Combining theory and observations [Elektronische Ressource] : a sample study of the interplay between cosmology and particle physics / Suchita C. Kulkarni

Suchita C. Kulkarni

Sujets

• Astronomie
• Physik

Informations

• Publié par: rheinische_friedrich-wilhelms-universitat_bonn
• Publié le: 01 janvier 2011
• Nombre de lectures: 8
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Combiningtheoryandobservations-asample
studyoftheinterplaybetweencosmologyand
particlephysics
Dissertation
zur
ErlangungdesDoktorgrades(Dr.rer.nat.)
der
Mathematisch-Naturwissenschaftlichen-Fakultät
der
RheinischenFriedrich-Wilhelms-UniversitätBonn
vorgelegtvon
SuchitaC.Kulkarni
aus
Dombivali-India
31stMay2011
Bonn2011Referent: Prof.Dr.ManuelDrees
Koreferent: Prof.Dr.HerbertDreiner
TagderPromotion: 08.08.2011
Erscheinungsjahr: 2011Tomyteacher Mr. KedarSoni,
whointroducedmeto theawesomeness ofphysics!
iAcknowledgements
Today, I take one more step towards my dream of being a physicist, I pause for a while and
look back to see the smiling faces of many who helped me. By blaming all of them who are
responsible for me to be here, I wish to express my gratitude and happiness for the fact that
theyarethere.
The biggest component of life is always the parents. (As long as you are single!) I thank
Aai, Baba and Prachi for letting me escape home and live life of a self-imposed exile. I shall
continuetodoso.
I thank Manuel, who has been both my boss and a friend. Without him, I would not have
dared to divulge in such diverse topics. Manuel, thanks for giving me the confidence that I
am capable of doing so. I will invariably miss the lunch and coffee table discussions. With-
out them, I would not have understood the Large Scale Structure of the Earth, from history
and geography to politics and economics. I also thank you for giving me the opportunityof
numerous tours around the world. You fulfilled one of the basic reasons for why I came to
research. Idearlywish,wecontinuetoworktogether.
IalsothankHerbi,mysecondmentorwhoalwayshelpedmeinmorethanoneway.
I take this opportunity to thank Cristiano and Prof. Klaus Desch for being my examiners. I
alsothankUniverseNETforthealwayshappeningresearchenvironment.
Satisfyingthequenchofindependentresearchis neverpossiblewithoutawesomecollabora-
tors. Frommyfirstcollaborator Prof. MitsuruKakizaki untilmycurrentgang,Ithankall for
numerous good evenings, free dinners and fantastic physics discussions. I especially thank
OscarandRenataformysuperbtimeinBrazil,IamsureIwillcontinuetovisityou.
Aboveall,lifeisemptywithoutfriends,withoutwhoseencouragementandconstantsupport
Iwouldhavenevercomesofar. ThankyouSuyog,Sandesh,PawanandNehaformailingme
fromtimetotimeaskingwhetheramalive ordead. Iamproudtohaveyouinmylife.
Anyone, who has left his/her country to come into a culture completely unknown would
knowtheexcitementand fear of facing it. Bondsand relationships are formed overa period
oftimetomakelifethemostbeautifulitcanbe. IthankmysistersAnu,PoornniandStelladi
and my jijus Suruand Giri forthingsnooneelsecould everhave givenme. (Amnottalking
about spoons Anu!) Suru, knowing how much of your time I have stolen to discuss about
cosmology, I thank you for never saying no! I also thank Karina, Tim, Phil, Brani and Anna
forprovingtomefromtimetotimethatamonthevergeofmadness! Thankyoufolks,details
ofmytimewithyouwillcorrespondtoanotherthesisinhumanrelationships. Iwonderhow
iiiwouldIhavesurvivedwithoutyou!
IspeciallythankTimforbeingthe“official”proof-readerofthisthesis. Youwouldhavefound
thousandsof(additional)mistakesinthisdocumentotherwise.
I am indebted to Duggles Adams for the hitchhiker’s guide to the galaxy from where I have
stolenquotesinthisthesis.
Finally,IthankalltheformerandcurrentgroupmembersofManuelandHerbi. Iwon’tforget
thesnow-fightsandthearguments. Ohyes! wealsotalkedaboutphysics! Thankyouguys,I
hadagreattimewithyouall.
ivContents
1. Introduction 1
1.1. Themeofthethesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Organizationofthethesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3. Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Tau polarization and CP-violation 5
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2. Spin-densitymatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3. Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1. Staumixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2. Lagrangianandcomplexcouplings . . . . . . . . . . . . . . . . . . . . . 10
2.3.3. Tauspindensitymatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.4. Tripleproducts-polarizationmeasurementreference . . . . . . . . . . . 12
2.3.5. NormaltaupolarizationandCP-asymmetry . . . . . . . . . . . . . . . . 13
2.3.6. ParameterdependenceoftheCP-asymmetry . . . . . . . . . . . . . . . . 14
2.4. Numericalresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1. Phasedependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.2. jA j tan dependenceandstaumixing . . . . . . . . . . . . . . . . . . 16
2.4.3. jj M dependenceandbranchingratios . . . . . . . . . . . . . . . . . 172
2.4.4. Impactofτ˜ decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
2.5. Summaryandconclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3. Semi-relativistic dark matter 23
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2. Standardrelicdensitycalculations . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1. Relativisticfreeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2. Non-relativisticfreeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3. Semi-relativisticfreeze-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1. AnnihilationviaS-wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.2. AnnihilationviaP-wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.3. SolutiontotheBoltzmannequation . . . . . . . . . . . . . . . . . . . . . 30
3.4. Semi-relativisticspeciesasdarkmattercandidate . . . . . . . . . . . . . . . . . 32
3.5. Alternativeusageofsemi-relativistic species . . . . . . . . . . . . . . . . . . . . 33
3.5.1. Entropyproductionviadecayofnon-relativisticspecies . . . . . . . . . 34
3.5.2. Entropyproductionviadecayofsemi-relativisticspecies . . . . . . . . . 35
4. Halo bias in cosmology 39
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2. Linearperturbationtheoryincosmology . . . . . . . . . . . . . . . . . . . . . . 41
vContents
4.3. Predictingnon-linearmatterpower-spectrum . . . . . . . . . . . . . . . . . . . . 44
4.4. Includingdarkmatterhaloesinperturbationtheory . . . . . . . . . . . . . . . . 51
4.4.1. Distributionofdarkmatterhaloes . . . . . . . . . . . . . . . . . . . . . . 52
4.4.2. Growthofmatterandhaloperturbations . . . . . . . . . . . . . . . . . . 53
4.5. Initialconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.5.1. Modelforinitialhalo bias . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.6. Lineartheoryforhaloperturbations . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.6.1. Theimportanceofthehalo velocitybias . . . . . . . . . . . . . . . . . . . 57
4.7. Analyticaltreatmentofnon-linearities . . . . . . . . . . . . . . . . . . . . . . . . 58
4.7.1. 1-loopperturbationtheory . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.7.2. Large-kresummationforthepropagator . . . . . . . . . . . . . . . . . . 60
4.7.3. UsingTimeRenormalizationGroup(TRG)equations . . . . . . . . . . . 61
4.8. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.8.1. Matter-halocrosspropagator . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.8.2. Matter-halocrosspowerspectrum . . . . . . . . . . . . . . . . . . . . . . 63
4.9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5. Conclusions 69
5.1. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
A. Modified Bessel Functions 71
B. Validity of the Maxwell–Boltzmann Distribution 73
C. Momenta and spin vectors 77
D. Phase space 79
E. Density matrix formalism 81
F. Stau decay widths 83
G. Complete analytic expressions of the 1-loop propagator and power spectrum 85
G.0.1. Propagator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
H. 1-loop PS 87
I. The resummed propagator 89
J. Taking into account the initial halo non-Gaussianity. 93
Bibliography 95
viChapter 1.
Introduction
Inthebeginningthe Universewascreated.
Thishas madealot ofpeople veryangryandbeenwidely regarded asabadmove.
1.1. Theme of the thesis
Although the creation of the Universe made a lot of people unhappy, a specific lot among
them, called physicists were very happy. They had acquired an environment to explore and
play with. Till date, they are busy figuring out when did it start, how did it happen and
speculatingaboutitsend.
The game of guessingabout the origin of the Universe and speculating about its end is very
complex and it falls under the broad topic of cosmology. So far, many cosmological models
have been proposed (not only by physicists but also by theologists) and many have been
falsified. Today, we have two well defined frameworks to unde