non‐gaussianity in the cmb: primordial and...

39
Non‐Gaussianity in the CMB: primordial and secondary Kendrick Smith University of Cambridge Los Cabos, Jan 2009 References: Smith, Hu and Kaplinghat astro‐ph/0607315 Smith and Zaldarriaga astro‐ph/0612571 Smith, Zahn, Dore and Nolta arxiv:0705.3980 Smith et al arxiv:0811.3916 Dvorkin and Smith arxiv:0812.1566 Smith, Senatore and Zaldarriaga to appear Senatore, Smith and Zaldarriaga to appear

Upload: hoangminh

Post on 10-Apr-2018

227 views

Category:

Documents


4 download

TRANSCRIPT

Page 1: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Non‐GaussianityintheCMB:primordialandsecondary

KendrickSmithUniversityofCambridgeLosCabos,Jan2009

References:

Smith,HuandKaplinghatastro‐ph/0607315SmithandZaldarriagaastro‐ph/0612571Smith,Zahn,DoreandNoltaarxiv:0705.3980Smithetalarxiv:0811.3916DvorkinandSmitharxiv:0812.1566Smith,SenatoreandZaldarriagatoappearSenatore,SmithandZaldarriagatoappear

Page 2: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Outline

1.  Secondarynon‐Gaussianity:gravitationallensinghowarethestatisticsoftheCMBaffected?whatcosmologicalinformationisadded?

2.Secondarynon‐Gaussianity:reionizationanewstatisticwhichisolatestheepochofpatchyreionization

3.Primordialnon‐Gaussianitywhatsignalscanonelookfor?newresultsfromWMAP(firstoptimalanalysis)

Page 3: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Part 1: CMB lensing

CMB photons are deflected by gravitational potentials between last scattering and observer. This remaps the CMB while preserving surface brightness:

!T (!n)! !T (!n + d(!n))where is a vector field giving the deflection angle along line of sight

!n

Deflection angles Unlensed CMB Lensed CMB

d(!n)

!"+

WayneHu

Page 4: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

To first order, the deflection field is a pure gradient:

where the lensing potential is given by the line-of-sight integral

Redshift kernel: broad peak at z ~ 2 RMS deflection: ~2.5 arcmin, coherent on degree scales (l ~ 100)

CMB acquires sensitivity to new parameters (e.g. neutrino mass)

da(!n) = !a!(!n)

!(!n) = !2" !!

0d"

#"! ! "

""!

$!("!n, #0 ! ")

CMB lensing: theory

AntonyLewis

d(!n)

Page 5: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

CMB lensing: power spectrum

Gravitationallensingappearsintemperatureandpolarization,butpolarizationismoresensitive

B‐modepolarizationisgenerated

Page 6: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

CMB lens reconstruction: idea

Idea: from observed CMB, reconstruct deflection angles (Hu 2001)

Lensed CMB Reconstruction + noise

!n

Deflection angles Unlensed CMB Lensed CMB

!"+

!"!n

Page 7: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

CMB lens reconstruction: quadratic estimator

Lensing potential weakly correlates Fourier modes with

Formally: can define estimator which is quadratic in CMB temperature:

Intuitively: use hot and cold spots of CMB as local probes of lensing potential (analagous to cosmic shear: galaxy ellipticities are used as probes)

l != l!

!!(l)

Lensed CMB Reconstruction + noise

!"!n

!T (l) T (l!)"" # [$l! · (l$ l!)]!(l$ l!)

!!(l) !"

d2l1(2")2

[(l · l1)Cl1 + (l · l2)Cl2 ]T (l1)T (l2)Ctot

l1Ctot

l2

(l2 = l" l1)

Page 8: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

CMBlensreconstruction:higher‐pointstatistics

Lensreconstructionnaturallyleadstohigher‐pointstatistics

e.g.takeCMBtemperatureT (n)! !!(l) (applyquadraticestimator)

! !C!!"

(takepowerspectrum)

defines4‐pointestimatorintheCMB

Or:takeCMBtemperature,galaxycounts

! !C!g"

g(n)T (n)! !!(l) (applyquadraticestimator)

(takecrosspowerspectrum)Defines(2+1)‐pointestimatorinthe(CMB,galaxy)fields

Canthinkofthelensingsignalformallyasacontributiontothe3‐pointor4‐pointfunction,butlensreconstructionismoreintuitive

Smithetal,0811.3916

Page 9: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

CMBlensing:lensreconstructionvspowerspectrum

ConsidertwomethodsforextractingCMBlensingsignal:

1.measureCMBpowerspectralensingmakessomecontribution,unlensedspectraactas“noise”2.measurepowerspectrumoflenspotential(4‐pointinCMB)withinreconstructionnoise(powerspectrum)

CTT! , CTE

! , CEE! , CBB

!

C!!"

Secondmethodhasbettersignal‐to‐noiseandismoreflexible

e.g.CMBlensingdetectioninWMAP3:

N!!"

CTT! :lensingis“detected”at0.3sigma

C!!" :1sigma

C!g" :3.5sigma(g=NVSSgalaxycounts)

Smithetal,0811.3916

Page 10: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

NVSS: NRAO VLA Sky Survey

1.4 GHz source catalog, 50% complete at 2.5 mJy

Mostly extragalactic sources: AGN-powered radio galaxies Quasars Star-forming galaxies

Well-suited for cross-correlating to WMAP lensing potential: Nearly full sky coverage Low shot noise High median redshift

(fsky = 0.8)(Ngal = 1.8! 106)(zmedian = 0.9)

Page 11: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

WMAP3-NVSS result with systematic errors

Detection significance: fit in one large bandpower, in multiple of fiducial model

Result: 1.15 +/- 0.34, i.e. a 3.4 sigma detection, in agreement with the expected level

Smith,Zahn,Dore&Nolta,0705.3980

Page 12: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

CMBlensreconstruction:futureprospects

C!!" Issensitivetolate‐universeobservablessuchas:

neutrinomassdarkenergyequationofstatecurvature

(forecastsforanall‐skypolarizationsatellite)

Needhigh‐resolutionCMBmeasurements:manyexperimentsonhorizon(SPT,ACT,Planck,Polarbear…)

Probeslargeangularscalesathighredshift(e.g.earlydarkenergy)

Smithetal,0811.3916

Page 13: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Outline

1.  Secondarynon‐Gaussianity:gravitationallensinghowarethestatisticsoftheCMBaffected?whatcosmologicalinformationisadded?

2.Secondarynon‐Gaussianity:reionizationanewstatisticwhichisolatestheepochofpatchyreionization

3.Primordialnon‐Gaussianitywhatsignalscanonelookfor?newresultsfromWMAP(firstoptimalanalysis)

Page 14: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Part2:reionizationandtheCMB

HowdoesreionizationaffecttheCMB?Considerhomogenousreionizationfirst(i.e.,x_e=functionofzonly)

Dvorkin&Smith,0812.1566

1.Screening:overallamplitudeofCMBpowerspectrum=Ase!2!

Createsdegeneracy:hardertomeasureA(tauactsas“nuisanceparameter”)Conversely,ifdegeneracycanbebroken,canconstrainreionization(e.g.WMAP5:)! = 0.087± 0.017

2.NewpolarizationfromThomsonscatteringafterreionization:GeneratesE‐modepeakat(horizonsize)thatcanbreakdegeneracy! ! 8

3.Dopplereffect:contributestolarge‐scaletemperatureanisotropyMostlycancelsalongline‐of‐sightsincev=“puregradient”tolowestorder

Page 15: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

ReionizationandtheCMB:patchyreionization

Considerareionizationbubblewithopticaldepthandradialvelocityvr

WhatCMBanisotropydoesthebubblegenerate?!bub

Zahnetal(2005)

!T (n) = !!bubT (n)![Q± iU ](n) = !!bub(Q± iU)(n)

!T (n) = !!bub(vr/c)

!(Q± iU)(n) = (!bub)!

610

2!

m=!2

±2Y2m(n)T2m(z,n)

1.Screening:

3.kSZ:

2.“Thomson”:

Page 16: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Patchyreconstruction:quadraticestimator?

Idea:ifreionizationispatchy,theopticaldepthisafield,notaconstant!(n)

Canwewritedownaquadraticestimator!!(l) (“taureconstruction”)analogoustotheestimator? (“lensreconstruction”)

Lensreconstruction“works”becauselensinggeneratesanisotropywhichlooks(heuristically)like()x(unlensedCMB):

!!(l)

Question:Doespatchyreionizationgenerateanisotropyofthesameform,withreplacedby?

!

Tlensed = Tunlensed + (!!) · (!Tunlensed) + · · ·(Q ± iU)lensed = (Q ± iU)unlensed + (!!) ·!(Q ± iU)unlensed + · · ·

! !

Page 17: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Anisotropygeneratedbythescreeningeffecthasform()x(unlensedCMB)=>screeningeffectis“captured”byquadraticestimatorformalism

Heuristically:amplitudeofrecombinationpeaksismodulatedbytau(regionofskywithlargertau=>lowerobservedacousticpeaks)

Patchyreconstruction:quadraticestimator?

1.Screeningeffect

!T (n) = !!(n)T (n)![Q± iU ](n) = !!(n)(Q± iU)(n)

!

Page 18: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Heuristically:large‐scaleE‐modefromreionizationismodulatedbytau(regionofskywithlargertau=>largerreionizationE‐mode)

GeneratesB‐modes,butmuchsmallerthanlensingatpowerspectrumlevel

Dvorkin&Smith,0812.1566

Patchyreconstruction:quadraticestimator?

2.Thomsonscattering(polarizationonly)

AnisotropygeneratedbyThomsonscatteringhasform()x(unlensedCMB)=>Thomsonscatteringis“captured”byquadraticestimatorformalism

!(Q± iU)(n) =!

610

!d!(n)

dz

2"

m=!2

±2Y2m(n)T2m(z,n)

" !(n)!0

(Q± iU)reion(n)

!

Page 19: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

ThekSZanisotropyisaline‐of‐sightintegral:

!T (n) = !1c

!dz

d!

dzvr(z,n)

Zahnetal(2005)

kSZfromreionizationcontributestothesmall‐scaletemperaturepowerspectrum

Patchyreconstruction:quadraticestimator?

3.kSZ(temperatureonly)

AnisotropygeneratedbykSZdoesnothaveform()x(unlensedCMB)=>kSZisnot“captured”byquadraticestimatorformalism

!

Page 20: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Patchyreionization:Quadraticestimator

Conclusion:screeningandpolarizedThomsoneffectscanbeusedtoconstructaquadraticestimatorfor(mathisthesameaslensreconstruction,butwithdifferentl‐weighting)

Fromhere,onecanconstructestimatorsasinthelensingcase:

!!(l) = (2-point in CMB fields T,E,B)!C!!

" = (4-point in CMB fields)!C!X

" = ((2+1)-point in CMB + cross-correlation field X)

Dvorkin&Smith,0812.1566

!(n)

Page 21: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Quadraticestimator:exaggeratedexample

Dvorkin&Smith,0812.1566

Page 22: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Quadraticestimator:signal‐to‐noise

Ideasforimprovingthesignal‐to‐noise:1.cross‐correlatewithothertracersofreionization2.combinewithlensreconstructiontojointlysolvefortauandphi

Dvorkin&Smith,0812.1566

Temperature Polarization

Page 23: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Parameterforecastsinatoyreionizationmodel

Twoobservables:Amplitudeofthepowerspectrumisdeterminedby

LocationofpeakisdeterminedbythetypicalbubbleradiusR

Ahigh‐sensitivitysatelliteexperimentcanconstrainbothatthe~10%level

Dvorkin&Smith,0812.1566

Page 24: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

ReionizationandtheCMB:conclusion

TwomethodsforextractingreionizationinformationfromCMB:1.kSZfromsmall‐scaletemperaturepowerspectrum2.quadraticestimator

Complementarystrengthsandweaknesses:

1.“sees”kSZ,butnotscreeningorpolarizedThomsonexperimentalsensitivityalreadyexists(SPT/ACT)probesreionizationbubblesonsmallscalespowerismixedwithothersecondaries,modelinguncertainty

2.“sees”screeningandpolarizedThomson,butnotkSZmorefuturistic,requireslow‐noisepolarizationprobestaufluctuationsonlargescalesisolatespatchysignal,mapcanbecross‐correlated,orusedfor“cleaning”

Unsolvedproblem:findstatistictoisolatethekSZsignalintemperature!

(2000 ! ! ! 4000)!!

(! = Drec/Rbub ! 300)

(2000 ! ! ! 4000)

Page 25: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Outline

1.  Secondarynon‐Gaussianity:gravitationallensinghowarethestatisticsoftheCMBaffected?whatcosmologicalinformationisadded?

2.Secondarynon‐Gaussianity:reionizationanewstatisticwhichisolatestheepochofpatchyreionization

3.Primordialnon‐Gaussianitywhatsignalscanonelookfor?newresultsfromWMAP(firstoptimalanalysis)

Page 26: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Part3:Primordialnon‐Gaussianity

In“vanilla”modelsofinflation,theinitialfluctuationsareGaussianThe3‐pointcorrelationfunctionfunctioniszero:

!!(k1)!(k2)!(k3)" = 0However,moreexoticmodelscanpredictnonzerothree‐pointfunctions“Local”shape:e.g.curvatonmodel

!(x) = !G(x) + f localNL !G(x)2

!!(k1)!(k2)!(k3)" # f equil.NL

!3"

i=1

k1 + k2 + k3 $ 2ki

k3i

#"3(

$

i

ki)

!!(k1)!(k2)!(k3)" # f localNL

!1

k31k

32

+ symm."

"3

#$

i

ki

%

“Equilateral”shape:higher‐derivativeinteractions,DBIinflation

Page 27: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Arethesetheonlyshapestolookfor?

Thetwocubicoperatorsdonotgenerate3‐pointfunctionswhicharepreciselyequal:

!(k1, k2, k3)k31k

32k

33k

3t

!

"k3t ! kt

#

$%

i<j

kikj

&

'! 3k1k2k3

(

) +12! 8!

k1k2k3k3t

Canorthogonalizethefamilyofbispectraparameterizedby

kt = k1 + k2 + k3

!(k1, k2, k3) = (kt ! 2k1)(kt ! 2k2)(kt ! 2k3)

Effectivefieldtheoryofinflation(Cheungetal2007):

!

Page 28: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Anew“folded”shape

Thereisa“window”atwhereanewshapeappears

Localshape:“squeezed”triangles()containthesignal‐to‐noiseEquilateralshape:equilateraltriangles()Foldedshape:“foldedtriangles”

Considercorrelationcoefficientwithequilateralshape,asfunctionof:

Senatore,SmithandZaldarriaga(toappear)

!

!1 ! !2, !3!1 ! !2 ! !3

(!1 + !2) ! !3

! ! 5.1

AnalysisinWMAP5forthcoming

Page 29: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Moregeneralshapeanalysis?

Powerspectrumanalogue:onecouldeither1.estimateC_l’sinl‐bins2.estimateP(k)ink‐bands3.estimateinflationaryparameters(n_s,running,….)

Bispectrum:analogously,onecouldeither:1.estimateb_{l1,l2,l3}inlbins2.estimateF(k1,k2,k3)inkbins3.estimatefnlparameters

Sofar,only#3hasbeenperformedonWMAPdata,but#1+2wouldbepossibleusingourmachinery

….Isthereagoodtheoreticalmotivationfordoingthis?

Page 30: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Three‐pointfunctionintheobservedCMB

Non‐gaussianinitialconditionsfrominflation+lineartransferfunctions=non‐GaussianCMB

f localNL = 0 f local

NL = 3000

MicheleLiguori

Optimalestimator:sumovertriples(l1,l2,l3)withinversesignal‐to‐noiseweighting

!T (l1)T (l2)T (l3)" # fNL!2

!"

i

li

#

Page 31: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

WMAPanalysis:background

f localNL = 32± 34

f localNL = 87± 30

Creminellietal(WMAP3)

Arobustdetectionwouldruleoutmostmodelsofinflation!(e.g.slow‐roll)Whichanalysisshouldbebelieved?

Yadav&Wandelt(WMAP3!!)

Komatsuetal(WMAP5)f localNL = 55± 30

Page 32: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Reasonforthediscrepancy:“step”atl=450

Q‐band(40GHz)

V‐band(60GHz)

W‐band(90GHz)

Yadav&Wandelt(2007)

Mustbecarefultoavoidmakingaposteriorichoices….!

UseofV+WismotivatedaprioriUseoflmax=750isnot

Page 33: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Problem:haveestimatesoffnlwithdifferentvaluesbutcomparablestatisticalerrors

Generalprinciple:inthissituation,either1.haveevidenceforsystematics2.estimatorissignificantlysuboptimal

e.g.(Creminellietal,WMAP3,lmax=350)(Yadav&Wandelt,WMAP3,lmax=750)

Isthisshiftbetweenandconsistentwithstatistics?

Ifso,oneshouldbeabletoreweighttheestimatorsothataddingthesmallscalesimprovesbymorethan4

Questions:1.Arethelargeandsmallscalesconsistent?(i.e.dotheygiveaconsistent?)2.AreWMAP3andWMAP5consistent?

f localNL = 32± 34

f localNL = 87± 30

!max = 350 !max = 750

!(f localNL )

Page 34: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Motivationforoptimalestimator:

1.smallererrorbars(forWMAP5)2.eliminatearbitrarychoices:differentimplementationsshouldagreeprecisely3.cannotgetmultipleestimateswithcomparableerrors;getsingle“bottomline”estimateforagivendataset

Optimalestimator

d! (S + N)!1d

!(f localNL ) = 21

Page 35: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Results:WMAP5optimalanalysis

WMAP5 optimal: !4 < f localNL < 80 (95% CL)

WMAP5 suboptimal: !11 < f localNL < 121 (95% CL)

+SDSS (Slosar et al 2008): !1 < f localNL < 61 (95% CL)

Smith,SenatoreandZaldarriaga(toappear)

Page 36: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Results:arethelargeandsmallscalesconsistent?

Quantifythisbydefining:

!fNL = !fNL(!max = 750)! !fNL(!max = 350)

Insimulation:!fNL = 19 (at 1!)

!fNL = 52

InWMAP3,wefind:

!fNL = 32!fNL = 20 (optimalestimator)

(suboptimal)somedisagreementw/Yadav‐Wandelt(2007):

InWMAP5,wefind:!fNL = 9 (optimalestimator)

(suboptimal)!fNL = 16withgoodagreementwithKomatsu(2008)

Smith,SenatoreandZaldarriaga(toappear)

Page 37: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Results:areWMAP3andWMAP5consistent?

Define:Wefind:(optimalestimator)(suboptimal)

Insimulation:,soWMAP3andWMAP5areconsistent

!fNL = !fNL(WMAP5)! !fNL(WMAP3)!fNL = !20!fNL = !25

!fNL = 16 (at 1!)

Smith,SenatoreandZaldarriaga(toappear)

Page 38: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Speculation:whataboutthehighsignificanceinWMAP3?

Yadav&Wandelt(2007):2.9sigma,Ourpipeline:2.3sigma,(suboptimalestimator)2.5sigma,(optimal)

Probabilityofa2.5sigmaresultbychance:1.25%Canwereally“dismiss”thehighsignificanceinseenWMAP3?

Howmanyequally“interesting”parameterscouldwehavelookedfor?

Inaddition,mighthavefoundsomethinginWMAP1‐only,orinWMAP5‐only….

Nowconsider:whathappenswhenweaddmoredata?WehaveinWMAP3Supposeisreally56;thenweexpecttogetinWMAP5SupposeWMAP3isstatisticalfluke;thenweexpectashifttowardzero….

f localNL , f equilateral

NL , r, w0,!K , (dns/d ln k), !0, !!1

!f localNL = 87

!f localNL = 69

!f localNL = 56

!f localNL = 56

f localNL f local

NL ! 56

Page 39: Non‐Gaussianity in the CMB: primordial and secondarybccp.berkeley.edu/beach_program/presentations09/CATBsmith.pdf · Non‐Gaussianity in the CMB: primordial and secondary ... CMB

Primordialnon‐Gaussianity:systematictests‐large‐scaleforegrounds:‐small‐scaleforegrounds:negligible‐pointsources:negligible‐three‐pointfunctionfromsecondaries:

Primordialnon‐Gaussianity:conclusions‐Systematicsseemcompletelyundercontrol!‐Firstimplementationofoptimalestimator:reducesfrom30to21‐Eliminatesarbitrarychoiceswhichcomplicateinterpretationofresults‐Wecurrentlyfindjustunder2sigma

f localNL ! few (conservativegalacticmask,aftercleaning)

f localNL ! few (largest:ISW‐lensing)

!(f localNL )

f localNL

!4 < f localNL < 81 (WMAP5)

!1 < f localNL < 61 (WMAP5+Sloan)