String theory in the early universe Rhiannon Gwyn Physics Department McGill University Montreal, Quebec June 2009 A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy c Rhiannon Gwyn, 2009. All rights reserved Abstract String theory is a rich and elegant framework which many believe furnishes a UV-complete unified theory of the fundamental interactions, including gravity. However, if true, it holds at energy scales out of the reach of any terrestrial particle accelerator. While we cannot observe the string regime directly, we live in a universe which has been evolving from the string scale since shortly after the Big Bang. It is possible that string theory underlies cosmological processes like inflation, and that cosmology could confirm or constrain stringy physics in the early universe. This makes the intersection of string theory with the early universe a potential window into otherwise inaccessible physics. The results of three papers at this intersection are presented in this thesis. First, we address a longstanding problem: the apparent incompatibility of the experimentally constrained axion decay constant with most string theoretic realisations of the axion. Using warped compactifications in heterotic string theory, we show that the axion decay constant can be lowered to acceptable values by the warp factor. Next, we move to the subject of cosmic strings: linelike topological defects formed during phase transitions in the early universe. It was realised recently that cosmic superstrings are produced in many models of brane inflation, and that cos- mic superstrings are stable and can have tensions within the observational bounds. Although they are now known not to be the primary generators of primordial density perturbations leading to structure formation, the evolution of cosmic string networks could have important consequences for astrophysics and cosmology. In particular, there are quantitative differences between cosmic superstring networks and GUT cosmic string networks. We investigate the properties of cosmic superstring networks in warped backgrounds, where they are expected to be produced at the end of brane inflation. We give the tension and properties of three-string junctions of different kinds in i these networks. Finally, we examine the possibility that cosmic strings in heterotic string theory could be responsible for generating the galactic magnetic fields that seeded those observed today. We were able to construct suitable strings from wrapped M5-branes. Demanding that they support charged zero modes forces us into a more general heterotic M–theory picture, in which the moduli of a large moduli space of M-theory compactifications are time dependent and evolve cosmologically. Thus a string theory solution of this problem both implies constraints on the string theory construction and has cosmological implications which might be testable with future observations. The breadth of topics covered in this thesis is a reflection of the importance of the stringy regime in the early universe, the effects of which may be felt in many different contexts today. The intersection of string theory with cosmology is thus a complex and exciting field in the study of fundamental particle physics. ii R´esum´e Plusieurs croient voir en la th´eorie des cordes une riche et ´el´egante fa¸con d’obtenir une th´eorie UV compl`ete et unifi´ee des interactions fondamentales, incluant la gravit´e. Mˆeme si elle s’av´erait vrai, son application se restreindrait toutefois `ades ´energies hors d’atteinte des acc´el´erateurs de particules terrestres. Malgr´equ’on ne puisse observer le r´egime des cordes directement, l’univers dans lequel nous vivons a ´evolu´e`apartir d’une ´echelle comparable `ala taille d’une corde peu de temps apr`es le Big Bang. Il est donc possible que la th´eorie des cordes soit `al’origine de processus cosmologiques comme l’inflation et que l’´etude de ces derniers permette de confirmer ou de contraindre la physique des cordes alors que l’univers ´etait jeune. Ainsi, `al’intersection de la th´eorie des cordes et du r´egime dans lequel se baignait l’univers naissant se trouve probablement une fenˆetre pour la physique qui serait autrement inatteignable. Dans cette th`ese, nous pr´esentons les travaux de trois articles reli´es `acette intersection. Premi`erement, nous nous int´eressons `aun probl`eme de longue date: l’apparente incompatibilit´eentre la valeur de la constante de d´esint´egration de l’axion contrainte exp´erimentalement et celle pr´edite par la plupart des th´eories de cordes. En utilisant les compactifications d´eform´ees de la th´eorie h´et´erotique des cordes, nous montrons que la constante de d´esint´egration de l’axion peut ˆetre diminu´ee `ades valeurs acceptables grˆace au facteur de d´eformation. Par la suite, nous nous tournons vers l’´etude des cordes cosmiques: les d´efauts topologiques de type << ligne >> se formant lors des transitions de phase dans l’univers naissant. Il fut d´ecouvert r´ecemment que des supercordes cosmiques peuvent ˆetre produites par plusieurs mod`eles d’inflation de branes. Ces supercordes peuvent ˆetre stables et mˆeme avoir des valeurs de tension `al’int´erieur des limites observables. Bien qu’on sache maintenant qu’elles ne sont pas les sources principales `al’origine du m´ecanisme de g´en´eration des fluctuations de densit´e primordiale de l’univers menant `ala formation de structures, l’´evolution des r´eseaux iii de cordes cosmiques peut avoir d’importantes cons´equences pour l’astrophysique et la cosmologie. En particulier, il existe des diff´erences quantitatives entre les r´eseaux de supercordes cosmiques et les r´eseaux de cordes cosmiques GUT. Nous investiguons par la suite les propri´et´es des r´eseaux de supercordes cosmiques dans un arri`ere-plan d´eform´e, l`ao`uils sont suppos´es se former `ala fin de l’´epoque d’inflation des branes. Nous calculons la tension et les propri´et´es de jonctions `atrois cordes dans diverses configurations de ces r´eseaux. Nous examinons finalement la possibilit´eque des cordes cosmiques issues de la th´eorie h´et´erotique des cordes puissent ˆetre responsables pour la g´en´eration des champs magn´etiques galactiques `al’origine de ceux observ´es aujourd’hui. Nous sommes capable de construire des cordes `apartir de M5-branes repli´ees. Toutefois, la n´ecessit´equ’elles produisent des modes z´ero charg´es nous impose un cadre plus g´en´eral de la th´eorie h´et´erotique M dans laquelle les modules d’un large espace de modules des compactifications de la th´eorie M sont d´ependant du temps et ´evoluent `al’´echelle cosmologique. Ainsi, une solution de la th´eorie des cordes `ace probl`eme non seulement implique une contrainte sur la construction de cette th´eorie mais poss`edent ´egalement des implications cosmologiques pouvant ˆetre test´ees par le biais d’observations futures. L’´etendue des sujets couverts dans cette th`ese refl`ete de l’importance associ´ee au r´egime propre `ala th´eorie des cordes dans l’univers naissant et des effets qui en d´ecoulent dans diff´erents contextes d’aujourd’hui. Ceci fait de l’intersection de la th´eorie des cordes et de la cosmologie une fenˆetre complexe et excitante pour la physique des particules. iv Acknowledgements First of all, I would like to thank my supervisor, Keshav Dasgupta, for his seemingly boundless time and help. I am indebted to him for patiently teaching me string theory and guiding my work in all the projects undertaken during my Ph.D. I am also grateful for his support and encouragement throughout. Financial and moral support for travelling and attending various schools and conferences is also greatly appreciated. I would also like to thank the other faculty members in the high energy theory group at McGill, from whom I have learnt a great deal. I am indebted to Jim Cline, Alex Maloney and Guy Moore, and especially Robert Brandenberger. My Master’s supervisor Robert de Mello Koch’s support and encouragement have been indispensable. Anke Knauf has been a source of support, an inspiration and a font of wisdom. I have also learnt a great deal from conversations with and lessons from the other postdocs at McGill: thanks to Hassan Firouzjahi, Andrew Frey, Omid Saremi and Bret Underwood. I would also like to thank my collaborators Stephon Alexander, Josh Guffin and Sheldon Katz. I’d like to thank my officemates and peers past and present: thanks to Neil Barnaby, Aaron Berndsen, Simon Carot- Huot, Racha Cheaib, Lynda Cockins, Rebecca Danos, Paul Franche, Johanna Karouby, Nima Lashkari, Dana Lindemann, Subodh Patil, Natalia Shuhmaher, James Sully, Aaron Vincent, Alisha Wissanji, Hiroki Yamashita and especially Ra’ad Mia, who makes great curries. My time at summer schools and conferences has been invaluable. I’d like to thank the lecturers and organisers of the Jerusalem winter school, PiTP, Les Houches and TASI. At these schools I learnt a lot of physics, both from lectures and from interactions with lecturers, postdocs and fellow students. I am grateful to them for all the many discussions and support from across the globe (and also to the inventors of high-speed internet). Without attempting a complete list, I would v like to thank Murad Alim, Ines Aniceto, Chris Beem, Adam Brown, Alejandra Castro, Sophia Domokos, Lisa Dyson, Damien George, Manuela Kuraxizi, Louis Leblond, Nelia Mann, Arvind Murugan, Jonathan Pritchard, Rakib Rahman, Sarah Shandera, Alex Sellerholm, Jihye Seo, Julian Sonner, David Starr, Linda Uruchurtu, Amanda Weltman Murugan and Ketan Vyas. In particular I’d like to thank Navin Sivanandam. I hereby forgive him for almost driving me into the Grand Canyon.