CosmologicaltestsusinglensingandclusteringamplitudesinKiDS-1000

ChrisBlake(Swinburne)

Thescienceofcosmologyhasbeentransformedbyaremarkablegrowthindataoverthepast2decades…

… whichwehaveusedtobuildadetailedmodelofthehistoryoftheUniverse

Imagecredit:D.Aguilar,HarvardCFA

Themoststartlingdiscoveryisthatthecosmicexpansionseemstobeaccelerating!

Imagecredit:TheCosmicPerspective

Thisisthe“darkenergyproblem”:theattempttounderstandthephysicsofcosmicacceleration,anditsimplications

Thedarkenergyproblem

• TheacceleratingcosmicexpansioncannotbeproducedbyapplyingGeneralRelativitytoahomogeneousandisotropicUniversecontainingmatterandradiation

𝐺"# =8𝜋𝐺𝑐( 𝑇"#

𝐺"# =8𝜋𝐺𝑐( 𝑇"# − Λ𝑔"#

Thedarkenergyproblem

• Acceleratingexpansioncanbeproducedbyaddingacosmologicalconstantterm

• AwiderangeofdataisconsistentwithaUniversewherethecurrentenergydensityis~𝟕𝟎% cosmologicalconstantand~𝟑𝟎%matter

Whyisthisaproblem?

Λ234~ 10789𝑀<=>?@A(

• Whyistheenergydensityinthecosmologicalconstant“unnaturallylow”?[manytensofordersofmagnitudelowerthanexpectedfromquantummechanicalprocessesinvolvingstandardparticles]

• Whyaretheenergydensitiesincosmologicalconstantandmatterroughlyequaltoday? [“coincidenceproblem”]

• Isthecosmologicalconstantasignofnewphysics?

Otherexplanations?

• “AcceleratingcosmicexpansioncannotbeproducedapplyingGR toahomogeneous/isotropic Universecontainingmatterandradiation”

• Modifygravitationalphysics?[e.g.Einstein-Hilbertaction]

• Allowforeffectsofinhomogeneity?[veryhard!]

• Addextra“source”?[e.g.dynamicalscalarfield]

Let’snotworryaboutcosmologicalconstantandseekanothersolution!

Whatdoesitmeanto“modifygravity”?

• Addsomekindof“fifthforce”[tothefourwealreadyhave]

• ButwehaveextremelyaccuratelaboratoryandsolarsystemtestsofGeneralRelativity!

• Adda“screeningmechanism”whichallowsthefifthforcetovarywithenvironment

Cosmologicalobservations

Growthofperturbationswithintheexpanding

background

Homogeneousexpansionofthe

Universe

Imagecredit:Millenniumsimulation

Cosmological Analysis of BOSS galaxies 25

0.1 1.00.2 0.5 2.0z

10

20

30

dist

ance

/rd�

z

DM(z)/rd�

z

DV (z)/rd�

z

zDH(z)/rd�

z

6dFGS

SDSS MGS

SDSS DR7

WiggleZ

BOSS Galaxy DR12

BOSS Ly�-auto DR11

BOSS Ly�-cross DR11

Figure 14. The “Hubble diagram” from the world collection of spectroscopic BAO detections. Blue, red, and green points show BAO measurements of DV /rd,DM/rd, and DH/rd, respectively, from the sources indicated in the legend. These can be compared to the correspondingly coloured lines, which representspredictions of the fiducial Planck ⇤CDM model (with ⌦m = 0.3156, h = 0.6727). The scaling by

p

z is arbitrary, chosen to compress the dynamic rangesufficiently to make error bars visible on the plot. For visual clarity, the Ly↵ cross-correlation points have been shifted slightly in redshift; auto-correlationpoints are plotted at the correct effective redshift. Measurements shown by open points are not incorporated in our cosmological parameter analysis becausethey are not independent of the BOSS measurements.

presented in Table 9 and denoted as G-M et al. (2016 a+b+c). Thecombination of these three sets of results is presented at the endof Gil-Marın et al. (2016c). As before, this case is compared toour full-shape column of Table 7, approximating LOWZ to our lowredshift bin and CMASS to our high redshift bin, where the vol-ume difference factor has been taken into account. Our DM mea-surement of 1.7% in the low redshift bin and 1.8% in the high red-shift bin compares to 1.5% and 1.1%, respectively, in Gil-Marın2016 a+b+c. Regarding H(z), our measurement of 2.8% in boththe low and high redshift bins compares to 2.5% and 1.8% in Gil-Marın 2016 a+b+c. Finally our f�8 constraint of 9.5% and 8.9% inthe low and high redshift bin compares to the LOWZ and CMASSmeasurements of 9.2% and 6.0% by Gil-Marin 2016a+b+c. Onecan attribute the improvement in Gil-Marın 2016a+b+c when com-pared to our measurement to the use of the bispectrum, which hasnot been used in our analysis.

c� 2016 RAS, MNRAS 000, 1–38

Cosmologicalobservations

• Thecosmicexpansionhistoryhasbeenmeasuredwith~1%accuracyusingsupernovae andbaryonacousticoscillations

• Thecosmicgrowthhistoryhasnotyetbeenmeasuredasaccurately,butiscrucialfordistinguishingphysics

Credit:Alam etal.(2017)

Credit:Betoule etal.(2014)

Cosmologicalobservations• TherearearichvarietyofobservablesignaturesoftheclumpyUniverse…

• Clusteringofgalaxies

• Velocitiesofobjects

• Gravitationallensing

• Abundance/propertiesofobjects

• EnvironmentaleffectsImagecredit:SloanDigitalSkySurvey

Lensingandlarge-scalestructureGravitationallensingreferstothedeflectionsoflightfromdistantgalaxiesasittravelsthroughthecosmicweb…

Imagecredit:S.Colombi

Lensingandlarge-scalestructure

Clumpofmatter(unknowndensity)

Backgroundsourcesbehind

theclump

Galaxy-galaxylensing

Thesesourcesarelensed!

Galaxy-galaxylensing

Galaxy-galaxylensing

Coherenttangentialalignment

Turnintogalaxy-lensingcross-correlationfunction

projectedseparation

averagetangentialshear

(I’vealsoaddedsomenoisehere)

Galaxy-galaxylensingmeansthe“lensingofbackgroundgalaxiesaroundforegroundgalaxies”

Theamplitudeofthisfunctiontellsustheeffectofgravityonlight

Galaxiesaroundtheclump

Redshift-spacedistortion

Thesegalaxiesareinmotion!

Redshift-spacedistortion

Redshift-spacedistortion

Coherentincreaseinredshifts

Coherentdecreaseinredshifts Turninto

galaxycorrelationfunction

Apparentre

dshift-spaceseparatio

n

Apparentprojectedseparation

Resultfrom2dFGRS(Hawkinsetal.2002)

The“amountofsquashing”tellsustheeffectofgravityonvelocities

Observer

Lensingandlarge-scalestructure

Tangen

tialshe

arRe

dshift-spaceseparatio

n

Projectedseparation

Projectedseparation

Effectoftheclump’sgravityonlight(relativistic)

Effectoftheclump’sgravityonvelocities(non-relativistic)

Dothesehavetheratio

predictedbyGR??

Mathematicalinterlude…

• Tomodelgalaxymotionsandlightdeflectionsweperturbthespace-timemetric…

• Instandardgeneralrelativity,𝜓 = 𝜙.Thisisnotnecessarilythecasein“modifiedgravity”scenarios

• Wecantestthisbymeasuringthepropertiesof𝜓and𝜙 usingcosmologicalobservations

𝑑𝑠F = −𝑐F 1 + 2𝜓 ��, 𝑡 𝑑𝑡F + 𝑎(𝑡)F 1 − 2𝜙(��, 𝑡) 𝑑��F

Thesearethe“metricgravitationalpotentials”

Mathematicalinterlude…

𝑑𝑠F = −𝑐F 1 + 2𝜓 ��, 𝑡 𝑑𝑡F + 𝑎(𝑡)F 1 − 2𝜙(��, 𝑡) 𝑑��F

• Gravitationallensingissensitiveto(𝜙 + 𝜓) alongtheline-of-sight

• GrowthofstructureissensitivetoNewtonianpotential𝜓

• Weneedtomeasurebothinordertotestwhether𝜓 = 𝜙

Intriguingcurrentresults!Onlargescales:KiDS-450weaklensinganalysisfinds2-3𝜎“tension”withPlanckinpreferredvaluesof(𝜎Q, ΩS) Lensing of CMASS 11

0.1 1.0 10.0R [Mpc/h]

2

4

6

8

10

R x

∆Σ

[

Mpc

MO •

pc -2 ]

0.1 1.0 10.0R [Mpc/h]

1.0

1.5

2.0

∆Σ

mod

/∆Σ

mea

s

Reid+14, MedResReid+14, HiRes

Reid+14, cen/satSaito+16, MDR1

Saito+16, MDPL2Rodriguez-Torres+16

Alam+16

Figure 7. Comparison of the g-g lensing signal with predictions from galaxy-halo models constrained by the clustering of CMASS. Thegrey shaded region represents models drawn from the 68% confidence region for the Saito et al. (2016) MDR1 model. The “spike” inthe predictions in the right hand panel is simply cause by a downward fluctuation of the measured lensing signal at r ∼ 0.2 h−1 Mpcas can be seen in the left panel. Regardless of the methodology (SHAM or HOD), the adopted cosmology, or the resolution of theN-body simulation, models constrained by the clustering of CMASS predict a lensing amplitude that is larger by ∼ 20-40% than ourmeasurement. This is not caused by different assumptions regarding h. The measurement and model predictions both assume a comovinglength scale for R and for ∆Σ. Our code for computing ∆Σ yields the same result as an independent derivation by one of our co-authors.In Section A6 we show that CS82 lensing gives consistent results compared to SDSS. Finally, our code for computing model predictionsyields the same result as the halotools software package (Hearin et al. 2016).

0.1 1.0 10.0R [Mpc/h]

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12

R x

∆Σ

[

Mpc

MO •

pc -2 ]

z=[0.43,0.51]

Saito+16 MDR1RT+16

0.1 1.0 10.0R [Mpc/h]

2

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R x

∆Σ

[

Mpc

MO •

pc -2 ]

z=[0.51,0.57]

0.1 1.0 10.0R [Mpc/h]

2

4

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8

10

12

R x ∆Σ [

Mpc M O •

pc -2 ]

z=[0.57,0.7]

Figure 8. Redshift evolution of the CMASS g-g lensing signal compared to predictions from Saito et al. (2016) andRodrıguez-Torres et al. (2015). The Saito et al. (2016) model matches the lensing signal at low redshifts but then over-predicts thelensing signal at higher redshifts. The Rodrıguez-Torres et al. (2015) model over-predicts the lensing signal by ∼ 20-40% at all redshifts.

5.1 Systematic Effects

Could systematic effects explain the low amplitude of thelensing signal? Here we summarize and discuss the dominanteffects which could impact our measurement. Further detailson the various tests that we have performed can be foundin the Appendices.

Our dominant source of systematic uncertainty is asso-

ciated with the photo-zs of source galaxies. If the photo-zs ofsource galaxies are biased, this may lead to a bias when eval-uating the geometric factor Σcrit (Equation 3). How muchwould the photo-zs have to be wrong in order to explainFigure 7? It is difficult to give a succinct answer to this ques-tion because Σcrit responds non linearly to zS. However, togive an idea: when zL = 0.55 a 30% effect on ∆Σ requires a

MNRAS 000, 000–000 (0000)

Onsmallscales:measuredlensingsignaturearoundLuminousRedGalaxiesissignificantlylowerthanpredicted

Whetherthesediscrepanciesresultfromstatistics,systematics,astrophysicsornewcosmologicalphysicsremainstobeseen!

Hildebrandtetal.(2020) Leauthaud etal.(2017)

Kilo-DegreeSurvey(KiDS)

• Multi-band(ugri)imagingsurveyof1500degF usingtheVST’sOmegaCAM instrument (1000degF released)

• Optimizedforweakgravitationallensingmeasurements

Imagecredit:H.Hildebrandt

BaryonOscillationSpectroscopicSurvey(BOSS)

• Largestexistinggalaxyredshiftsurvey(2009-2014)targetting LuminousRedGalaxiesover10,000degF

• Excellentmeasurementsofexpansionhistoryandgrowthhistory oftheUniverse(BAOs,RSD).

Imagecredits:SloanDigitalSkySurvey

2-degreeFieldLensingSurvey(2dFLenS)

• Spectroscopicfollow-upofKiDS andotherlensingsurveysover50AATnights(Sep2014– Jan2016)

• Sampleof70,000LRGs/brightgalaxiesforcross-correlationswithweaklensingandphoto-zcalibration

Imagecredit:SamHintonImagecredit:AngelLopez-Sanchez

Overlapareas

• Analyselensing/clusteringmeasurementsinoverlapareas

BOSS2dFLenS

KiDS-1000

Redshifttomography

Splitlensesinto5tomographicbinsofwidth∆𝑧 = 0.1

Galaxy-galaxylensing

𝜃Averagetangential

ellipticity component𝑒\(𝜃)ofeachsource-lenspair

source(photo-𝑧) lens

(spec-𝑧)

De-project𝜃 → 𝑅 usinglensspec-𝑧 andconverttomasssurfacedensity∆𝛴(𝑅)

∆Σ 𝑅 = Σa 𝑧b, 𝑧c 𝑒\(𝜃) Σa 𝑧b, 𝑧c =𝑐F

4𝜋𝐺 𝜒c

1 + 𝑧b 𝜒b(𝜒c − 𝜒b)

• Lensingmeasuresthedifferentialprojectedmassdensityrelativetothebackground…

Galaxy-galaxylensing

• Onsmall(1-halo)scales< 2ℎ7hMpc,thesignalisdifficulttomodel(non-linear,stochastic,non-local)

• We“suppress”contributionsfromthesescalesusing“annulardifferentialsurfacedensity”statistics…

• Ensures𝜓lS = 0 for𝑅 = 𝑅9

𝜓lS 𝑅, 𝑅9 = ∆Σ 𝑅 −𝑅9𝑅

F∆Σ(𝑅9) 𝑅9

(wechoose𝑅9 = 2ℎ7hMpc,wemakeextensivetestsofourmethodsusingsimulations…)

Methods(fineprint)• WemeasureGGLstatistic∆Σ(𝑅),

projectedclustering𝑤n(𝑅) anduseBOSSvaluesofRSDparameter𝛽

• Weapplyphoto-𝒛 dilutioncorrectionsusingpoint-based(spec-𝑧,photo-𝑧)calibrationsample

• Weapplymultiplicativeshearbias(𝑚)-corrections

• WeuseanalyticGaussiancovarianceplusnoiseterms

• Wegeneratelensing/clusteringstatisticsusingperturbationtheorymodelmarginalizingoverbiasparameters(𝑏s, 𝑏ts)

Covarianceacrossthebinsoflensredshift,source

tomographicsampleandscale

Galaxy-galaxylensing• Projectedmassdensity,∆Σ(𝑅)

ModelisaGRpredictioncalibratedbytheclustering,containingnofreeparameters

Modeldoesnotdescribesmallscales𝑅 < 2ℎ7hMpc

• Aftersuppressionofsmallscales,𝜓lS(𝑅)

Clustering• Projectedclustering,𝑤n(𝑅)

• Aftersuppressionofsmallscales,𝜓ll(𝑅)

Amplituderatiotest

• Wenowconstructtheamplituderatiotest:

𝐸v 𝑅 =Amplitudeofgalaxy − galaxylensing

Amplitudeofgalaxyvelocities =1𝛽ΥlS(𝑅)Υll(𝑅)

=ΩS𝑓

Lensingamplitude

Projectedclusteringamplitude

Redshift-spacedistortionamplitude(fromBOSSpapers)

InGRmodels(withsomeapproximations!),𝐸v(𝑅) isscale-independent andhasa

predictedredshiftdependenceΩS/𝑓(𝑧)where𝑓 = growthrateofstructure

Amplituderatiotest

If𝐸v 𝑅 isscale-independent,wecanoptimallycombinemeasurementsforeachlensredshiftbinintoanaverage 𝐸v …

AmplituderatiotestThisisthepredictionofthePlanck(2018)CMBanalysisfor𝐸v = ΩS/𝑓

AmplituderatiotestHerearethescale-averagedKiDS-1000measurements

AssumingaflatΛCDMmodel,wefindΩS = 0.27 ± 0.04

Amplituderatiotest

Comparingtotheliterature…

KiDS-1000allows~15 − 20%measurementsin∆𝑧 = 0.1 bins

Prospectsforthefuture!

DarkEnergySpectroscopicInstrument(DESI) RubinObservatory(LSST)

• UpcomingfacilitiessuchasDESI,4MOST, LSSTand Euclidwillenhancetheprecisionofthesetestsbyafactorof10

• → Further,precisetestsofgravitationalphysics

Imagecredit:M.Chung,LBL Imagecredit:LSSTcorporation

Prospectsforthefuture!

• Fishermatrixforecastsforcurrentandfuturedatasets…

Summary

• Complementarytestsforgravitycanbeconstructedusinglarge-scalestructureand weakgravitationallensing

• NewdatasetsfromKiDS-1000,inconjunctionwithBOSSand2dFLenS,haveallowedustoperformanaccurate“amplituderatiotest”onscalesupto100ℎ7hMpc

• Thescale- andredshift-dependenceoftheresultsareconsistwithGRinaUniversewhereΩS = 0.27 ± 0.04

• UpcomingfacilitiessuchasDESI,4MOST,LSST andEuclidwillenhancetheprecisionofthesetestsbyafactorof10

Imagecredit:G.Poole

Extraslides