primordial and doppler modulations with planck
TRANSCRIPT
Primordial and Doppler modulations with Planck
Antony Lewis
On behalf of the Planck collaboration
http://cosmologist.info/
โข Primordial modulations and power asymmetryโข ๐๐๐ฟ trispectrumโข Kinematic Doppler dipoles
Outline
๐ โผ ๐(๐|ฮฉ) is statistically anisotropic in direction ฮฉ
โ ๐ โผ โซ ๐(๐, ฮฉ)๐ฮฉ is statistically isotropic and non-Gaussian
Note: statistical anisotropy โก trispectrum
z~1000
14 000 Mpc
z=0ฮธ
Squeezed shape โ large-scale modulationsโ
Primordial curvature modulation:
e.g. local NG
Long + short modes: ๐0 = ๐๐ + ๐๐
i.e. modulated ๐ โผ ๐๐ 1 + ๐ with ๐ =6๐๐๐ฟ
5๐๐
Large-scale modulations โ
CMB bispectrum โผ6
5๐๐๐ฟ๐ถ๐ฟ
๐๐โ(๐ถ๐2 + ๐ถ๐3)
CMB trispectrum โผ6
5๐๐๐ฟ
2๐ถ๐ฟ๐โ๐โ(๐ถ๐1 + ๐ถ๐2) (๐ถ๐3 + ๐ถ๐4)
๐2
๐3๐ฟ
๐4
๐ฟ
๐3
๐1๐2
Define ๐๐๐ฟ trispectrum by (almost all S/N at ๐ฟ < 10, half in dipole)
Pearson, Lewis, Regan arXiv: 1201.1010
๐ =6๐๐๐ฟ
5๐๐ + ๐
(optimal to percent level)
Combined estimator for nearly scale-invariant modulation
Note ๐ โผ ๐(10โ3) โ ๐๐๐ฟ โผ 500
๐ =6๐๐๐ฟ5
๐๐
Pipeline almost identical to CMB lensing, but with different weight functions.General anisotropy estimator is
Just need to reconstruct ๐( ๐ง) to find its power spectrum
QML estimator for f:
Hanson & Lewis 2009
Mean field(estimate from sims)
Optimally filtered temperature
Modulation mean field: mainly noise + mask
143x143
143x217
Avoids uncertainty in noise modelling(mask is well known)
Kinematic dipole signal
Aberration
๐ โ ๐ + โ( ๐ โ ๐)
- just like a dipole lensingconvergence
Modulation
Illustrated for ๐ฃ
๐= 0.85
Challinor & van Leeuwen 2002
known dipole amplitude and direction
๐ฃ
๐โ 1.23 ร 10โ3
Modulation ๐ = ๐ฅ coth๐ฅ
2
2โ 1 ๐ โ ๐ โก ๐๐ ๐ โ ๐
100 GHz143 GHz217 GHz353 GHz545 GHz857 GHz
Planck maps: 1.5235914
Approx boost factor Map modulation amplitude
0.18%0.24%0.37%0.64%1.1%1.7%
๐๐ = ๐ฅ coth๐ฅ
2/2 โ 1
Note: SMICA maps are a complicated mixture; modulation effect not currently included in FFP6 sims
Use 143, 217 only (with dust subtraction from 857)
Dipole kinematic effect using appropriate quadratic estimators
Note: not included in parameter analysis
- bias due to aberration average over mask โผ 0.25๐
143x217 modulation reconstruction (๐ฟ โค 5)- map of estimated modulation field ๐
Kinematics not subtracted
Kinematics subtractedin mean field from sims
Modulation pseudo-power spectrum
๐
Consistent with zero except for anomalous octopole
Octopole signal varies between frequencies:(large auto-quadrupole expected from noise bias)
Anomalous signal seems to be mostly due to 217
- may be related to ๐ฝร (frequency dependence from dust?)
Estimator result
Gaussian simulations:
Note: signal most L<5 - small number of modes
Skewed distribution
Upper limits weaker than you might expect
Conservative upper limit, allowing octopole to be physicalusing Bayesian posterior
Consistent with Gaussian null hypothesis (octopole has small weight)
Planck ๐๐ต๐ณ trispectrum constraint ๐ฟmax = 2 ๐ฟmax = 10
Scale-dependent dipole modulation and power asymmetries
Full analysis suggests no non-kinematic dipole power asymmetry
Can also look for scale-dependent effect: filter range of scales used in quadratic estimator
(new results, thanks Duncan)
Planck 217x143 (kinematic subtracted)WMAP 5 (Hanson & Lewis 2009)
Power modulation dipole amplitude for ๐ โค ๐max
Modulation < 1% for ๐ โค ๐max = 500 Modulation < 0.2% for ๐max = 1500 โ 2000
1%
0.1%
Kinematic subtracted
Kinematics not subtracted
(as in Doppler paper but here pure modulation estimator)
Power dipole directions (๐ โค ๐max)
Power dipoles in ฮl = 100 bands
Kinematic subtracted
Kinematics not subtracted
Conclusionsโข 5๐ detection of kinematic dipole effects in Planck maps
โข Large-scale modulation power โnearlyโ consistent with zero after kinematic subtraction (foreground octopole?)
โข Conservative limit ๐๐๐ฟ < 2800 (95% CL)
โข Power at ๐ โค 400 consistent with WMAP and previous analyses(must be โ maps looks the same)
โข Dipole power modulations at low L do not persist to high L after kinematic subtraction: |f| < 0.2% at ๐max = 2000.(but possible foreground issues, ongoing work..)
โข Kinematic effects currently not included in Planck isotropy paper results, e.g. hemisphere and patch anisotropy constraints.Different model, mask, maps, filteringโฆ so not directly comparable; ongoing workโฆ
๐ โฅ 1100 only
SMICA (sims subtract aberration but not modulation)
Power in ฮl = 100 bands
Cumulative