CMBlensingandfuturepolarizationexperiments

KendrickSmithChicago,July2009

Mainreference:K.Smith,A.Cooray,S.Das,O.Dore,D.Hanson,C.Hirata,M.Kaplinghat,B.Keating,M.LoVerde,N.Miller,G.Rocha,M.Shimon,O.Zahn(arxiv:0811.3916)

CMBlensing:introduction

CMBphotonsaredeflectedbygravitationalpotentialsbetweenlastscatteringandobserver.ThisremapstheCMBwhilepreservingsurfacebrightness:

whereisavectorfieldgivingthedeflectionanglealonglineofsight

Deflectionangles UnlensedCMB LensedCMB

d(!n)

!"+

WayneHu

!T (n)lensed = !T (n + d(n))unlensed

(Q± iU)(n)lensed = (Q± iU)(n + d(n))unlensed

CMBlensing:E‐modepowerspectrum

Lensingsmoothstheacousticpeaksandaddspowerinthedampingtail(butisnotalargeeffectintheE‐modespectrum)

Linearevolution+scalarsources‐>E‐modes

!ab =!!a!b "

12gab!2

"!“Gradient‐like”modeinpolarization!ab

reionization

recombination

peak:40(uK)^2

CMBlensing:B‐modepowerspectrum

Non‐scalarsources(e.g.GWbackgroundparameterizedbytensor‐to‐scalarratior)ORnonlinearevolution‐>B‐modes

“Curl‐like”modeinpolarization!ab !ab =12

(!ac!b + !bc!a)!c"

GravitationallensingislargestguaranteedB‐mode(second‐ordereffect)CanthinkoflensingasconvertingprimaryE‐modetomixtureofEandB

reionizationbump(l=8)

recombinationbump(l=60)

peak:0.1(uK)^2(!)

CMBlensing:deflectionfield

AntonyLewis

da(!n) = !2"a

" !!

0d!

#!! ! !

!!!

$!(!!n, "0 ! !)Nocurlcomponent:

Radialkernelinline‐of‐sightintegralisbroadlypeakedatz~2Powerspectrumbroadlypeakedatl~40,RMSofdeflectionfield=2.5arcmin

“Degree‐sizedlensescarryingarcminute‐sizeddeflections,sourcedbyLSSatz~2”

Outline

1.LensreconstructionestimatorsAgeneralframeworkforconstructinghigher‐pointstatisticsforlensing

2.CosmologicalinformationfromCMBlensingNeutrinomass,darkenergy,spatialcurvature

3.GravitationallensingasacontaminantofthegravitywaveB‐modeProspectsfor“delensing”

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

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

!!(l) !"

d2l1(2")2

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

l1Ctot

l2

(l2 = l" l1)

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

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

CMB lens reconstruction: WMAP-NVSS analysis

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

Systematic errors were found to be small

Smith,Zahn,Dore&Nolta,0705.3980 (seealsoHirataetal2008)

CMBlensreconstruction:futureprospects

Weareenteringanerawherehigh‐resolutionCMBexperimentswill“contain”lensingexperiments

Polarizationisultimatelymoresensitivethantemperature(becauseofB‐mode)

BeyondthelensingB‐mode:patchyreionization

ReionizationbubblesgenerateB‐modes:

Viascattering(dominatesonlargescales)

Viascreening(largereffectonsmallscales)

Dvorkin,Hu&Smith0902.4413

Dvorkin&Smith,0812.1566

Canconstructquadraticestimatortoreconstructbubbles(analogoustolensreconstruction,withdeflectionfieldreplacedbyopticaldepth)

da(n)!!(n)

Outline

1.LensreconstructionestimatorsAgeneralframeworkforconstructinghigher‐pointstatisticsforlensing

2.CosmologicalinformationfromCMBlensingNeutrinomass,darkenergy,spatialcurvature

3.GravitationallensingasacontaminantofthegravitywaveB‐modeProspectsfor“delensing”

ConsidertheWMAPsix‐parameterspace:

AngulardiameterdistancedegeneracyinunlensedCMB

{!bh2,!mh2, As, !, ns,!!}

First5parametersarewell‐constrainedthroughshapeofpowerspectrum

Constraintoncomesentirelythroughangularpeakscale:!!

angulardiameterdistancetorecombinationdistancesoundcantravelbeforerecombination

SupposethatN“lateuniverse”parametersareadded.

Thenonlyonecombination(correspondingto)isconstrainedbytheCMB

GeneratesN‐fold“angulardiameterdistancedegeneracy”inparameterspace

(!K , m! , w, wa, . . .)

!a = "D!s!

!"!"

D!

CMBlensingbreakstheangulardiameterdistancedegeneracy

ExamplefromHu2001:w=‐1andw=‐2/3modelswithsameD!

UnlensedtemperaturepowerspectrumDeflectionanglepowerspectrum

Neutrinomass

Neutrinooscillationexperimentsmeasurebetweenspecies!m2!

!m231 = (0.049 eV± 0.0012)2Currentcombinedanalysisofworlddata:

!m221 = (0.0087 eV± 0.00013)2

Cosmologyiscomplementary:lensingpotentialismainlysensitiveto!

!

m!

Smithetal,0811.3916

Darkenergy

Inmanyparameterizations(e.g.constant‐w),CMBlensingconstrainsdarkenergyweaklybecauseredshiftkernel(peakedatz~2)ispoorlymatchedtoredshiftswheredarkenergyisimportant(z<~1)

Smithetal,0811.3916

Earlydarkenergy

Doran&Robbersparameterization(2006):

!!(a) =!0

! ! !e!(1! a!3w0)

!0! + (1! !0

!)a3w0+ !e

!(1! a!3w0)

Trackermodel:

z ! 0 !!(z)! !0! w(z)! w0

z !"As and

As !!(z)! !e! andw(z)! 0

DePutter,Zahn&Linder(2009)

SNAP+unlensedCMBpol SNAP+lensedCMBpol

Curvatureandjointconstraints

!

"1 0.34 !0.82

0.34 1 !0.63!0.82 !0.63 1

#

$

!m!

w

!K

CMBlensingcanbeusedforconstraininganyparameterwhichwouldbe“lost”intheangulardiameterdistancedegeneracyintheunlensedCMB

!m! w !K

Becausefulldeflectionpowerspectrumismeasured,canconstrainmultipleparameterssimultaneously

Smithetal,0811.3916

Outline

1.LensreconstructionestimatorsAgeneralframeworkforconstructinghigher‐pointstatisticsforlensing

2.CosmologicalinformationfromCMBlensingNeutrinomass,darkenergy,spatialcurvature

3.GravitationallensingasacontaminantofthegravitywaveB‐modeProspectsfor“delensing”

reionizationbump(l=8)

recombinationbump(l=60)

GravitywaveB‐modeasaprobeofinflation

Qualitativedistinctionbetweenmodelswithdetectablerandundetectablysmallre.g.incontextofsingle‐fieldinflationwithcanonicalkineticterm,

S =!

d4x!"g

"M2

Pl

2R" 1

2(!")2 " V (")

#

modelswithdetectablegravitywavesaremodelsinwhich:

energyscaleofinflationisGUT‐scale

changeininflatonpere‐foldingisPlanckscale

timepere‐foldingisafewx10^5Plancktimes

(d!)/(d log a) = (0.354 MPl)(r1/2)

(dt)/(d log a) = (9150M!1Pl )(r!1/2)

!1/4 = (3.35! 1016 GeV)(r1/4)

B‐modepowerspectraatlowl

Lensinglookslikewhitenoisewithamplitude(!P )lensing = 5.5 µK-arcmin

(!P )e!ective =!

(!P )2instrumental + (!P )2lensingCombineswithinstrumentalnoise:

Lensingbecomesdominantsourceoferrorwheninstrumentalnoise<~5.5uK‐arcmin

Deflectionangles

!"

!n

Delensing:idea

LensedCMB

!"

“Delensed”CMB

lensreconstruction

applyinverseoflens

EstimateunlensedCMB,bycombiningobserved(lensed)CMBwithstatisticalreconstructionoflens

DelensedCMBhassmallerlensedB‐modethanoriginallensedCMB=>improvedDelensingusesB‐modeobservationsonsmallscalesto“clean”thelargescales

!(r)

Forecastsfor“r”areverysensitivetoassumptionsaboutforegrounds

e.g.considersimplemode‐countingforecast:

1!(r)2

=fsky

2

!

!

(2" + 1)"

(CBB! )r=1

(CBB! )lensing + NBB

!

#2

Reionizationbumphas10timesthestatisticalweightofrecombinationbump

Quadrupolehasthesamestatisticalweightasalll>2modescombined

Wewillavoidquotingvaluesfor,willinsteadquoteforeground‐independentquantities(e.g.ratiobetweentwovaluesofwithsameforegroundassumptions)!(r)

!(r)

Improvementin“r”duetodelensing

Fornoiselevelssignificantlybetterthan5uK‐arcmin,delensingwithafew‐arcminbeamallowsoneto“beat”thenoisefloorfromlensing

Smithetal,0811.3916

“No‐go”result:cannotdelenspolarizationusingsmall‐scaletemperature

Assume(idealtemperatureexperimentuptolmax)+(idealE‐modesforalll)

Smithetal,0811.3916

“No‐go”result:cannotdelenspolarizationusinglarge‐scalestructure

Assume(idealLSSsurveyouttoredshiftzmax)+(idealE‐modesforalll)

Smithetal,0811.3916

Summary

Lensingcanbeextractedfromthesmall‐scaleCMBusinghigher‐pointstatistics

BreaksangulardiameterdistancedegeneracyinunlensedCMB,mapsgravitationalpotentialsathighredshiftonlargestscalesofuniverse

PolarizationultimatelyprovidesbetterS/Nthantemperature

DelensingthegravitywaveB‐mode:onescenariowheresmall‐scalepolarizationisrequired

Delensingallowsonetobeatthe5uK‐arcminnoisefloorfromlensing