marius millea - mpa
TRANSCRIPT
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Marius Millea
@cosmicmar@marius311
A 2020s Vision of CMB Lensing
B Modes From Space – MPA Garching – Dec 18, 2019
With: SPT Collaboration, Ethan Anderes, Ben Wandelt
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Outline● The quadratic estimate (QE) and beyond● Discuss different approaches and present our
Bayesian method● Preview of some results from the South Pole
Telescope● Future extensions
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The need for delensing
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● These are forecasts or highly simplified analyses● How do we do this to real data?
Quadratic estimate noise spectrum
Forecast for iterating
1e-09
1e-08
1e-07
0 300 600 900 1200 1500
Con
verg
ence
pow
er p
er m
ode,
Cκκ L
Multipole number, L
Ref. Expt. A Error in lens reconstruction: quadratic vs. iterative estimators
Raw CκκLQuad. est. (sim.)
Quad. est. (theor.)Iter. est. (sim.)
Fisher limit
1e-09
1e-08
1e-07
0 300 600 900 1200 1500Multipole number, L
Ref. Expt. B Raw Cκκ
LQuad. est. (sim.)Quad. est. (theor.)
Iter. est. (sim.)Fisher limit
1e-09
1e-08
1e-07
0 300 600 900 1200 1500Multipole number, L
Ref. Expt. C Raw Cκκ
LQuad. est. (sim.)Quad. est. (theor.)
Iter. est. (sim.)Fisher limit
1e-09
1e-08
1e-07
0 300 600 900 1200
Con
verg
ence
pow
er p
er m
ode,
Cκκ L
Multipole number, L
Ref. Expt. D Raw Cκκ
LQuad. est. (sim.)Quad. est. (theor.)
Iter. est. (sim.)Fisher limit
1e-09
1e-08
1e-07
0 300 600 900 1200 1500Multipole number, L
Ref. Expt. E Raw Cκκ
LQuad. est. (sim.)Quad. est. (theor.)
Iter. est. (sim.)Fisher limit
0 300 600 900 1200 1500Multipole number, L
Ref. Expt. F Raw Cκκ
LQuad. est. (sim.)Quad. est. (theor.)
Iter. est. (sim.)Fisher limit
Hirata & Seljak (2003)
CMB-S4-like experiment
True Fisher forecast
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CMB 2D power-spectrumIsotropic Gaussian random fields:
CMB “fields”
Lensed fields:
Quadratic estimator is suboptimal because it misses this information
Quadratic estimate:
The data
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● DeepCMB (Caldeira et al. 2018)– Achieves noise levels comparable to the iterative-forecast – Challenges in how to quantify uncertainty
● Gradient inversion (Horowitz et al. 2018, Hadzhiyska et al. 2018)– Simple, but only optimal in the asymptotic limit of small scales
● Optimal filtering (Mirmelstein et al. 2019)– A way to more optimally filter a QE ϕ map before taking its power spectrum– May be useful mainly in the short term
● Iterative QE– Does not actually exist
● Bayesian methods...
Towards optimality
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“Joint” posterior (MM,Anderes,Wandelt 2018):
Notation:
“Marginal” posterior (Hirata&Seljak 2003; Polarbear et al. 2019):
Data model: Priors:
Reparametrizations are crucial LenseFlow allows lensing gradients
Bayesian Lensing
Killer, computationally
Any MAP estimate is biased & θ-dependent
Cosmological parameters
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The posterior is extremely degenerate / NG
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Unl
ens
ed p
ixel
val
ues
Lens
ed
pix
el v
alue
s
Traditional lensing:
LenseFlow:
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Upcoming South Pole Telescope Analysis
Deepest 100deg2 polarization measurements to-date at the angular scales most relevant for lensing.
Spatially varying noise Non-white noise Anisotropic x-fer func
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(preliminary slide removed)
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400deg2 of CMB-S4-like observations
MM, Anderes, Wandelt, in prep
We can sample r, check coverage, and compute exact Fisher information
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What else will we need to include in future CMB lensing analyses?
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For point sources in the 1-halo regime:For point sources in the 1-halo regime:
work with Emmanuel Schaan
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Generative neural network
Prior distribution
Galactic Dust GANs Aylor et al. 2019
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Generative neural network
Prior distribution
Galactic Dust GANs Aylor et al. 2019
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Conclusions
● Through the 2020s, all lensing analyses will eventually go beyond the QE
● The Bayesian solutions seems a promising way forward– (Bayesian ≠ sampling though)
● It can currently be used as a benchmark of any other methods● We are working towards using this for the South Pole
Observatory and eventually CMB-S4 and LiteBIRD
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cosmicmar.com/CMBLensing.jlInstall
Use
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Problems with point estimates and the marginal posterior
MM & Seljak, in prep
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Different simulated realizations of data:
● Any frequentist analysis would have missed this● May explain why we are not reaching the Fisher limit
The 1σ error bar varies by a factor of 2 depending on the data realization.
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