Precise and Accurate Measurements of Cosmological Parameters from Galaxy Clustering and ...

141 Pages·2014·3.94 MB·English

ScuoladiDottoratoinFisica,AstrofisicaeFisicaApplicata
DipartimentodiFisica
CorsodiDottoratoinFisica,AstrofisicaeFisicaApplicata
CicloXXVI
Precise and Accurate Measurements
of Cosmological Parameters from
Galaxy Clustering and Motions
SettoreScientificoDisciplinareFIS/05
Supervisore: ProfessorMarcoBERSANELLI
Co-supervisore: ProfessorLuigiGUZZO
TesidiDottoratodi:
DavideBIANCHI
ii
AnnoAccademico2013/2014
Commissionofthefinalexamination:
ExternalReferee:
ProfessorWillPERCIVAL
ExternalMember:
ProfessorSabinoMATARRESE
ExternalMember:
ProfessorStefanoBORGANI
Finalexamination:
Date21/03/2014
Universita` degliStudidiMilano,DipartimentodiFisica,Milano,Italy
ToObi-Wan
Coverillustration:
UmbertoBoccioni-Statid’animo(ciclon. 1): Quellichevanno
MIURsubjects:
FIS/05
PACS:
98.80.-k

Contents
ListofFigures ix
ListofTables xiii
Abstract xiii
Preface xvi
1 Cosmology 1
1.1 Homogeneousandisotropicmodel 1
1.2 Darkenergy(anddarkmatter) 5
1.3 Cosmologicalparameters 6
1.4 Linearperturbations 7
1.5 NewtonianlimitandJeanslength 9
1.6 Evolutionoftheperturbations 11
1.7 Overalldescription 11
1.8 Hotandcolddarkmatter 12
1.9 Growthrate 12
1.10 n-pointsstatistics 13
1.11 Bias 16
1.12 Redshiftspacedistortions(RSD) 16
2 Statistical and systematic errors in redshift-space distortion measure-
mentsfromlargesurveys 25
2.1 Simulateddataanderrorestimation 27
2.2 MeasuringRedshift-SpaceDistortions 30
2.3 Systematicerrorsinmeasurementsofthegrowthrate 35
vii
2.4 Forecastingstatisticalerrorsinfuturesurveys 43
2.5 SummaryandDiscussion 52
3 Principalcomponentanalysisofthepairwisevelocitydistributions 57
3.1 Introductiontotheprincipalcomponentanalysis 58
3.2 Measuringthepairwisevelocitydistributionfunctions 59
3.3 PCAreconstructionofthevelocityPDFs 63
3.4 Summaryanddiscussion 72
4 Towards an improved model of redshift-space distortions: a compact
bivariate Gaussian description for the galaxy pairwise velocity distri-
bution 81
4.1 ModellingRedshift-SpaceDistortions 83
4.2 TestsonSimulations 91
4.3 DiscussionandConclusions 96
4.4 Inperspective 97
5 Summary 101
A Detailsontheimplementationofthedispersionmodel 105
A.1 Definitionofthelikelihoodfunctiontoestimateβ 105
A.2 Additional systematic effect when using the deprojected correla-
tionfunction 110
B Details on modelling the overall velocity distribution as a weighted
meanoflocalvelocitydistributions 113
B.1 Derivation of the moments of the overall velocity distribution
P
asafunctionofthecentralmomentsof 113
F
B.2 Amplitudeofthelocaldistribution 115
Bibliography 117
Acknowledgments 121
viii
List of Figures
1.1 Buildingblocksofthedispersionmodel 22
2.1 Real-spacecorrelationfunctionsandbiases 31
2.2 Biasfactoroverawiderangeofseparations 33
2.3 Comparisonofthebiasvaluesmeasuredfromthesimulatedcata-
loguesasafunctionoftheirthresholdmass,M ,withthepredic-
cut
tionsoftheSMT01andT+10models. Thetopaxisalsoreportsthe
numberofparticlesperhalo,N ,correspondingtothecatalogue
cut
thresholdmass. 35
2.4 Redshift-spacecorrelationfunctions 36
2.5 Distorsionparameterβ asafunctionofthemass 38
2.6 Linearvs. linear-exponentialmodel 39
2.7 Redshift-spacecorrelationfunctionfortheMillenniummocks 42
2.8 Relativeerroronβ asafunctionofbiasandnumberdensity 46
2.9 Relativeerroronβasafunctionofvolume,biasandnumberdensity 47
2.10 Relative error on β as a function of the number density: Monre
Carlovs. Fishermatrix 48
2.11 Relativeerroronβasafunctionofthebias: MonreCarlovs. Fisher
matrix 49
3.1 Measurementsofthevelocitydistribution (v )forthecatalogue
k
P
z1M110 62
3.2 Isocontours of mean, standard deviation, skewness and kurtosis
ofthevelocityPDFs,forthecataloguesz1M110andz1M247 64
3.3 Isocontours of mean, standard deviation, skewness and kurtosis
ofthevelocityPDFs,forthecataloguesz0M110andz0M247 65
ix
x LISTOFFIGURES
3.4 PCA-eigenvaluesofthevelocityPDFs 66
3.5 FirstsixPCA-eigenvectorsofthevelocityPDFs 67
3.6 Comparison between the isocontours of the correlation function
directly measured in redshift space and those obtained via the
streamingmodel,forthecataloguez1M110 69
3.7 Comparison between the isocontours of the correlation function
directly measured in redshift space and those obtained via the
streamingmodel,forthecataloguez1M165 70
3.8 Comparison between the isocontours of the correlation function
directly measured in redshift space and those obtained via the
streamingmodel,forthecataloguez1M247 71
3.9 Comparison between the redshift-space correlation function ob-
tained by applying the streaming model to the original velocity
distributionsandthoseobtainedbyapplyingthesameprocedure
tothePCA-reconstructeddistributions(cataloguez1M110) 73
3.10 Comparison between the redshift-space correlation function ob-
tained by applying the streaming model to the original velocity
distributionsandthoseobtainedbyapplyingthesameprocedure
tothePCA-reconstructeddistributions(cataloguez1M165) 74
3.11 Comparison between the redshift-space correlation function ob-
tained by applying the streaming model to the original velocity
distributionsandthoseobtainedbyapplyingthesameprocedure
tothePCA-reconstructeddistributions(cataloguez1M247) 75
3.12 Direct measurementsofthe velocity distributionscompared with
their projection on a four-dimensional PCA-subspace (catalogue
z1M110) 76
3.13 ComponentsofthevelocityPDFswithrespecttothePCA-eigenvectors 77
3.14 Isocontours of the components of the velocity PDFs with respect
tothefirstsixPCA-eigenvectors 78
4.1 Twodimensionalsketchoftheprocedureadoptedtomeasurethe
localvelocitymoments 92
4.2 Pairwisevelocitydistributionfunctionalongthelineofsight 93
4.3 Redshift-spacecorrelationfunctions 95
4.4 Pairwisegalaxyvelocitydistributionalongthelineofsightfordif-
ferentgravitymodelsatfourdifferentredshifts 99
A.1 Meanvalueandrelativescatterofthedistortionparameterβ,asa
functionofthedensityfortwodifferentdefinitionsofthelikelihood106