Universidad Autonoma´ de Madrid Facultad de Ciencias Departamento de F´ısica Teorica´ HIGGS COSMOLOGY From the Early to the Late Universe Memoria de Tesis Doctoral realizada por Javier Rubio Pe~na presentada ante el Departamento de F´ısicaTe´orica de la Universidad Aut´onomade Madrid para la obtenci´ondel T´ıtulode Doctor en Ciencias. Tesis Doctoral dirigida por Juan Garc´ıa-Bellido Capdevila del Departamento de F´ısicaTe´oricay el I.F.T. de la Universidad Aut´onomade Madrid Madrid, Junio 2011. Abstract Inflation is nowadays a well established paradigm consistent with all the observations, related both to the background and to the matter perturbations in the Universe. The nature of the inflaton, as well as the overall picture of the transition between the inflationary and radiation eras, depend crucially on the different microphysics models in which inflation is embedded. The absence of a suitable candidate in the usual formulation of the Standard Model has motivated the search for alternatives in different extensions of the standard theory, as Supersymmetry or String Theory. Unfortunately, the strength of the couplings among the inflaton and the different matter species present in those models is generically unknown. This fact makes difficult the determination of the dominant reheating mechanism at the end of inflation and the associated efficiency of the reheating stage. In this PhD thesis we adopt a very different and reductionist point of view. We study the possibility of inflation to be a natural consequence of the Standard Model, rather than an indication of its weakness. The role of the inflaton is played by the Higgs boson, non-minimally coupled to gravity. No new degrees of freedom apart from those already present in the electroweak theory are initially added. The non-minimal coupling rescues the Higgs field from the known difficulties for generating inflation, being its value determined by cosmological observations. The novelty and great advantage of the model is precisely its connection with a well-known microphysical mechanism, hopefully accessible in the present accelerator experiments. All the couplings among the Higgs and the Standard Model particles are known at the electroweak scale and can be extrapolated to the reheating era through the renormalization group equations. For the first time, the initial conditions of the hot Big Bang can be potentially determined, without invoking new speculative physics beyond the electroweak scale. Some modest extensions of the simplest Higgs Inflation model, based on scale invariance and Unimodular Gravity, are able to accommodate not only the early but also the late time acceleration of the Universe. Contrary to other beyond the Standard Model theories, they introduce just an extra degree of freedom, the dilaton, which plays however a central role, tracking the present expansion rate of the Universe. The close connection between the inflationary and dark energy dominated eras leads to highly non-trivial consistency relations between the spectral tilt of CMB anisotropies and the present equation of state of dark energy. Resumen Inflaci´ones a d´ıa de hoy un paradigma bien establecido consistente con todas las obser- vaciones. Su naturaleza, as´ı como los aspectos globales de la transici´onentre el estado inflacionario y la ´epoca dominada por materia, dependen en gran medida de los diferentes modelos microsc´opicosen los que se implementa. La ausencia de un candidato a inflat´onen el Modelo Est´andar ha motivado la busqueda de alternativas en extensiones de esta teor´ıa, como Supersimetr´ıao teor´ıa de cuerdas. Desafortunadamente, desconocemos la intensidad de los acoplos entre el inflaton y el contenido de materia de dicho modelos. Este hecho dificulta la determinaci´ondel mecanismo de recalentamiento dominante y su eficiencia. En esta t´esis abordaremos el problema desde un punto de vista muy diferente y reduccionista. Estudiare- mos el inflat´onno como una indicaci´onde la debilidad del modelo est´andar, sino como una consecuencia natural del mismo. Ser´ael propio campo de Higgs, ya presente en el Modelo Est´andar,el que juege el papel de inflat´onmediante un acoplo no m´ınimoa gravedad. No se incorporar´aninicialmente nuevos grados de libertad, m´asall´ade los ya presentes en la teor´ıaelectrod´ebil.La novedad, y al mismo tiempo gran ventaja, de este modelo es precisa- mente su conexi´oncon un mecanismo microf´ısicobien conocido, y que podr´ıaser accesible en los aceleradores de part´ıculasactuales. Todos los acoplos entre el Higgs y las part´ıculas del Modelo Est´andarse conocen a la escala electrod´ebil, pudi´endoseextrapolar a la era del recalentamiento mediante las ecuaciones del grupo de renormalizaci´on.La determinaci´onde las condiciones iniciales del Big Bang es por primera vez posible sin la necesidad de invocar nueva y especulativa f´ısicam´asall´ade la escala electrod´ebil. Algunas extensiones relativa- mente modestas de Higgs Inflation, basadas en invarianza de escala y gravedad unimodular, son capaces de acomodar no s´oloel estad´ıo inflacionario, sino tambi´enla aceleraci´ondel universo actual. Contrariamente a otros modelos, estas extensiones introducen solamente un grado de libertad adicional, el dilat´on,que juega sin embargo un papel central en el modelo, determinando la tasa de expansi´onactual del mismo. La gran conexi´onentre el proceso inflacionario y la energ´ıaoscura da lugar a relaciones de consistencia altamente no triviales entre el tilte espectral de las anisotrop´ıasdel CMB y la ecuaci´onde estado de energ´ıaoscura. A mi familia, que me lo ha dado todo. Acknowledgements A todos los que la presente vieren y entendieren. Inicio de las Leyes Org´anicas. I am indebted to many people for their help and support during the last few years. I am particularly thankful to my supervisor Juan Garc´ıa-Bellidofor sharing with me his insight in the interplay between particle physic and cosmology. My view of understanding the physics, my critical view of it as well as maybe my prejudices are clearly influenced by him. I would like also to thank all the members of SISSA-Trieste, MPI-Munich and EPFL-Lausanne for the hospitality and very pleasant working environment during the development of part of the research presented in this thesis. I am particularly thankful to Stefano Liberati, Ignacio Cirac and Mikhail Shaposhnikov for allowing me to visit those institutions and for guiding me in the exploration of their very diverse disciplines. Great thanks to Daniel Zenhausern and Daniel G. Figueroa for the fruitful and enjoyable collaborations we had in Madrid and Lausanne respectively. Thanks also to Anupam Mazumdar, Jose Pedro Mimoso and Stefano Liberati for their comments and suggestions about this manuscript and for bringing to my attention references which would have otherwise missed in the large literature. Finally I would like to mention the efficient secretarial staff of the Department and Institute of Theoretical Physics for all the bureaucratic help along the past few years. In the most personal part of these acknowledgments, I would like to thank my co- PhD students and friends in Madrid: Roberto, Bea, Domenico, Luis, Norberto, Jaime, Joao, Brian, Ana, Josu, Javis, Migueles and many others who will surely forgive me not to include their name in this long list. Among them I would like to convey my special affection to Fran and Pilar, for all we have shared during these years and for helping me so much with the technicalities of this thesis. In the past few years, I met a lot of people in different workshops and meetings and some of them have also become good friends. Thanks Hector, Aurelio, Guillem, Noela, Marco, Julien, Iker for all the good moments we lived. Among my carissimi amici out of the Institute deserve a special mention Cristina and Jose, for being there in all my bad moments before, during and hopefully after the preparation of this thesis. They are a central part of my life. Great friends are also Mar´ıay Pedro, with whom I spent one of the best vacations of my life and hopefully many others. Thanks Mar´ıafor that wonderful piece of advise that you gave me in Zamora. Last, but not least, I wish to thank my fathers Tino and Emilia, my sister Beatriz and my lovely grandparents for their invaluable and unconditional support along all my life. Everything I am I owe to you. Qu´ete parece desto, Sancho? - dijo Don Quijote - Bien podr´an los encantadores quitarme la ventura, pero el esfuerzo y el ´animo,ser´aimposible. Segunda parte del Ingenioso Caballero Don Quijote de la Mancha Miguel de Cervantes - Buena est´a- dijo Sancho -; f´ırmelavuestra merced. No es menester firmarla -dijo Don Quijote-, sino solamente poner mi r´ubrica. Primera parte del Ingenioso Caballero Don Quijote de la Mancha Miguel de Cervantes Declaration The material presented in this PhD thesis is based on original contributions done during the course of my PhD studies. In particular the results scattered through Chapters2,3 and5 are based on Ref. 2 on the list below, while the main results of Chapter4 are contained in Ref. 1 This last chapter is also influenced by Ref. 3. although the details have not been included for being yet work in progress. Chapter1 describe the motivation of the Higgs-driven inflationary models considered in this PhD thesis, while a summary of the main results of this thesis is presented in Chapter6. The appendicesA andB contains mainly non-original contributions included to clarify some technical aspects of this PhD thesis. On the other hand the results presented in AppendixC constitute also original material. 1. Preheating in the Standard Model with the Higgs-Inflaton Coupled to Gravity. Juan Garcia-Bellido, Daniel G. Figueroa and Javier Rubio Phys. Rev. D 79 063531 (2009) 2. Higgs Cosmology: From the Early to the Late Universe.