Table Of Content

Introduction to Cosmic Inflation and Dark Energy Series in Astronomy and Astrophysics The Series in Astronomy and Astrophysics includes books on all aspects of theoretical and experimental astronomy and astrophysics. Books in the series range in level from textbooks and handbooks to more advanced expositions of current research. Series Editors: M Birkinshaw, University of Bristol, UK J Silk, University of Oxford, UK G Fuller, University of Manchester, UK Recent books in the series Dark Sky, Dark Matter J M Overduin and P S Wesson Dust in the Galactic Environment, 2nd Edition D C B Whittet The Physics of Interstellar Dust E Krügel Very High Energy Gamma-Ray Astronomy T C Weekes Numerical Methods in Astrophysics: An Introduction P Bodenheimer, G P Laughlin, M Rózyczka, H W Yorke An Introduction to the Physics of Interstellar Dust Endrik Krugel Astrobiology: An Introduction Alan Longstaff Fundamentals of Radio Astronomy: Observational Methods Jonathan M Marr, Ronald L Snell, and Stanley E Kurtz Stellar Explosions: Hydrodynamics and Nucleosynthesis Jordi José Cosmology for Physicists David Lyth Cosmology Nicola Vittorio Cosmology and the Early Universe Pasquale Di Bari Fundamentals of Radio Astronomy: Astrophysics Ronald L. Snell, Stanley E. Kurtz, and Jonathan M. Marr Introduction to Cosmic Inflation and Dark Energy Konstantinos Dimopoulos Introduction to Cosmic Inflation and Dark Energy Konstantinos Dimopoulos Firsteditionpublished2021 byCRCPress 6000BrokenSoundParkwayNW,Suite300,BocaRaton,FL33487-2742 andbyCRCPress 2ParkSquare,MiltonPark,Abingdon,Oxon,OX144RN (cid:13)c 2021Taylor&FrancisGroup,LLC CRCPressisanimprintofTaylor&FrancisGroup,LLC Reasonableeffortshavebeenmadetopublishreliabledataandinformation,buttheauthorandpublisher cannotassumeresponsibilityforthevalidityofallmaterialsortheconsequencesoftheiruse.Theauthors andpublishershaveattemptedtotracethecopyrightholdersofallmaterialreproducedinthispublication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyrightmaterialhasnotbeenacknowledgedpleasewriteandletusknowsowemayrectifyinanyfuture reprint. 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Description:Firstedition.|BocaRaton:CRCPress,2020.|Series: Seriesinastronomyandastrophysics|Includesbibliographical referencesandindex. Identifiers:LCCN2020024113|ISBN9780815386759(hardback)|ISBN 9781351174862(ebook) Subjects:LCSH:Cosmology--History.|Darkenergy(Astronomy)|Bigbang theory. Classification:LCCQB981.D562020|DDC523.1/8--dc23 LCrecordavailableathttps://lccn.loc.gov/2020024113 ISBN:978-0-8153-8675-9(hbk) ISBN:978-1-351-17486-2(ebk) TypesetinLMRoman byNovaTechsetPrivateLimited,Bengaluru&Chennai,India Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com VisittheeResources:www.routledge.com/9780815386759 Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Dynamics and Content of the Universe . . . . . . . . . . . . . . . . . . . 4 3 History of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4 Inflation Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5 CMB Primordial Anisotropy and Structure in the Universe . . . . . . 91 6 The Inflationary Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7 Models of Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 8 Beyond Slow-Roll Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9 Dynamic Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 10 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 A A Taste of General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . 257 B Correlators of the Curvature Perturbation . . . . . . . . . . . . . . . . . 260 C Light Scalar Field Superhorizon Spectrum . . . . . . . . . . . . . . . . . 262 D Field Equation and Energy-Momentum of a Free Scalar Field . . . . . 265 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 v Preface Sometime in 2017, I was asked to review an introductory book on general relativity and cosmology. The book was very well written, especially the part on general relativity. However, to my amazement, hardly anything was mentioned on the topics of cosmic inflation and dark energy. I sent my report to the publishing company emphasising this point. They asked me if I would be interested in writing a book. Did I have a proposal for one? At this point, I realised that most of the existing introductory books on cosmology have very little material on cosmic inflation and dark energy, even though a sizeable fraction of cosmological research activity is concentrated in these fields. Sure, there are a number of excellent textbooks for specialists, but not much for senior undergraduate or early graduate students. And there is so much that one can say on the subject at this level. I felt that this situation must be remedied. This is how I first came up with the idea of this book. I have been teaching cosmology to undergraduate and graduate students for more than 15 years now.Iam gratefultomyundergraduate cosmologystudents, whosefeedback(eitherfrom end-of-yearquestionnairesorbecauseofmanyinsightfulquestionsduringthelectures)throughout the years enabled me to improve and refine my lecture notes, upon which a large part of this book is based. I should also include here my master’s and doctorate students. Of particular help was my former master’s student, Evelina Petkova, who read through the first draft of thebackgroundcosmologychapters;mycurrentdoctoratestudent,SamuelSánchezLópez,who readthroughtheentiredraft;andmyformerdoctoratestudent,CharlotteOwen,whoalsoread through the whole draft and additionally provided me with a couple of graphs (Figures 6.2 and 7.6) well after her graduation and despite working full-time. Their detailed comments and suggestions were invaluable. I should also thank my former doctorate student, Leonora Donaldson- Wood, who created the plots in Figures 9.2 and 9.8 as part of two of our published papers. Special thanks go to my friend and collaborator, Carsten van de Bruck, who kindly offered to read through the manuscript and came back to me with pointers and suggestions. My knowledge and understanding of cosmology and in particular of cosmic inflation and dark energy is shaped by more than two decades of active research, interactions with numerous collaborators,andparticipationandpresentationstoalargenumberofconferences(manyofthe graphsIhavedesignedinthebookhavetheiroriginsinoldpresentationslides).Myunderstand- ing was particularly boosted and shaped through interaction and collaboration with my friend and mentor, David H. Lyth, while I should also thank my former supervisor, Anne-Christine Davis,andmyprominentcollaborator,GeorgeLazarides.ThePhysicsDepartmentofLancaster University should also be thanked for providing me with the opportunity to write this book, in the form of a sabbatical leave during which the bulk of the book was written. I would also like to thank CRC Press for their continuous support. Finally,noneofthiswouldhavebeenpossiblewithoutthelovingsupportofmywife,Marilita Papastathi.Apartfromreadingthroughmostofthemanuscript(withheruniquepointofview), shehasbeenconstantlyencouragingmeandpromptingmetomoveforward,allowingmespace to work, and putting up with my preoccupation with this demanding project. I think that her biggest effect was believing in me so, in turn, I was persuaded to believe in myself. I thank her from the bottom of my heart. vii 1 Introduction Cosmology can be defined as the study of the Universe as a system, much like astrophysics can be defined as the study of stars as systems (a star is called “astro” (α´’στρo) in Greek). The termcosmologyderivesfromtheGreekwordCosmos(Kóσµoς),whichliterallymeansbeauty.In fact,thetermscosmologyandcosmeticshavethesameroot!Theabovedefinitionofcosmology, however, begs the question: What is the Universe? The Oxford English Dictionary defines the Universeas“Thewholeofexistingthings”(includingspaceandtime,Ishouldadd)or“allthings (including the Earth, the heavens, and all the phenomena of space) considered as constituting a systematic whole.” Why do people study cosmology? Well, one answer could be that cosmology leads to an understanding of how Nature works on the largest possible scales. This is a focal point for humancuriosity,especiallyforthesehumanswhocallthemselvesphysicists.Now,forphysicists, there are also practical advantages in studying cosmology. Indeed, cosmology is the meeting point of different areas of physics such as astrophysics, general relativity (the study of gravity) and particle physics. Cosmology facilitates communication of knowledge between these areas. Forastrophysicsinparticular,cosmologysetsthestageforastrophysicalprocesses:forexample, starandgalaxyformation,abundanceofelementsintheUniverse,ageofstellarsystems,andso on.Withrespecttoparticlephysics,cosmologyassistsinthestudyoffundamentaltheory.This isbecauseintheearlyUniverseextremeconditionsweremanifested,atenergiessohighthatare impossibletocreateinthelab.Phenomenaoccurringinsuchconditionsmayleavetracesbehind, which, when observed, can offer insights on particle and high-energy physics, for example, on the unification of fundamental forces. In a sense, cosmology uses the entire Universe as a giant laboratory aiming to reveal fundamental physics on energies well beyond the reach of Earth- based experiments such as colliders. Yakov B. Zel’dovich, the prominent soviet cosmologist, famously said “the very early Universe is an accelerator for poor people.” The observational side of cosmology is clearly astronomical, using telescopes, balloons, and satellites, while the theoretical part is mainly particle theory and employs what is known or conjectured about fundamental physics. Moving past physicists, there are profound implications of cosmology of philosophical and even existential nature. For example, it is clear that understanding our place in the Cosmos is a step towards understanding ourselves. Throughout the history of humankind virtually every civilisation had a cosmogony myth, thatisatheoryfortheoriginoftheUniverse.Gradually,withtheadvanceofscience,ourunder- standing of the Cosmos was stripped from folklore, religion, and “common sense” prejudices. In thelasthundredyearsorso,aunifiedpictureemergedtothepointthatphysicists,andespecially cosmologists, feel that, in broad terms, almost the entire history of the Universe is now known, withmostunresolvedquestionsconcentratedinafractionofthefirstsecondofitsexistence.This is a tremendous achievement, of course, but we need to be reminded that cosmologists are only 1