Cosmologywithweaklensing

BhuvJainUniversityofPennsylvania

DarkEnergySurveyCollaboration(withtheSPTandACTcollaborations).Atthismeeting:AlexAmon,BobArmstrong,ChihwayChang,TimEifler,

DanielGruen,EricHuff,ElisabethKrause,SimonSamuroff,MichaelTroxel,RisaWechsler

SubaruHSCandKiDScollaborationshaveongoingweaklensingsurveys.

Outline

– Cosmology,January2019

– Lensingdatavectorsandsensitivitytocosmology

– Systematicsandmodelingchallenges

– ‘Smallscale’lensing

CMBpowerspectra

Powerspectraoftemperatureandpolarizationfluctuations.PlanckCollaboration2018

IsΛCDM the right model?

Surelookslikeit…withintheerrorbars,foronecombinationofgrowth&geometryPlanckCollaboration2018

Low-zSupernovaevs.otherprobesofH0

Themostsignificanttensionincosmologytoday! PlanckCollaboration2018

Highzvs.Lowz:matterfluctuations

Over2-sigmatensionusing2018resultsfromHSC,KiDS,DES.Wecoulduseafactorof2improvementonthegalaxyside!PlanckCollaboration2018

�7

17

LRG

vsW

iggleZ

BAO

vsSN

CFHTLen

SvsKiD

S

HvsHSL

CMBTT

vsCMBL

CMBEE

vsCMBL

CMBTE

vsCMBL

CMBTTTEEE

vsCMBL

lowlvsCMBTT

lowlvsCMBEE

lowlvsCMBTE

lowlvsCMBTTTEEE

CMB

vsBG

CMB

vsW

L

CMB

vsH0

CMB

vsGC

BG

vsGC

GC

vsW

L

BG

vsW

L

P4

P3

P2

P1

1 � P1

1 � P2

1 � P3

sign

ifica

nce

Confirmation

Tension

5%

95%

5%

95%

MAP log-likelihood di↵erenceP (QDMAP > Q

obsDMAP)

update parameter shiftsP (QUDM > Q

obsUDM)

1D rule of thumbP (T1 > T

obs1 )

1D exactP (T1 > T

obs1 )

FIG. 5. The statistical significance of di↵erent CDEs for various data set couples: the di↵erence in log-likelihood at maximumposterior (MAP), QDMAP from Eq. (52), the update parameter shifts test, QUDM from Eq. (53), the exact 1D parameter shifts,T1 from Eq. (39), and the “rule of thumb di↵erence in mean”, as the Gaussian approximation of T1 from Eq. (40). Di↵erentcolors indicate di↵erent tests, as shown in legend. The labels report di↵erent levels of statistical significance: P1 ⌘ 32%,P2 ⌘ 5%, P3 ⌘ 0.3%, P4 ⌘ 0.007%. Values that are identified as failure modes of one of the estimators are not shown in figure.The darker shade indicates results that are not statistically significant.

observed value of the update parameter shift we need toevaluate:

QUDM ⌘ (�✓̄U )T (Cp1 � Cp12)�1 (�✓̄U ) . (54)

The second data set can only add information on top ofthe first data set so that (Cp1 � Cp12) has to be positivedefinite in the absence of numerical noise. In the pres-ence of numerical noise, it is better to first transform tothe KL basis since it is mutually orthogonal in the met-rics defined by Cp1 and Cp12. We solve the generalizedeigenvalue problem to find the KL modes, �

a, of the twocovariances:

X

⌫

Cµ⌫p1 �

a⌫ = �

aX

⌫

Cµ⌫p12 �

a⌫ . (55)

Here the eigenmodes are defined to be orthonormal inthe Cp12 metric

X

µ⌫

�a

µ Cµ⌫p12�

b⌫ = �

ab, (56)

and since they are orthogonal in the Cp1 metric, but withvariance �

a�

ab, the KL basis provides linear combina-tions of the parameters that are mutually independent

and ordered by the improvement in the variance of 12over 1. If we now define the linear combination of pa-rameter di↵erences in the KL basis as

�pa =

X

µ

�a

µ �✓̄µU (57)

we obtain

QUDM ⌘NKLX

a=1

(�pa)2

�a � 1. (58)

While this transformation, when NKL is the full set of KLmodes, gives exactly the same value as Eq. (54), it alsohighlights the problem of numerical noise. If 12 does notimprove over 1 substantially in a given mode, then �

a ⇡ 1and numerical noise in the estimation of covariances cre-ate large errors in QUDM. The KL decomposition allowsus to place a well defined lower cuto↵ on this improve-ment in order to remove unwanted numerical noise fromthe estimator. In practical applications there is a hierar-chy of KL modes so that noise and data modes are wellseparated in the spectrum. We use a simple algorithm tofind this separation point and define the optimal cuto↵

14

Data set Ne↵ N

CMBTT 14.3 21

CMBEE 8.1 13

CMBTE 7.9 15

CMBL 2.5 7

SN 3.0 8

BAO 3.1 6

LRG 2.5 6

WiggleZ 1.9 6

CFHTLenS 1.8 7

KiDS 1.8 7

TABLE II. The number of e↵ective parameters, Ne↵ , and thenumber of nominal parameters, N , for the di↵erent data setsthat we consider.

Gaussian priors [38]. CMB lensing has four uncon-strained parameters ⌧ , ns, ⌦bh

2 and a calibration pa-rameter. A combination of the other cosmological pa-rameters, mainly As and ⌦ch

2, is well constrained by thelensing amplitude whereas the directions constraining theshape of the potential are only partially constrained. SNconstrain three parameters, the total matter density ⌦m

and two nuisance parameters, the intrinsic supernovaecolor and stretch. The BAO data set constrains threeparameters as it includes redshift space distortions mea-surements, so that only ⌧ and ns are unconstrained whileAs is mostly unconstrained. The LRG and WiggleZ datasets constrain slightly more than two parameters, thatare combinations of ⌦m, ⌦b and H0, thanks to the detec-tion of the BAO feature in the matter power spectrum.Both CFHTLenS and KiDS constrain two parameters,the amplitude of the weak lensing signal and the ampli-tude of intrinsic alignment. The latter, while not beingdetected, is slightly constrained over the prior and thusenters in degree of freedom counting.

The number of e↵ective parameters that combinationsof these data sets constrain is consistent with what wewould expect from these results. Notice that no physicalknowledge was input to get the results of Table II thatautomatically and accurately recover the physical resultsto a fraction of a parameter.

We can now turn to the probabilities associated withthe values of QMAP in the various cases, as displayedin Fig. 3. In applying these estimators to the data wecannot use the lowl and HSL data sets as their likelihoodis not Gaussian in the data points. We have to excludethe H data set as the full data likelihood is not providedand we just have the parameter likelihood.

As we can see from both Fig. 3 and Table V theCMBTT, CMBEE, CMBL, SN, BAO, WiggleZ data setare a reasonable fit to the data showing no tension norconfirmation at high statistical significance. The CMBLresult showcases the use of the maximum posterior as agoodness of fit measure. This data set has no irrelevant

parameters and if we were to count all its parameters asbeing optimized this would indicate the presence, at a5% probability to exceed, of tensions. Since the ⇤CDMmodel cannot use all its nominal parameters due to thepriors, it is actually still a good fit to the CMBL data.

The CMBTE data set in turn is not a good fit at highstatistical significance. The result is stable against degreeof freedom counting since the goodness of fit, in this case,is dominated by the number of data points in the fit.Since, as noted in [38], the coadded frequency spectrumis a good fit we suspect that this result is dominatedby frequency dependent rather than cosmological e↵ects,e.g. foreground and systematics modeling, especially inthe 100 GHz ⇥ 217 GHz and 100 GHz ⇥ 100 GHz spectrathat have been highlighted in [38], at about the samestatistical significance.

The full CMB goodness of fit is dominated by the TEresults, whose statistical significance gets diluted by theincreased number of data points in the joint data set.The results for the CMBTTTEEE data set further con-firms this showing that the discrepancy in the fit cannotbe attributed to CMBL measurements. Moreover, thegoodness of fit results for all data sets joined together(ALL) is dominated too by CMB results since this is thedata set with the largest number of data points.

At slightly lower statistical significance we find thatthe CFHTLenS and KiDS data sets are a bad fit and thegoodness of fit of their union further confirms this at highstatistical significance. Notice that this result is partic-ularly worrisome since both data sets are cut at linearcosmological scales and thus should not be influenced bythe, possibly improper, modeling of non-linearities. Thestatistical significance of the goodness of fit to the jointWL data set is only slightly lower than the product ofthe single data sets, showing that the bad fits are almostindependent. These results could be, at least in the caseof the KiDS data set, due to lack of modeling of sur-vey geometry in the covariance, as reported in [58]. Thesame explanation does not apply to CFHTLenS whosecovariance was obtained through simulations.

At a statistical significance that is borderline betweensignificant and not significant we find that the LRG dataset is confirmation biased. Notice that, in this case,proper degree of freedom counting is crucial to the as-sessment of such e↵ects. If we were to assume that thisdata set measures all ⇤CDM parameters this result willnot be statistically significant. If we further assume thatthe two bias parameters that have been marginalized overare also constrained by the data, the statistical signifi-cance of confirmation bias would decrease becoming 96%for Ne↵ = 3.5 and 93% for Ne↵ = 4.5.

Finally we notice that the BG data set is a good fit,while being dominated by the SN data set that has moredata points with respect to the BAO one. The same ef-fect is seen for the GC data set where the statistical sig-nificance of confirmation in LRG measurements is over-weighted by the number of data points in the WiggleZdata set.

Tensionsincosmology

RaveriandHu2018

FromtheCMBtothelow-zuniverse

The universe was pretty different at last scattering! WMAP website

Whatnewphysicscouldresolvethetensions?

– Unusual dark energy properties – Early universe: new species or interactions – Modified gravity – ??

Whatnewdataanalysescouldsharpenorresolvethetensions? -2-pointcorrelationswithbiggerskycoverage -Bettermodeling! -Beyond2-pointcorrelations?Designerstatistics?

Whatotherphysicsisaccessibletoupcomingsurveys? -Darkmatter:awideopentopic? -Astrophysicsonavarietyofscales,e.g. *gas,light,massdistributionofclusters *galaxy‘bias’ *Debrisdisks,OortcloudsandPlanetX(Baxter+2018a,b)

– Cosmology, January 2019

– Lensing and sensitivity to cosmology

– Systematicsandmodeling challenges

– ‘Smallscale’lensing

Lensing formalism: metric perturbations

Lensingformalism:shear

�12

Observable effects arise from second derivatives of the lensing potential. Let’s set the two potentials equal and switch to projected quantities on the sky. We can describe all lensing phenomena via the scalar convergence κ and complex shear γ. Denoting derivatives via indices i,j:

Lensingbylarge-scalestructure

SeetalksongalaxyshearestimationandCMBkappamapping

Galaxysurveys:DESlensingmassmap

Chang et al. DES collaboration(2017)

DarkEnergySurvey:Year1massmap26milliongalaxiesover~1300sqdegrees(fullsurvey5000sqdeg).

�15

CMBlensing

CMBlensingtopicsdiscussedatthismeetingincludetestsofgravityanddelensing.SeetalksbyKimmyWu,NeelimaSehgal,SukhdeepSingh&CMBsessionsonWednesday

Galaxysurveys:Shear2-pointfunctions

Shear2-pointcorrelations.ApproachingS/N~100.Seetalksthisafternoonandtomorrow.Troxel+(DESCollaboration)2017;Hikage+(HSC)2018Hildebrandt+(KiDS)2017,Koehlinger+(KiDS)2018

Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0 7

Fig. 1. Tomographic cosmic shear power spectra of EE (red filled circles), BB (blue open triangles), and EB (yellow crosses) modes. The galaxy samples aredivided into four tomographic redshift bins using the Ephor AB photo-z code. The redshift ranges of the four tomographic bins are set to [0.3, 0.6], [0.6, 0.9],[0.9, 1.2], and [1.2,1.5], for binning number 1 to 4 (see also Table 1). The right-bottom panel shows the non-tomographic cosmic shear power spectrum.The multipole ranges of ` < 300 and ` > 1900 (shaded regions) are excluded in the cosmological analysis. The combined total detection significance of thetomographic EE-auto spectra is 16� in the range of 300 < ` < 1900 (unshaded regions), whereas both BB and EB-mode spectra are consistent with zero.

10% of the current statistical errors at least over the range of` of interest, 80 < ` < 2000. We also confirm that the inputvalues of ⌦m, �8, and S8 are successfully recovered from themock catalogs. Specifically, from the analysis of the mock cat-alogs we obtain ⌦m = 0.292± 0.014, �8 = 0.801± 0.020, andS8 = 0.791± 0.005, which are consistent with the input val-ues, ⌦m = 0.279, �8 = 0.82, and S8 = 0.791 to within the 68%credible interval. The credible intervals (error bars) are roughly1/

p100 of the accuracy we can achieve with the HSC first year

shear catalog.

We note that the cosmic shear (E-mode) power spectrum isrelated to the shear correlation functions ⇠+ and ⇠� as

⇠±(✓) =1

2⇡

Zd`` C`J0,4(`✓), (7)

where Jn(x) is the n-th order Bessel function of the first kind.While mathematically the cosmic shear power spectrum carriesthe same information as the shear two-point correlation func-tions for a full-sky uniform survey, this is not exactly true infinite-sky data. In addition, the covariance of the power spec-trum is diagonal in Gaussian fields, whereas the covarianceof the two-point correlation functions contains significant non-diagonal elements even for Gaussian fields. Since the Gaussianerror still dominates in the current cosmic shear measurements,the statistical independence is high among different ` modes.

3.2 Blinding

We have entered an era of precision cosmology. With a grow-ing number of cosmological probes, one has to carefully guard

�17

A History of Cosmic Shear

!15

7 OBSERVATIONAL RESULTS AND COSMOLOGICAL CONSTRAINTS 41

2006 2008 2010 2012 2014

year

0.5

0.6

0.7

0.8

0.9

1.0

1.1

�8(⌦

m/0.

3)↵

COSMOS100 deg2

CFHTLS/CFHTLenSSDSS-Stripe82DLSSDSS-DR7CMB

Figure 7. Mean and 68% error bars for the parameter �8 (⌦m/0.3)↵, for various cosmic shear

observations, plotted as function of their publication date (first arXiv submission). All parametervalues are given in Table 7.1. Di↵erent surveys are distinguished by colour as indicated in thefigure. Data points are shown for second-order statistics (circles), third-order (diamonds), 3D lensing(pentagons), galaxy-galaxy lensing (+ galaxy clustering; triangle), and CMB (squares).

et al. 2000, Van Waerbeke et al. 2000, Wittman et al. 2000). The observations were taken with

di↵erent cameras and telescopes — the Prime Focus Imaging Camera (PFIC) on the William-Herschel

Telescope (WHT), UH8K and CFH12K on the Canada-France Hawaii Telscope (CFHT), and the

Big Throughput Camera (BTC) on Blanco — and covered sky areas between 0.5 and 1.5 deg2. These

early analyses measured correlations of galaxy ellipticities that were larger than the expected residual

systematics. Limits on ⌦m and �8 could be obtained.

Those exploratory results were very soon followed by other surveys from a wide range of

telescopes, for example CFH12K/CFHT with the Red-sequence Cluster Survey (RCS) and VIRMOS-

DESCART (Van Waerbeke et al. 2001, Van Waerbeke et al. 2002, Hoekstra et al. 2002b, Hoekstra

et al. 2002c, van Waerbeke et al. 2005), FORS1 (FOcal Reducer and Spectrograph)/VLT (Very Large

Telescope; Maoli et al. 2001), the 75-deg2 survey with BTC/Blanco-CTIO (Jarvis et al. 2003, Jarvis

et al. 2006), PFIC/WHT (Massey et al. 2005), ESI (Echelle Spectrograph and Imager)/Keck II

(Bacon et al. 2003), WFI at MPG/ESO 2.2m with the Garching-Bonn Deep Survey (GaBoDS;

Hetterscheidt et al. 2007), and Suprime-Cam/Subaru (Hamana et al. 2003).

Cosmic shear then was measured using MegaCam/CFHT on the Canada-France Hawaii Legacy

Survey (CFHTLS). During five years this large program observed 170 square degrees in five optical

bands. First results from the first data release were published over 22 deg2 of the wide part (Hoekstra

et al. 2006) and the 3 out of the 4 deg2 of the deep part (Semboloni et al. 2005).

Apart from those ground-based observations, cosmic shear was successfully detected with the

2016 2018

DESKiDS

area, depth, analysis techniques, size of collaboration, error bars (?!)

Kilbinger (2015)

S8 ⌘ �8(⌦m/0.3)0.5<latexit sha1_base64="NgxRAJ8lNxYf4ELJ5NJEVK1bSrQ=">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</latexit><latexit sha1_base64="NgxRAJ8lNxYf4ELJ5NJEVK1bSrQ=">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</latexit><latexit sha1_base64="NgxRAJ8lNxYf4ELJ5NJEVK1bSrQ=">AAACFnicdZDLSgMxFIYzXmu9VV26CRahLhwz1kvdiW7cqWit0Kklk57WYDIzJhmhDPMUbnwVNy4UcSvufBvTWkFFD4T8fP85JOcPYsG1IeTdGRoeGR0bz03kJ6emZ2YLc/NnOkoUgyqLRKTOA6pB8BCqhhsB57ECKgMBteBqv+fXbkBpHoWnphtDQ9JOyNucUWNRs7B60kwrGfbhOuE32Ne8I2mPlPxDCR0rZbZG3PLKRUrczaxZKNqLeDtbBBOX9KsvKl7Zw96AFNGgjpqFN78VsURCaJigWtc9EptGSpXhTECW9xMNMWVXtAN1K0MqQTfS/loZXrakhduRsic0uE+/T6RUat2Vge2U1Fzq314P/uXVE9OuNFIexomBkH0+1E4ENhHuZYRbXAEzomsFZYrbv2J2SRVlxiaZtyF8bYr/F2frrkdc73ijuLs3iCOHFtESKiEPbaNddICOUBUxdIvu0SN6cu6cB+fZeflsHXIGMwvoRzmvH150njY=</latexit><latexit sha1_base64="NgxRAJ8lNxYf4ELJ5NJEVK1bSrQ=">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</latexit>

‘Tomography’:theevolutionofS8

Chang+(DESC)2018

HSC

Galaxy-CMB combined probes

δ(galaxypositions)γ(galaxyshears)κ(CMBlensing)

6possible2ptfunctions:<δδ><γγ><γδ><δκ><γκ><κκ>

Wemeasuretwo-pointcorrelationfunctionbetweentwofieldsasafunctionofangularseparation,θ:

DEScombinedprobes3x2-pointcorrelations:ElisabethKrausetalk

�19

5x2pt Basic Idea Cosmic shear

Galaxy clustering

Galaxy-galaxy lensing

Shear-CMB lensing cross-correlation

Galaxy-CMB lensing cross-correlation

Galaxy shapes: metacal

Galaxy positions: redmagic

CMB convergence: SPT+Planck

ThesearecombinedwithPlanck’stemperatureandpolarizationpowerspectra.

DES+SPT+PlanckanalysispaperswithY1data:Krause+2017,MacCrann+,Prat+,Elvin-Poole+,Troxel+,Baxter+,Omori+,DEScollaboration2017,2018

Nextup:DESY3data,withSPT+ACT+Planck.

Jointprobescosmology

�20

13

0.24 0.32 0.40 0.48�m

0.72

0.80

0.88

0.96

S 8�

�8(

�m/0

.3)0.

5

�CMB�CMB

5�2pt6�2pt

FIG. 4. Marginalized constraints on ⌦m and S 8 ⌘ �8(⌦m/0.3)0.5

for di↵erent combinations of correlation functions in the context of⇤CDM+⌫ cosmology: 5⇥2pt (gold), wCMBCMB (gray) and 6⇥2pt(purple). The wCMBCMB contours are derived from the Planck 2015lensing data [21]. The 5⇥2pt contours are identical to those in Fig. 2.The wCMBCMB constraints are complementary to those of the 5⇥2ptanalysis.

allows us to ignore covariance between the 5⇥2pt data vec-tor and the CMB lensing autospectrum. This simplificationcomes at no reduction in cosmological constraining power.Furthermore, the SPT+Planck and Planck-only measurementsof the CMB lensing autospectrum are consistent [68].

Ignoring the covariance between the 5⇥2pt data vector andthe Planck CMB lensing autospectrum measurements is justi-fied for several reasons. First, the CMB lensing auto-spectrumis most sensitive to large scale structure at z ⇠ 2, at signif-icantly higher redshifts than that probed by the 5⇥2pt datavector. Second, the instrumental noise in the SPT CMB tem-perature map is uncorrelated with noise in the Planck CMBlensing maps. Finally, and most significantly, the measure-ments of the 5⇥2pt data vector presented here are derived fromroughly 1300 deg2 of the sky, while the Planck lensing au-tospectrum measurements are full-sky. Consequently, a largefraction of the signal and noise in the Planck full-sky lensingmeasurements is uncorrelated with that of the 5⇥2pt data vec-tor. We therefore treat the Planck CMB lensing measurementsas independent of the 5⇥2pt measurements in this analysis.

The cosmological constraints from Planck lensing au-tospectrum measurements alone are shown as the grey con-tours in Fig. 4. The constraints from the 5⇥2pt analysisand those of the Planck lensing autospectrum overlap in thistwo dimensional projection of the multidimensional posteri-ors. We find an evidence ratio of log10 R = 4.1 when eval-uating consistency between the 5⇥2pt data vector and thePlanck lensing autospectrum measurements, indicating “de-

cisive” preference on the Je↵reys scale for the consistencymodel.

When using the PPD to assess consistency, we set D2 equalto wCMBCMB (✓) and set D1 equal to the 5⇥2pt data vector. Thep-value computed from the PPD is determined to be p = 0.09;there therefore no significant evidence for inconsistency be-tween the 5⇥2pt and wCMBCMB measurements in the context of⇤CDM. The distributions of the test statistic for the data andrealizations are shown in Fig. 6 in the Appendix.

F. Combined constraints from 5⇥2pt and the Planck lensing

autospectrum

Having found that the cosmological constraints from the5⇥2pt and Planck lensing analyses are statistically consistent,we perform a joint analysis of both datasets, i.e. of the 6⇥2ptdata vector. The constraints resulting from the analysis of thisjoint data vector are shown as the purple contours in Fig. 4(constraints on more parameters can be found in Section D).

As seen in Fig. 4, the DES+SPT+Planck 5⇥2pt analysisyields cosmological constraints that are complementary to theauto-spectrum of Planck CMB lensing, as evidenced by thenearly orthogonal degeneracy directions of the two contoursin ⌦m and S 8. When combining the constraints, we obtain forthe 6⇥2pt analysis:

⌦m = 0.271+0.022�0.016

�8 = 0.800+0.040�0.025

S 8 = 0.776+0.014�0.021.

The constraints on ⌦m and S 8 are 25% and 24% tighter, re-spectively, than those obtained from the 3⇥2pt analysis ofDES-Y1-3x2. The addition of Planck lensing provides ad-ditional constraining power coming from structure at higherredshifts than is probed by DES.

VII. DISCUSSION

We have presented a joint cosmological analysis of two-point correlation functions between galaxy density, galaxyshear and CMB lensing using data from DES, the SPT-SZsurvey and Planck. The 5⇥2pt observables — w�g�g (✓), ⇠±(✓),w�g�(✓), w�gCMB (✓), and w�tCMB (✓) — are sensitive to both thegeometry of the Universe and to the growth of structure outto redshift z . 1.3.4 The measurement process and analysishas been carried out using a rigorous blinding scheme, withcosmological constraints being unblinded only after nearly allanalysis choices were finalized and systematics checks hadpassed.

4 The cross-correlations with CMB depend on the distance to the last scatter-ing surface at z ⇠ 1100 through the lensing weight of Eq. 3. This sensitivityis purely geometric, though, and does not reflect sensitivity to large scalestructure at high redshifts.

12

0.20 0.24 0.28 0.32 0.36�m

0.60

0.75

0.90

1.05

S 8�

�8(

�m/0

.3)0.

5

5�2pt wide m prior3�2pt wide m prior5�2pt3�2pt

FIG. 3. Marginalized constraints on ⌦m and S 8 ⌘ �8(⌦m/0.3)0.5

for the 3⇥2pt (gray) and 5⇥2pt (gold) combinations of correlationfunctions in the context of ⇤CDM+⌫ cosmology when priors onmultiplicative shear bias are relaxed (filled contours). In this case,the cosmological constraints obtained from the 5⇥2pt data vector aresignificantly tighter than those resulting from the 3⇥2pt data vector.The dashed contours show the constraints when the fiducial priors onmultiplicative shear bias (see Table I) are applied.

Sample 3⇥2pt bi 5⇥2pt bi

0.15 < z < 0.30 1.42+0.13�0.08 1.41+0.11

�0.11

0.30 < z < 0.45 1.65+0.08�0.12 1.60+0.11

�0.09

0.45 < z < 0.60 1.60+0.11�0.08 1.60+0.09

�0.10

0.60 < z < 1.75 1.93+0.14�0.10 1.91+0.11

�0.11

0.75 < z < 1.90 2.01+0.13�0.14 1.96+0.15

�0.11

TABLE II. Constraints on the linear galaxy bias parameters, bi, fromthe 3⇥2pt and 5⇥2pt data vectors for the five redshift samples.

and multiplicative shear bias. For the fiducial DES-Y1 priorson multiplicative shear bias from DES-Y1-3x2, the degener-acy breaking is weak since multiplicative shear bias is alreadytightly constrained using data and simulation based methods,as described in [42]. However, if these priors are relaxed, the5⇥2pt analysis can obtain significantly tighter cosmologicalconstraints than the 3⇥2pt analysis. In essence, the cosmo-logical constraints can be made more robust to the e↵ects ofmultiplicative shear bias.

The 3⇥2pt and 5⇥2pt constraints on⌦m and S 8 when priorson multiplicative shear bias are relaxed to mi 2 [�1, 1] areshown in Fig. 3. In contrast to Fig. 2, the 5⇥2pt constraintsare significantly improved over 3⇥2pt when the multiplicativeshear bias constraints are relaxed.

For these relaxed priors, the data alone calibrate the multi-

Sample 3⇥2pt mi 5⇥2pt mi

0.20 < z < 0.43 �0.03+0.34�0.16 0.03+0.25

�0.15

0.43 < z < 0.63 �0.02+0.27�0.14 0.07+0.19

�0.11

0.63 < z < 0.90 �0.04+0.20�0.15 �0.01+0.13

�0.09

0.90 < z < 1.30 �0.02+0.18�0.17 �0.08+0.14

�0.08

TABLE III. Constraints on the shear calibration parameters, mi, fromthe 3⇥2pt and 5⇥2pt data vectors when priors on mi are relaxed. Inall cases, the posteriors obtained on the mi from the 5⇥2pt analysisare consistent with the priors adopted in the 3⇥2pt analysis of [9].

plicative shear bias. The resultant constraints on the shear cal-ibration parameters are shown in Table III. These constraintsare consistent with the fiducial shear calibration priors shownin Table I. In other words, we find no evidence for unac-counted systematics in DES measurements of galaxy shear.

We have also performed similar tests for other nuisanceparameters such as photo-z bias and IA. However, the ef-fect of self-calibration for these other parameters tends to besmaller than for shear calibration. As shown in B18, thisis because shear calibration, galaxy bias, and As are part ofa three-parameter degeneracy. Consequently, the 3⇥2pt datavector cannot tightly constrain these parameters without exter-nal priors on shear calibration. For the other systematics pa-rameters, however, such strong degeneracies are not present,and significant self-calibration can occur. Consequently, forthese parameters, adding the additional correlations with CMBdoes not add significant constraining power beyond that of the3⇥2pt data vector.

E. Consistency with Planck measurements of the CMB lensing

autospectrum

While the 5⇥2pt data vector includes cross-correlations ofgalaxies and galaxy shears with CMB lensing, it does not in-clude the CMB lensing auto-spectrum. Both the 5⇥2pt datavector and CMB lensing auto-spectrum are sensitive to thesame physics, although the CMB lensing auto-spectrum issensitive to higher redshifts as a result of the CMB lensingweight peaking at z ⇠ 2. Consistency between these twodatasets is therefore a powerful test of the data and the as-sumptions of the cosmological model.

Measurements of the CMB lensing autospectrum over the2500 deg2 patch covered by the SPT-SZ survey have been ob-tained from a combination of SPT and Planck data by [25],and this power spectrum has been used to generate cosmolog-ical constraints by [68]. Because of lower noise and higherresolution of the SPT maps relative to Planck, the cosmolog-ical constraints obtained in [68] are comparable to those ofthe full sky measurements of the CMB lensing autospectrumpresented in [21], despite the large di↵erence in sky coverage.

In this analysis, we choose to test for consistency betweenthe 5⇥2pt data vector and the Planck-only measurement of theCMB lensing autospectrum. The primary motivation for thischoice is that it significantly simplifies the analysis because it

WithDESY1,jointanalysiswithCMBenablestestsofcalibration,

DEScollaboration2018

13

FIG. 4. Marginalized constraints on ⌦m and S 8 ⌘ �8(⌦m/0.3)0.5

for di↵erent combinations of correlation functions in the context of⇤CDM+⌫ cosmology: 5⇥2pt (gold), wCMBCMB (gray) and 6⇥2pt(purple). The wCMBCMB contours are derived from the Planck 2015lensing data [21]. The 5⇥2pt contours are identical to those in Fig. 2.The wCMBCMB constraints are complementary to those of the 5⇥2ptanalysis.

allows us to ignore covariance between the 5⇥2pt data vec-tor and the CMB lensing autospectrum. This simplificationcomes at no reduction in cosmological constraining power.Furthermore, the SPT+Planck and Planck-only measurementsof the CMB lensing autospectrum are consistent [68].

Ignoring the covariance between the 5⇥2pt data vector andthe Planck CMB lensing autospectrum measurements is justi-fied for several reasons. First, the CMB lensing auto-spectrumis most sensitive to large scale structure at z ⇠ 2, at signif-icantly higher redshifts than that probed by the 5⇥2pt datavector. Second, the instrumental noise in the SPT CMB tem-perature map is uncorrelated with noise in the Planck CMBlensing maps. Finally, and most significantly, the measure-ments of the 5⇥2pt data vector presented here are derived fromroughly 1300 deg2 of the sky, while the Planck lensing au-tospectrum measurements are full-sky. Consequently, a largefraction of the signal and noise in the Planck full-sky lensingmeasurements is uncorrelated with that of the 5⇥2pt data vec-tor. We therefore treat the Planck CMB lensing measurementsas independent of the 5⇥2pt measurements in this analysis.

The cosmological constraints from Planck lensing au-tospectrum measurements alone are shown as the grey con-tours in Fig. 4. The constraints from the 5⇥2pt analysisand those of the Planck lensing autospectrum overlap in thistwo dimensional projection of the multidimensional posteri-ors. We find an evidence ratio of log10 R = 4.1 when eval-uating consistency between the 5⇥2pt data vector and thePlanck lensing autospectrum measurements, indicating “de-

cisive” preference on the Je↵reys scale for the consistencymodel.

When using the PPD to assess consistency, we set D2 equalto wCMBCMB (✓) and set D1 equal to the 5⇥2pt data vector. Thep-value computed from the PPD is determined to be p = 0.09;there therefore no significant evidence for inconsistency be-tween the 5⇥2pt and wCMBCMB measurements in the context of⇤CDM. The distributions of the test statistic for the data andrealizations are shown in Fig. 6 in the Appendix.

F. Combined constraints from 5⇥2pt and the Planck lensing

autospectrum

Having found that the cosmological constraints from the5⇥2pt and Planck lensing analyses are statistically consistent,we perform a joint analysis of both datasets, i.e. of the 6⇥2ptdata vector. The constraints resulting from the analysis of thisjoint data vector are shown as the purple contours in Fig. 4(constraints on more parameters can be found in Section D).

As seen in Fig. 4, the DES+SPT+Planck 5⇥2pt analysisyields cosmological constraints that are complementary to theauto-spectrum of Planck CMB lensing, as evidenced by thenearly orthogonal degeneracy directions of the two contoursin ⌦m and S 8. When combining the constraints, we obtain forthe 6⇥2pt analysis:

⌦m = 0.271+0.022�0.016

�8 = 0.800+0.040�0.025

S 8 = 0.776+0.014�0.021.

The constraints on ⌦m and S 8 are 25% and 24% tighter, re-spectively, than those obtained from the 3⇥2pt analysis ofDES-Y1-3x2. The addition of Planck lensing provides ad-ditional constraining power coming from structure at higherredshifts than is probed by DES.

VII. DISCUSSION

We have presented a joint cosmological analysis of two-point correlation functions between galaxy density, galaxyshear and CMB lensing using data from DES, the SPT-SZsurvey and Planck. The 5⇥2pt observables — w�g�g (✓), ⇠±(✓),w�g�(✓), w�gCMB (✓), and w�tCMB (✓) — are sensitive to both thegeometry of the Universe and to the growth of structure outto redshift z . 1.3.4 The measurement process and analysishas been carried out using a rigorous blinding scheme, withcosmological constraints being unblinded only after nearly allanalysis choices were finalized and systematics checks hadpassed.

4 The cross-correlations with CMB depend on the distance to the last scatter-ing surface at z ⇠ 1100 through the lensing weight of Eq. 3. This sensitivityis purely geometric, though, and does not reflect sensitivity to large scalestructure at high redshifts.

andimprovedparameterconstraints(jointlywithPlanckof):

– Cosmology, January 2019

– Lensing data vectors and sensitivity to cosmology

– Systematicsandmodeling challenges

– ‘Smallscale’lensing

Modeling• Smallscales

– Imageanalysis

– Higherorder‘corrections’

– Intrinsicalignments

– Baryons

– HOD

• Galaxybias• Simulationsandmocks• Predictionsandcovariancesforothermodels

– Simsandmocksvsanalyticalapproximations?

• Covariancesforjointprobes• Priorsandotheringredientsneededforcomparingandcombiningdatasets

• Alargefractionoftalksareonthekeysystematics!

Priors,scalecuts,covariance,andmore…consistencyinshear2-pointanalyses!Baseline vs. Unified

A Unified Analysis of Four Cosmic Shear Surveys 13

0.2 0.4 0.6 0.8

�m

0.45

0.60

0.75

0.90

1.05

S8

Baseline

DLSCFHTLenSDES-SVKiDS-450

Figure 6. Here we compare the constraints of the four surveys from the published results and the WLPIPE reanalysis. We show the marginalized constraintson Wm and S8 ⌘ s8(Wm/0.3)0.5 from the paper-provided chains (the Published Baseline case, left panel) and from WLPIPE in the Baseline case. Note thatcompared to the Published Nominal results, here the KiDS-450 contours do not include baryonic effects, while the CFHTLenS contours do not include anysystematic uncertainties.

Table 4. Comparison metrics for all pairs of surveys in the Published Base-line analysis case: constraints from the individual collaborations that wechoose as baseline to reproduce. For the S8 values, we list the mean and the16% and 84% confidence intervals. For CFHTLenS and KiDS-450, theseare different from the Published Nominal analysis case: constraints fromthe individual collaborations that can be viewed as the representative re-sults.

(1) DLS (2) CFHTLenS (3) DES-SV (4) KiDS-450

S8 0.818+0.030�0.030 0.731+0.030

�0.030 0.813+0.059�0.058 0.727+0.033

�0.032DS8-(1) – 2.1 0.076 2.1DS8-(2) – – 1.2 0.087DS8-(3) – – – 1.3

that in the data configuration used in the individual surveys, theraw statistical power of the measurement is similar for DLS andCFHTLenS, while DES-SV is about half the S/N and KiDS-450 isin between. One interesting observation is that DLS achieves thehigh S/N even with a significantly smaller area – this highlightsthe power of having high-redshift data. A slightly worrying point isthat the goodness-of-fits for DLS and CFHTLenS are quite low. Forthe pair-wise DS8, we find trends reflecting what is seen from thefigures – all four surveys are broadly consistent with Table 3 show-ing some low-level discrepancies (1.5s ) in S8 between CFHTLenSand DLS.

For the Published Baseline chains, we list the S8 constraintsand DS8 values in Table 4. We do not list the goodness-of-fit heresince they are not all available in the papers, and are not directlycomparable with the values in Table 3. We just quote two num-bers that available: in Joudaki et al. (2017a), the reduced c2 for thefiducial CFHTLenS analysis best-fit is 1.5, whereas in Hildebrandtet al. (2017), the reduced c2 for the fiducial KiDS-450 analysis

Table 5. S8 constraints, S/N and goodness of fit when we change one anal-ysis choice at a time in the analysis pipeline from the Baseline case (seeTable 3). For the S8 values, we list the mean and the 16% and 84% con-fidence intervals. The sections of this table correspond to discussions inSec. 5.2, Sec. 5.3 and Sec. 5.4.

(1) DLS (2) CFHTLenS (3) DES-SV (4) KiDS-450

Gaussian covariance matrix (Sec. 5.2)S8 0.845+0.030

�0.030 0.739+0.024�0.025 0.834+0.052

�0.050 0.767+0.030�0.030

S/N 26.0 22.2 12.7 20.4c2/n 412.5/235 344.3/275 34.6/30 133.0/124p.t.e. 7.0⇥10�12 0.0028 0.26 0.27

Conservative scale cuts (Sec. 5.3)S8 0.928+0.050

�0.050 0.731+0.052�0.050 0.799+0.068

�0.069 0.754+0.055�0.055

S/N 15.4 16.6 10.0 10.5c2/n 112.1/89 228.3/132 28.4/25 62.8/56p.t.e. 0.050 4.0⇥10�7 0.29 0.24

DES-SV priors (Sec. 5.4)S8 0.851+0.042

�0.042 0.657+0.052�0.052 0.803+0.059

�0.058 0.764+0.038�0.038

c2/n 319.5/235 412.2/275 26.9/30 121.5/124p.t.e. 2.0⇥10�4 1.6⇥10�7 0.63 0.55

KiDS-450 priors (Sec. 5.4)S8 0.818+0.033

�0.033 0.677+0.039�0.039 0.807+0.059

�0.059 0.771+0.033�0.033

c2/n 323.6/235 412.5/275 27.0/30 122.2/124p.t.e. 1.1⇥10�4 1.5⇥10�7 0.63 0.53

best-fit is 1.3. In Troxel et al. (2018), it was shown that the reducedc2 for the fiducial KiDS-450 improves to 1.0 when accounting forthe survey geometry.

MNRAS 000, 000–000 (0000)

A Unified Analysis of Four Cosmic Shear Surveys 17

0.2 0.4 0.6 0.8

�m

0.45

0.60

0.75

0.90

1.05

S8

Published Nominal

DLSCFHTLenSDES-SVKiDS-450

0.2 0.4 0.6 0.8

�m

0.50

0.75

1.00

1.25

1.50

�8

0.2 0.4 0.6 0.8

�m

0.45

0.60

0.75

0.90

1.05

S8

DLSCFHTLenSDES-SVKiDS-450

Matched (i)

0.2 0.4 0.6 0.8

�m

0.50

0.75

1.00

1.25

1.50

�8

Figure 11. Final comparison of the cosmological constraints from the four surveys according to the literature (Published Nominal, left) and according to ourunified analysis framework (right, Matched) – we show the marginalized constraints for Wm, S8 ⌘ s8(Wm/0.3)0.5 and s8 for the four cosmic shear surveys. Inthe right panel, we use Gaussian analytic covariances, conservative scale cuts and the KiDS-450 priors. We note that for the CFHTLenS Published Nominalconstraints, we show all three settings MIN (solid), MID (dashed) and MAX (dotted) in Joudaki et al. (2017a).

Figure 12. Same as the upper right panel of Fig. 11, but now using DES-SVpriors.

Table 6. Comparison metrics corresponding to the right panel of Fig. 11.That is, all analysis choices matched: Gaussian COSMOLIKE covariancematrix, conservative scale cuts, same IA treatments, and KiDS-450 cosmo-logical priors. For the S8 values, we list the mean and the 16% and 84%confidence intervals.

(1) DLS (2) CFHTLenS (3) DES-SV (4) KiDS-450

S8 0.942+0.046�0.045 0.657+0.071

�0.070 0.844+0.062�0.061 0.755+0.048

�0.049S/N 17.4 15.1 11.6 12.1c2/n 137.8/89 176.3/132 32.7/26 71.5/56p.t.e. 7.0⇥10�4 0.0060 0.17 0.079DS8-(1) – 3.4 1.3 2.9DS8-(2) – – 2.0 1.1DS8-(3) – – – 1.2BF-(1) – -1.1 1.6 -0.50BF-(2) – – 0.70 1.3BF-(3) – – – 1.1

tics is similar to that captured by the DS8 metric in this case, thoughthe message of consistency/inconsistency is somewhat weaker – the

MNRAS 000, 000–000 (0000)

!35OngoingexerciseinmodelingchoicesbytheWLcommunityChang+(DESC)2018

6x2ptFunctions:Issues

• SZcontaminationofCMBlensingmaps• CosmicInfraredBackground• Smallscaleissues• RealvsFourierspace• SPT,ACT+Planck• +Allthe3x2ptissues

�24

– Cosmology, January 2019

– Lensing data vectors and sensitivity to cosmology

– Systematicsandmodeling challenges

– ‘Smallscale’lensing

Sphericalinfall

• (some)Matterinfallingonto(some)galaxyclustersisstillreachingturnaround:splashback

• Isthatanaturalboundaryforclusterhalos?• Isituseful?

– halomassdefinition

– galaxy‘formation’:quenching…

– newphysicssuchasdarkmatterinteractions

Splashback in simulations

Dashed circle: radius at which accreted matter reaches apocenter Diemer, Kravtsov; More et al; Adhikari et al

More et al 2016; Baxter et al 2017; Chang et al 2017: https://arxiv.org/abs/1702.01722 ; 1710.06808

Halo profile: light and mass

Galaxy profile

Lensing profile

HaloProfileModel

Simulation based model from Diemer & Krastov (2014) model

Is there a halo boundary <-> Is the ftrans term = 1?

Miscentering model from matching optical and X-ray data

Lensing

�29

Truncationof1-haloprofile

Splashback in light vs. mass

- Haveweobservedatruephase-spaceboundary?Yes

- Dogalaxiesandmasstrackeachother?~Yes.

- IsitattheradiusexpectedinCDMhalos??Notinthiscase…20%smaller

- Whatnewphysicscanwetestattheboundary?

Changetal2017

Splashback: SZ vs optical clusters

Shin+ (DES/SPT/ACT Collaboration) 2018

Galaxyinfallandphasespace

Apowerlawprofileforbluegalaxiesisconsistentwithrecentlyaccretedsubhalos,iethattheyarequenchedinlessthantheclustercrossingtimeShin+ (DES/SPT/ACT Collaboration) 2018

Splashback: models and cosmology

Adhikari et al 2018

Modifiedgravitydependence:complicated,dynamicalfrictionispromising

Darkenergydependence:weak,percentlevelAnalyticalmodelworkswell

Voidlensing

�34

VoidFinding:2Dand3D

• VoidfinderinSanchezetal2016:searchforunderdensitiesin2Dgalaxyfields:• Itprojectstracergalaxiesinaredshiftsliceof

thicknessof100Mpc/hontoaHEALpixmap.• Foreachslice,itcomputesthetracerdensity

contrastmapandsmoothsitwithaGaussianfilter.

• Foreachslice,startwiththemostunderdensepixelanddefineitasthefirstvoidcenter.growacircularshellaroundthatpixeluntilthedensity->meandensity…+2moresteps!

• VoidFinding:3D– PubliclyavailablevoidfinderVIDE

(Sutteretal.,2014):

Voids:massandlight

�36

Lineargalaxybiasconsistentwithmeasuredgalaxyandlensingprofiles.Forscales>Rvoid/2andforallvoidswith10<Rvoid<60Mpc/hFang+(DES),inpreparation

Barreira+2016andBaker+2018showedthatsomegravitymodelscanbetestedwith10percentlevelvoidlensingmeasurements,becausevoidsevadescreening.Comparisonofgalaxies(halos)andlensingisespeciallyuseful.

Galaxyprofile

Shearprofile

Preliminary

Troughs,Peaks,andmore

• Higherordercorrelations• Peaks,densitysplitstatistics,topology,…• Theoreticalworkaimedatsurveysneeded!

�37

7

101 102

� [arcmin]

�2

�1

0

1

2

� t

⇥10�3

quintile 5

quintile 4

quintile 3

quintile 2

quintile 1

101 102

� [arcmin]

�2

�1

0

1

2

� t

⇥10�3

quintile 5

quintile 4

quintile 3

quintile 2

quintile 1

(a)split by density, zs = 0.63 � 0.90, ✓T = 200

(b)split by source redshift, ✓T = 200, top/bottom quintile only

(c)split by smoothing scale, zs = 0.63 � 0.90, top/bottom quintile only

FIG. 3. Shear signal around overdense and uncerdense lines of sight in DES Y1, split by line-of-sight density quintile (top row), source redshiftzs (central row) from BPZ run on METACALIBRATION (left) and MOF (right) photometry, and aperture radius (bottom panel). Our fiducial datavector is the shear around the most underdense and most overdense quintile of ✓T = 200 lines of sight as seen by sources in zs = 0.63� 0.90.Left-hand panels: measurements with METACALIBRATION shears. Right-hand panels: measurements with IM3SHAPE. Error bars are from 100jackknife resamplings of the survey, consistent with our model covariance (section IV). Dotted lines indicate model prediction at maximumlikelihood parameters (section VI) and are a good fit to the data (�2 = 171 (METACALIBRATION) and 201 (IM3SHAPE) for ⇡ 200 d.o.f., asdetermined only after unblinding).

Gruen+,Friedrich+2018

Surveysofthe2020’s

�38

• Measurement:shear,photozestimationandmore.• Simulations:modelpredictionsforDMandgravitytheories• Theoryandmodeling:newmodels;nonlinearregime;detailed

implementationof‘beyond2-point’statistics;covariances…• FigurefromAndrinaNicola