CMB lensing and delensing

Anthony Challinor and Olivier Doré

Current state of the art

Planck Collaboration 2016

4,000 resolved modesS/N = 40 (power spectrum)

Where we want to be …

>105 resolved modesS/N > 300 (power spectrum)

TT/EB dominance in future

• EB particularly helpful for pol. noise < 5 μK arcmin- Polarization reconstructions less susceptible to extragalactic contamintion (e.g., tSZ) but more so to Galactic foregrounds

S/N = 40 S/N > 300

Goals for CMB lensing/delensing

• 4-pt φxφ (neutrino mass etc.)

• 3-pt φxLSS (growth of structure, dark energy, mitigation of systematics/self-calibration)

• Delensing (improve inflation constraints + Neff etc.)

• Halo lensing (cluster mass calibration at high redshift)

Issues addressed in this session

• How do we achieve these goals?

• Survey requirements (resolution, sensitivity, frequency coverage, sky coverage)

• Space or ground?

• An ultimate diffuse lensing mission?

Sensitivity and resolution

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Pol. noise level

Cosmology from φxφ

Neutrino masses

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Allison+ 2015

• Complementary to optical weak lensing- Higher-z, mostly linear regime, no intrinsic-alignment issues

• Comparable precision on neutrino mass to e.g., Euclid lensing

Parameter degeneracies for mn

0.1185 0.1200 0.1215

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Constraint on t important: degrades to 30 meV with Planck prior s(t) = 0.01

• Cosmic-variance-limited t [s(t) = 0.002] becomes limiting for Nmodes > 105

Issue I: extragalactic foregrounds• Issue in T-based reconstruction• tSZ and CIB

- tSZxtSZxφ and (tSZ)4 both important (van Engelen+ 2014)• Mitigation:

- Masking (loss of signal for tSZ)- Modelling (e.g., Planck for unclustered sources)- tSZ nulling (on gradient leg; Madhavacheril & Hill 2018)

0 500 1000 1500 2000 2500 L

−0.06

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Standard masking, lmax = 3000

0 500 1000 1500 2000 2500 3000L

Aggressive masking, lmax = 2500

CIB2−κ corr.tSZ2−κ corr.CIB 4−pt.tSZ 4−pt.5 mJy

5x1014 Msol1 mJy1x1014 Msol

150 GHz

van Engelen+ 2014

Issue 2: Galactic foregrounds

• Main issue for EB reconstruction

• Care (mainly) about 4-pt non-Gaussianity on intermediate and small scales

- Very limited empirical information on these scales

• Mitigation:- Multi-frequency cleaning- “Local” analysis with foreground power included in lensing filters to downweight contaminated modes

Results on 150 GHz simulations

• Data-derived simulations (Planck FFP8) but do not capture small-scale NG from small-scale B field

No dust Worst 600-deg2 dust field Dust inc. in lensing filters

AC+CORE 2017

Requirements for φxφ• Mostly care about Nmodes for power spectrum science

- Generally favours large sky coverage at fixed Ndet

• Neutrino mass requires precise t measurement- Low-l E-mode polarization from space (e.g., LiteBIRD)- Precision on mass (with BAO) saturates around Nmodes~105

- kSZ from patchy reionization (Ferraro & Smith 2018)

• Multi-frequency at high resolution prudent but less demanding than for low-l B-mode science

- Need for Galactic simulations properly capturing small-scale non-Gaussianity

Cosmology from φxLSS

Giannantonio+ 2016

Growth of structurehCMB⌃i / b(z)D2(z)h⌃⌃i / b2(z)D2(z)

0 500 1000 1500 2000 2500 3000

ℓ

0.0

0.5

1.0

1.5

2.0

ℓC

κCM

Bκgal

ℓ(×

10−6) Planck

WMAP 9

Hand+2013; see also Liu & Hill 2015

• Current detections around 3s • Will improve to >50s with e.g., DES 5-yr x SPT-3G• X-correlation more immune to additive systematic effects• Full joint analysis can calibrate multiplicative bias effects in shape measurement and intrinsic alignments

Kirk+ 2016

Galaxy lensing-CMB lensing

Issue: extragalactic foregrounds

• tSZ and CIB are issues in T-based reconstruction• Only, e.g., tSZxtSZxLSS now enters • Mitigation:

- Masking - Modelling - tSZ nulling (on gradient leg; Madhavacheril & Hill 2018)

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Desired x-correlation Fg-fg-LSS bispectrum

Requirements for φxLSS

• Overlap with optical surveys

• Generally favours wide survey

• Galactic foregrounds less of an issue (no bias but can inflate errors)

• Extragalactic foregrounds in TT require cleaning/ modelling/agressive masking

- Gradient-leg cleaning (e.g., with Planck)

Delensing

Lensing and inflation constraints

Factor 6.5 hit by lensing for both scales (no signal c.v.)

Lensing relatively more important for recombination signal for non-zero r

Lensing limits ability to test these models at high significance

No lensing

AC+CORE Collaboration 2017

• Gradient approximation accurate for large-angle B-modes• Residual lensing has power spectrum

Delensing the CMB

• Remap CMB with Wiener-filtered tracer I of CMB lensing

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Internal delensing with Planck

Carron, Lewis & AC 2017

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0.4

0.5

0.6

0.7

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Bias from dependent recon. noise• Consider B-mode template delensing with XY estimator:

Carron, Lewis & AC 2017; see also Sehgal+ 2017; Teng+ 2011; Namikawa 2017

Bdelens ⇠ B � EW �W(X,Y )

• Power spectrum after delensing:

CBBdelens ⇠ hBBi � 2hBEW �W(X,Y )i+ hEW �W(X,Y )EW �W(X,Y )i

If reconstruction noise were independent of CMB, just gives usual

2hBEW�Wi

In practice, reconstruction dependent on CMB giving dominant bias

2BEW �W(X,Y ) + 2BEW �W(X,Y )

• r-dependent bias if X or Y=B and overlapping scales

Modelling the bias

• Non-trivial power spectrum covariance also

200 400 600 800 1000 1200 1400`

2

3

4

5

6

CB

B`

[10�

6µK

2]

analytic CBB,resl with � indep. of CMB

hCBB,resl i400sims with �EB

green + hBtempBtempic,IV

green + hBtempBtempiG

green + hBtempBobsiG

green + three corrections

Baleato-Lizancos+AC in prep.; see also Namikawa 2017

Delensed power from sims

Expectation for independent recon. noise

2 arcmin beam; 7 µKarcmin noise

Including dominant bias term

B-mode noise power level

More optimal lens reconstruction

4 6 8 10 12 14

✓fwhm [arcmin]1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6↵

=�(r

) nodel

ens/

�(r

) del

ens

2 µK-arcmin2 µK-arcmin, it.3 µK-arcmin3 µK-arcmin, it.

Quadratic estimator for lensing reconstruction

Fact

or b

y w

hich

del

ensi

ng

impr

oves

s(r

) fo

r r=

0

AC+CORE Collaboration 2017

“Optimal” lensing reconstruction

External delensingGNILC 353 GHz + WISE co-add

-0.1 0.1CMB lensing convergence

GNILC 353 GHz + WISE + Planck lens co-add

-0.1 0.1CMB lensing convergence

500 1000 1500 2000

l

0.0

0.1

0.2

0.3

0.4

0.5

0.6

⇢2 l(S

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CIB contribution

WISE contribution

Planck contribution

CIB + WISE + Planck

Contribution to the low-l CBBlCIB+gal.

CIB+gal.+CMB

Byeonghee+ 2017

• Need high-z sources (CIB, LSST galaxies etc.)• Residual power can be modelled from empirical spectra

Remove around 40% of lensing power with signal-dominated E-modes

Requirements for BB delensing

• Overlap of high-resolution survey with degree-scale B-mode survey (e.g., CMB-S4)

• Sensitivity better than 5 µKarcmin

• Bias from non-Gaussian Galactic foregrounds not yet quantified

- Residual B-mode power involves up to 6-pt function

Halo lensing

Halo lensing

Baxter+ 2017

6.5s detection of cluster lensing

• Statistical mass calibration for large samples at high redshift

See also Baxter+ 2015; Planck Collaboration 2016; Madhavacheril+ 2015; Geach & Peacock 2017

Requirements for halo lensing

• Arcmin resolution• Rejection of tSZ and IR emission from cluster galaxies• Large area

101

0.01

0.1

1

∆T=∆P/21/2 (µK’)

∆M

/M (

N/1

03)1

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ET

EB

θFWHM=1’; l<lbeam

Hu+ 2007

Frac

tiona

l mas

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ror

on 1

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clus

ter

stac

k

Ultimate diffuse lensing mission?

• To write

de Zotti+2016

6

FIG. 3: Ratio between line luminosity, L, and star formation rate, M�, for various lines observed ingalaxies and taken from Table 1 of [23]. For the first 7 lines this ratio is measured from a sample oflow redshift galaxies. The other lines have been calibrated based on the galaxy M82. Some weakerlines, for example for HCN, have been omitted for clarity.

the fluctuations from a particular redshift by cross correlating the emission in two di�erentlines. If one compares the fluctuations at two di�erent wavelengths, which correspond to thesame redshift for two di�erent emission lines, the fluctuations will be strongly correlated.However, the signal from any other lines arises from galaxies at di�erent redshifts which arevery far apart and thus will have much weaker correlation (see Figure 4). In this way, onecan measure either the two-point correlation function or power spectrum of galaxies at sometarget redshift weighted by the total emission in the spectral lines being cross correlated.

The cross power spectrum at a wavenumber k can be written as,

P1,2(⇥k) = S1S2b2P (⇥k) + Pshot, (1)

where S1 and S2 are the average fluxes in lines 1 and 2 respectively, b is the average biasfactor of the galactic sources, P (⇥k) is the matter power spectrum, and Pshot is the shot-noisepower spectrum due to the discrete nature of galaxies. Visbal & Loeb (2010) showed thatthe root-mean-square error in measuring the cross power spectrum at a particular k-modeis given by,

�P 21,2 =

1

2(P 2

1,2 + P1totalP2total), (2)

where P1total and P2total are the total power spectra corresponding to the first line andsecond line being cross correlated. Each of these includes a term for the power spectrum ofcontaminating lines, the target line, and detector noise. Figure 5 shows the expected errors inthe determination of the cross power spectrum using the OI(63 µm) and OIII(52 µm) lines ata redshift z = 6 for an optimized spectrometer on a 3.5 meter space-borne infrared telescopesimilar to SPICA, providing background limited sensitivity for 100 di�raction limited beams

Visbal, Trac, Loeb 2011

There is more to extra-galactic galaxies than CIB!

Ultimate diffuse lensing mission?

Serra, OD, Lagache 2017

Potentially a challenge to measure the primordial distortions

Ultimate diffuse lensing mission?

• To write

Serra, OD, Lagache 17

Schaan, Spergel, Ferraro 2018Foreman+ 2018

• But an opportunity to perfectly delense and measure the growth of structures…• We are at a KISS workshop after all!