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2 Particle Dynamics in an Expanding Universe 5 2.1 the Friedmann Equations European Research Universität Hamburg Council DER FORSCHUNG I DER LEHRE | DER BILDUNG PRIMORDIAL NUCLEOSYNTHESIS IN THE PRESENCE OF MEV-SCALE DARK SECTORS Dissertation zur Erlangung des Doktorgrades an der Fakultät für Mathematik, Informatik und Naturwissenschaften Fachbereich Physik der Universitat Hamburg vorgelegt von Marco Hufnagel aus Hamburg 2020 Gutachter der Dissertation: Dr. Kai Schmidt-Hoberg Prof. Dr. Geraldine Servant Zusammensetzung der Prüfungskommission: Dr. Kai Schmidt-Hoberg Prof. Dr. Geraldine Servant Prof. Dr. Jochen Liske Prof. Dr. Gudrid Moortgat-Pick Dr. Torben Ferber Vorsitzender der Prüfungskommission: Prof. Dr. Jochen Liske Datum der Disputation: 15.06.2020 Vorsitzender des Fach-Promotionsausschusses PHYSIK: Prof. Dr. Günter H. W. Sigl Leiter des Fachbereichs PHYSIK: Prof. Dr. Wolfgang Hansen Dekan der Fakultät MIN: Prof. Dr. Heinrich Graener “Come on, Rory! It isn't rocket science, it's just quantum physics!” - The Doctor “This is not the time for vanity. It's the time to show the universe how amazingly awesome I am!” - Captain Qwark Dedicated to all the equations I have solved before. i Abstract In this thesis, we perform a comprehensive study of Big Bang nucleosynthesis constraints on different dark-sector models with MeV-scale particles which are neither fully relativistic nor fully non-relativistic during all relevant temperatures. To this end, we derive a generic set of equations that can be used to determine the light-element abundances for many different dark-sector scenarios. In particular, we take into account all relevant effects that might alter the creation of light elements in the early universe, including modifications to the Hubble rate and time-temperature relation, an adjusted best-fit value for the baryon-to-photon ratio due to an altered effective number of neutrinos, a modified neutrino-decoupling temperature as well as late-time modifications of the nuclear abundances due to photodisintegration. We then solve these equations for the case of dark sectors with MeV-scale particles that are created in the early universe and later decay into either dark or electromagnetic radiation. In the former case, the dark and the visible sectors are completely decoupled, and we show that even such scenarios can be severely constrained if the initial temperature ratio of both sectors is suffi­ ciently large. In the latter case, the particle decay can instead lead to a severe entropy injection into the SM heat bath, and we show that the final constraints can be very different from the naive order-of-magnitude estimates that are usually employed for such scenarios. We then turn to the case of MeV-scale dark matter that can annihilate into all kinematically available SM states, including electrons/positrons, photons, and neutrinos. In this context, we first up­ date the lower bound on the mass of thermal dark matter using improved determinations of the nuclear abundances. Afterwards, we calculate the corresponding constraints on the an­ nihilation cross-section of dark matter and show that, for p-wave suppressed annihilations, the bounds from nucleosynthesis are much stronger than the ones from the CMB and even competitive with the strongest bounds from other indirect searches. Finally, we apply our results to models with self-interacting dark matter as well as to models with axion-like par­ ticles. In the former case, we show that for scalar mediators, most parts of parameter space leading to sizable self-interactions are already excluded by a combination of direct-detection experiments and constraints from nucleosynthesis. In the latter case, we further evaluate the robustness of our constraints by allowing various additional effects that may weaken the bounds of the standard scenario. We find that, while the bounds can indeed be weakened, very relevant robust constraints remain. ii Zusammenfassung In dieser Arbeit betrachten wir Modelle mit verschiedenen dünklen Sektoren ünd üntersü- chen die Verwendbarkeit von Vorhersagen der primordialen Nukleosynthese zur Einschrän- küng des jeweiligen Parameterbereiches dieser Modelle. Dabei konzentrieren wir üns aüf Modelle mit Teilchen nahe der MeV-Skala, welche im Bereich der relevanten Temperatu­ ren weder ultra-relativistisch noch nicht-relativistisch sind. Zu diesem Zweck leiten wir ein generisches System von Gleichungen her, welches anschließend verwendet werden kann, um die Häufigkeit der leichten, im frühen Universum erzeugten, Elemente für verschiede­ ne Szenarien vorherzusagen. Dabei berücksichtigen wir alle Effekte, welche die Erzeugung dieser Elemente potenziell beeinflussen können, einschließlich einer möglichen Modifikati­ on der Hubble Rate und der Zeit-Temperatur-Beziehung, einer Änderung des Verhältnisses der Baryonen- und Photonenzahl aufgrund einer geänderten Anzahl effektiver Neutrinos, ei­ ner modifizierten Entkopplungstemperatur der Neutrinos und die nachträgliche Änderung der Änzahl leichter Elemente mittels Photodesintegration. In einem ersten Schritt wenden wir diese Gleichungen dann auf Modelle mit Teilchen nahe der MeV-Skala an, welche im frühen Universum zunächst erzeugt werden und anschließend entweder in dunkle oder elek­ tromagnetische Strahlung zerfallen. Im ersten Fall sind der dunkle und der sichtbare Sektor komplett entkoppelt und wir zeigen, dass auch der Parameterraum solcher Modelle deut­ lich eingeschrankt werden kann, solange das Verhältnis der Temperaturen beider Sektoren ausreichend groß ist. Im zweiten Fall führt der Teilchenzerfall zu einer deutlichen Entropie­ injektion in das Warmebad des SMs und wir zeigen, dass sich die Ergebnisse unserer umfas­ senden Analyse deutlich von den einfachen Abschätzungen unterscheiden konnen, welche normalerweise für solche Szenarien herangezogen werden. Anschließend betrachten wir Mo­ delle mit einem Dunkle-Materie-Kandidaten nahe der MeV-Skala, welcher zusätzlich in die kinematisch erlaubten SM-Teilchen, sprich Elektronen/Positronen, Photonen und Neutrinos, annihilieren kann. In diesem Zusammenhang aktualisieren wir zunächst die unter Schran­ ke an die Masse thermischer Dunkler Materie unter Verwendung aktuellster Messergebnisse. Nachfolgend berechnen wir, welche Einschränkungen sich für den Ännihilationswirkungs- querschnitt ergeben und zeigen, dass diese im Fall von p-Wellen unterdrückten Annihilatio­ nen, deutlich starker sind als jene vom CMB, und sogar vergleichbar mit den Ergebnissen anderer indirekter Suchen. Abschließend betrachten wir Modelle mit selbstwechselwirken­ der Dunkler Materie, sowie Modelle mit Axion-ahnlichen Teilchen. Im ersten Fall zeigen wir, dass für skalare Teilchen die meisten Bereiche mit phänomenologisch relevanten Selbstwech­ selwirkungen bereits durch eine Kombination indirekter und direkter Suchen ausgeschlossen sind. Im zweiten Fall untersuchen wir zusätzlich die Robustheit unserer Ergebnisse und zei­ gen, dass unterschiedliche Effekte die Resultate zwar abschwachen konnen, in jedem Fall aber deutliche Einschrankungen des Parameterraums verbleiben. iii THIS THESIS IS BASED ON THE FOLLOWING PUBLICATIONS: M. Hufnagel, K. Schmidt-Hoberg, and S. Wild, BBN constraints on MeV-scale dark sectors. Part I. Sterile decays, JCAP 1802 (2018) 044, [arXiv:1712.03972] M. Hufnagel, K. Schmidt-Hoberg, and S. Wild, BBN constraints on MeV-scale dark sectors. Part II. Electromagnetic decays, JCAP 1811 (2018) 032, [arXiv:1808.09324] P. F. Depta, M. Hufnagel, K. Schmidt-Hoberg, and S. Wild, BBN constraints on the anni­ hilation of MeV-scale dark matter, JCAP 1904 (2019) 029, [arXiv:1901.06944] K. Bondarenko, A. Boyarsky, T. Bringmann, M. Hufnagel, K. Schmidt-Hoberg, and A. Sokolenko, Direct detection and complementary constraints for sub-GeV dark matter, JHEP 03 (2020) 118, [arXiv:1909.08632] P. F. Depta, M. Hufnagel, and K. Schmidt-Hoberg, Robust cosmological constraints on axion-like particles, JCAP 05 (2020) 009, [arXiv:2002.08370] OTHER PUBLICATIONS THAT ARE NOT PART OF THIS THESIS: M. Garny, J. Heisig, M. Hufnagel, and B. Lülf, Top-philic dark matter within and beyond the WIMP paradigm, Phys. Rev. D97 (2018), no. 7 075002, [arXiv:1802.00814] M. Garny, J. Heisig, M. Hufnagel, B. Lülf, and S. Vogl, Conversion-driven freeze-out: Dark matter genesis beyond the WIMP paradigm, PoS CORFU2018 (2019) 092, [arXiv:1904.00238] iv v Contents Contents 1 Introduction 1 2 Particle dynamics in an expanding universe 5 2.1 The Friedmann equations .................................................................................................. 5 2.2 The relativistic Boltzmann equation ............................................................................... 6 2.2.1 The Boltzmann equation in an expanding universe .................................... 7 2.2.2 The collision operator in its general form ........................................................ 8 2.2.3 Thermodynamical quantities ............................................................................... 11 2.2.4 Local thermal equilibrium ..................................................................................... 13 2.2.5 A note on Maxwell-Boltzmann distributions ................................................. 17 3 Big Bang Nucleosynthesis 19 3.1 Particle evolution during nucleosynthesis ..................................................................... 19 3.1.1 Electromagnetic radiation ..................................................................................... 20 3.1.2 Neutrinos ..................................................................................................................
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