.6.2 From lifetime of neutron stars . 58 3.7 Conclusion . 59 3.8 Acknowledgements . 61 3.9 Appendix: Tables of Q-ball and neutron star lifetimes . 61 4 Primordial Black Holes from Q-ball Clustering :::::::::::::::: 63 4.1 Introduction . 63 4.2 Formation of Q-balls . 65 vi 4.3 Q-ball charge/mass distributions . 66 4.3.1 Single length scale . 68 4.3.2 Multiple length scales . 69 4.4 Q-ball and PBH densities . 71 4.4.1 Q-ball density at fragmentation . 71 4.4.2 Q-ball density perturbations due to fluctuations . 71 4.4.3 Primordial black hole density . 73 4.4.4 Black hole mass spectrum . 75 4.5 Cosmological history . 77 4.5.1 Initial radiation dominated era . 78 4.5.2 Q-ball dominated era . 78 4.5.3 Standard cosmological era . 79 4.6 Observational constraints . 80 4.7 Parameter space . 82 4.8 Topological defects . 84 4.9 Discussion . 85 4.10 Conclusion . 88 4.11 Acknowledgements . 89 4.12 Appendix: Evolution of energy densities . 89 4.12.1 Radiation . 89 4.12.2 Q-balls . 90 4.12.3 Black holes . 90 5 Primordial Black Holes from Inflaton Fragmentation into Oscillons ::: 92 5.1 Introduction . 92 vii 5.2 Oscillons . 93 5.3 Parametric Resonance . 94 5.4 Density Perturbations . 96 5.5 Formation of black holes . 98 5.6 Evolution to present day . 99 5.7 Reheating . 100 5.8 Acknowledgments . 101 References ::::::::::::::::::::::::::::::::::::::::: 102 viii LIST OF FIGURES 1.1 Schematic diagram of the theory space of dark matter. .2 2.1 Boson star total kinetic energy as a function of scaled separation distance x = d=`. 17 2.2 Boson star self-interaction energy as a function of scaled separation distance x = d=`........................................... 18 2.3 Boson star gravitational energy as a function of scaled separation distance x = d=`. 21 2.4 Effective potential (total energy) as a function of scaled separation distance x = d=`. 22 60 −2 2.5 Snapshots of two colliding boson stars with N1 = N2 = 10 , ξ1 = ξ2 = 10 , α = 0 and v0 = 0 ................................... 26 60 −2 2.6 Snapshots of two colliding boson stars with N1 = N2 = 10 , ξ1 = ξ2 = 10 , −15 α = 0 and v0 = 7 10 ............................... 27 × 60 −2 2.7 Snapshots of two colliding boson stars with N1 = N2 = 10 , ξ1 = ξ2 = 10 , α = π, and v0 = 0 ................................... 28 60 1 2.8 Snapshots of two colliding boson stars with N1 = N2 = 10 , ξ1 = ξ2 = 10 , α = π, v0 = 0 ..................................... 28 60 2 −2 2.9 Snapshots of two colliding boson stars with N1 = 10N2 = 10 , ξ1 = 10 ξ2 = 10 , α = π, v0 = 0 ..................................... 29 60 2 1 2.10 Snapshots of two colliding boson stars with N1 = 4N2 = 10 , ξ1 = 4 ξ2 = 10 , α = 0, v0 = 0 ..................................... 30 2.11 Collapse and evolution of an unstable soliton with N = 1060 and ξ = 10 .... 30 − 2.12 Collapse of unstable soliton with small perturbations filtered out . 31 3.1 Schematic scalar potential with a flat direction which is lifted by higher-dimension terms near φ Λ................................... 40 j j ∼ 3.2 Feynman diagram representation of the matrix element responsible for decay of the Q-ball into phonons. 46 ix 3.3 Evolution of charge within the Q-ball at the center of a neutron star . 55 3.4 Charge Q contained within a Q-ball and the number of neutrons consumed by the Q-ball over the life of the neutron star . 56 3.5 Plot of Q-ball lifetimes in free space . 57 3.6 Plot of neutron star lifetimes after being infected by a Q-ball . 58 3.7 Plot of neutron star lifetimes after being infected by a Q-ball (very high dimension operators) . 60 4.1 Schematic illustration of 4 histograms each containing 100 samples from the same Poisson distribution (λ = 100)............................ 67 4.2 Fraction of Q-ball energy that goes into black holes . 74 4.3 Differential PBH/Q-ball density ratio as a function of η = M=Mf ........ 76 4.4 Evolution of energy density over cosmological history . 77 4.5 Comparison of observational PBH constraints fcon(M) = ΩPBH(M)=ΩDM with the dark matter fraction per logarithmic interval . 81 4.6 Parameter space available to PBH production model . 83 5.1 Fraction of super-critical overdensities as a function of the scale factor a(t) ... 95 5.2 DM fraction in primordial black holes. Evolution of cosmological density for parameters of Model A. 97 x LIST OF TABLES 3.1 Table of Q-ball lifetimes (in years) for various lifting potentials . 61 3.2 Table of infected neutron star lifetimes (in years) for various lifting potentials . 62 5.1 Parameter sets for three different PBH production scenarios. 98 xi VITA 2010-2011 Engineering intern with Kyocera America’s Research and Development di- vision. Developed etching procedures for SEM microscopy of solder grain boundaries. 2011-2013 Engineering intern with General Atomcs’ Inertial Fusion Technology divi- sion. Developed fuel injection method for NIF indirect-drive fusion utilizing inductive acceleration and steering of laser targets. 2013 B.S. in Physics, with a minor in Mathematics, UCSD. 2013-2018 Teaching Assistant, Physics and Astronomy Department, UCLA. Taught a variety of discussion and lab sections. Subjects included classical mechan- ics, electrodynamics, quantum mechanics, hydrodynamics, special relativ- ity, particle physics, cosmology. 2014 M.S. in Physics, UCLA. 2014-2018 Research Assistant, Physics and Astronomy Department, UCLA. Studied dark matter, particle astrophysics and cosmology under the supervision of thesis advisor Alexander Kusenko. PUBLICATIONS Primordial Black Holes from Inflaton Fragmentation into Oscillons, E. Cotner, A. Kusenko and V. Takhistov, arXiv:1801.03321 (2018) Primordial black holes from scalar field evolution in the early universe, E. Cotner and A. Kusenko, Phys. Rev. D 96, no. 10, 103002 (2017) xii Primordial black holes from supersymmetry in the early universe, Phys. Rev. Lett. 119, no. 3, 031103 (2017) Astrophysical constraints on dark-matter Q-balls in the presence of baryon-violating opera- tors, E. Cotner and A. Kusenko, Phys. Rev. D 94, no. 12, 123006 (2016) Collisional interactions between self-interacting nonrelativistic boson stars: Effective poten- tial analysis and numerical simulations, E. Cotner, Phys. Rev. D 94, no. 6, 063503 (2016) xiii CHAPTER 1 Background 1.1 History One of the most intriguing scientific questions of our time is the identity of “dark matter", a mysterious substance that pervades the universe.
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