Table Of ContentIntroduction to Cosmic Inflation
and Dark Energy
Series in Astronomy and Astrophysics
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Introduction to Cosmic Inflation and Dark Energy
Konstantinos Dimopoulos
Introduction to Cosmic Inflation
and Dark Energy
Konstantinos Dimopoulos
Firsteditionpublished2021
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Title:Introductiontocosmicinflationanddarkenergy/Konstantinos
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Description:Firstedition.|BocaRaton:CRCPress,2020.|Series:
Seriesinastronomyandastrophysics|Includesbibliographical
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Identifiers:LCCN2020024113|ISBN9780815386759(hardback)|ISBN
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Subjects:LCSH:Cosmology--History.|Darkenergy(Astronomy)|Bigbang
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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)through-
out 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 particu-
lar 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 sug-
gestions 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
