statistical anisotropy in cmb maps - cosmologist · 2010. 3. 20. · statistically isotropic cmb...
TRANSCRIPT
![Page 1: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/1.jpg)
Statistical anisotropy in CMB maps
Antony Lewishttp://cosmologist.info/
Hanson & Lewis: 0908.0963Hanson, Lewis & Challinor: 1003.0198
![Page 2: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/2.jpg)
The Vanilla Universe Assumptions
• Translation invariance - statistical homogeneity(observers see the same things on average after spatial translation)
• Rotational invariance - statistical isotropy(observations at a point the same under sky rotation on average)
• Primordial adiabatic nearly scale-invariant Gaussian fluctuations filling a flat universe
Statistically isotropic CMB with Gaussian fluctuations andsmooth power spectrum
![Page 3: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/3.jpg)
• CMB lensing
• Power asymmetries• Anisotropic primordial power
• Spatially-modulated primordial power• Non-Gaussianity
Gaussian statistical anisotropy
+ various systematics, anisotropic noise, beam-effects, …
![Page 4: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/4.jpg)
Gaussian anisotropic models
Or is it a statistically isotropic non-Gaussian model??
SH SH SH SH SHSHSH
SH
SH
SH SH SH
SH
![Page 5: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/5.jpg)
Anisotropy estimators
Maximum likelihood:
First iteration solution: Quadratic Maximum Likelihood (QML)
![Page 6: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/6.jpg)
Sky modulation?
Popular modulation model:
QML estimator for f:
Cold spot?
WMAP power reconstruction(V band, KQ85 mask, foreground
cleaned; reconstruction smoothed to 10 degrees)
Following Eriksen et al, WMAP, etc..
![Page 7: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/7.jpg)
+ peakof QML dipole
![Page 8: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/8.jpg)
Dipole amplitude as function of lmax
Only ~1% modulation allowed on small scales
Consistent with Hirata 2009- Very small observed anisotropy in quasar distribution
Modulation power spectrum lmax=64
![Page 9: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/9.jpg)
Primordial power spectrum anisotropy
Look for direction-dependence in primordial power spectrum:
Anisotropic covariance:
Simple case:
e.g.Ackerman et.al. astro-ph/0701357Gumrukcuoglu et al 0707.4179
![Page 10: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/10.jpg)
Reconstruct g(k)
QML estimator:
Many-sigma quadrupole primordial power anisotropy??
WMAP5
![Page 11: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/11.jpg)
Direction close to ecliptic!Also varies with frequencyand detector.
![Page 12: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/12.jpg)
Beam asymmetries? Check with analytic model of scan strategy
Beam shape multipolesScan strategy
WMAP model Hirata et al astro-ph/0406004.
![Page 13: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/13.jpg)
![Page 14: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/14.jpg)
Monte Carlo with subtraction of mean field analytic model of beam asymmetries
can be explained as correlated noise
No detection..
Consistent with Pullen et al 2010
constraint from large-scale structure 1003.0673
![Page 15: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/15.jpg)
Primordial spatial modulation
Gaussian and statistically homogeneousModulation field
At recombination
![Page 16: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/16.jpg)
Bispectrum non-Gaussianity• Local model: small scale power correlated with large-scale temperature
• Considering large-scale modes to be fixed, expect power anisotropy
Liguori et al 2007
Local primordial non-Gaussianity
![Page 17: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/17.jpg)
Conclusions
• Can easily test for a variety of Gaussian anisotropic models using QML estimators
• Marginal evidence for L<~64 dipole power asymmetry in WMAP, small at high L
• Strong evidence for primordial power anisotropy model using uncorrected WMAP maps
- varies between detectors, ecliptic alignment
- appears to be fully explained by beam asymmetries
• Powerful method to test for a wide class anisotropic theoretical models AND instrumental systematics
![Page 18: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/18.jpg)
Comparison with simulations
Symmetric beam and asymmetric beam simulations of Wehus et al, 0904.3998
![Page 19: Statistical anisotropy in CMB maps - cosmologist · 2010. 3. 20. · Statistically isotropic CMB with Gaussian fluctuations and smooth power spectrum • CMB lensing • Power asymmetries](https://reader036.vdocument.in/reader036/viewer/2022081621/612915100d2c5704f1655688/html5/thumbnails/19.jpg)