CMB lensing and delensing - kiss.caltech.edu · Goals for CMB lensing/delensing •4-pt φxφ...
Transcript of CMB lensing and delensing - kiss.caltech.edu · Goals for CMB lensing/delensing •4-pt φxφ...
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
EB
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Pol. noise level
Cosmology from φxφ
Neutrino masses
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⌃m⌫ = 0.3 eV
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
−0.04
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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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Carron, Lewis & AC 2017
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AC+CORE Collaboration 2017
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�
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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
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ens/
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ens
2 µK-arcmin2 µK-arcmin, it.3 µK-arcmin3 µK-arcmin, it.
Quadratic estimator for lensing reconstruction
Fact
or b
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hich
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ensi
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oves
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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
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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
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θFWHM=1’; l<lbeam
Hu+ 2007
Frac
tiona
l mas
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ror
on 1
000
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!