CMB, lensing, and non- Gaussianities

1. CMB, lensing, and non-Gaussianities Antony Lewis http://cosmologist.info/ Lewis arXiv:1107.5431 Hanson & Lewis arXiv:0908.0963Lewis, Challinor & Hanson arXiv:1101.2234 Pearson, Lewis & Regan arXiv:1201.1010Howlett, Lewis, Challinor & Hall arXiv:1201.3654 + (mostly) work by other people Moriond March 2012

2. Evolution of the universe Opaque Transparent Hu & White, Sci. Am., 290 44 (2004)

3. CMB temperature Last scattering surface End of inflation gravity+pressure+diffusion perturbations Linear theory predictions very accurate Gaussian fluctuations from inflation remain Gaussian

4. z=0 θ 14 000 Mpc z~1000

5. Observed CMB temperature power spectrum WMAP 7 Larson et al, arXiv:1001.4635 Keisler et al, arXiv:1105.3182 Constrain theory of early universe+ evolution parameters and geometry Observations

6. e.g. Geometry: curvature closed flat θ θ We see:

7. or is it just closer?? flat flat θ θ We see: Degeneracies between parameters

8. Sample from (sample all possible model universes given the data) Samples in 6D parameterspace (e.g. using MCMC, adaptive importance sampling, etc.CosmoMC, PMC, MultiNest…). Density of samples relative probability of that region of parameter space

9. WMAP 7

10. Constrain some combinations of parameters accurately Acoustic-scale degeneracy: constant Assume flat, w=-1 Planck forecast Howlett, Lewis, Challinor & Hall arXiv:1201.3654 Use other information to break remaining degeneracies, and provide complementary information

11. Beyond the power spectrum Flat sky approximation: Gaussian + statistical isotropy: - power spectrum encodes all the information - modes with different wavenumber are independent

12. Non-Gaussianity – general possibilities Bispectrum Flat sky approximation: If you know , sign of tells you which sign of is more likely Trispectrum N-spectra…

13. Equilateral b>0 + = + + b<0

14. Millennium simulation

15. Near-equilateral to flattened: b>0 b<0

16. Local (squeezed) b>0 + + = + T( b<0 Squeezed bispectrum is a correlation of small-scale power with large-scale modes

17. Primordial local non-Gaussianity e.g. Liguori et al 2007 Single-field slow-roll inflation Any significant detection would rule out large classes of inflation models New information that is not present in the power spectrum

18. e.g. CMB Lensing: modulation due to large-scale gravitational lenses Last scattering surface Inhomogeneous universe - photons deflected Observer

19. Demagnified Magnified Unlensed + shear (shape) modulation

20. Marginalized over modulation field X (unobservable directly) : - Non-Gaussian statistically isotropic temperature distribution Power spectra of lensed CMB (no longer contains all the information) TT EE BB

21. Reconstructing the modulation field For a given (fixed) modulation field: - Anisotropic Gaussian temperature distribution - Modes correlated for Model-dependent function you can calculate for Can reconstruct the modulation field ! - For small modulations can construct “optimal” QML estimator by summing filtered fields appropriately over Zaldarriaga, Hu, Hanson, etc..

22. Lensing: (nearly) optimal reconstruction of CMB lensing potential, Reconstructed (Planck noise, Wiener filtered) True (simulated) (Credit: Duncan Hanson)

23. 1. Reconstruct the modulation field from quadratic combinations of small-sale modes How to detect squeezed non-Gaussianity? 2. Correlate it with large-scale to measure bispectrum Correlation of modulation with large-scale T e.g. primordial local non-Gaussianity (this is a bit oversimplified for … but right idea)

24. 2b. Calculate modulation power spectrum: measures trispectrum Power spectrum of modulation field e.g. primordial local non-Gaussianity e.g. Reduced trispectrum Power spectrum of the modulation field at recombination (this is an accurate practical method for because almost all the signal is in very squeezed shapes, )

25. From reconstructed can estimate lensing power spectrum ( trispectrum) Reduced trispectrum Real data! South Pole Telescope CMB lensing reconstruction Forecasts Hu: astro-ph/0108090 Engelen et al, arXiv:1202.0546 + Das et al, arXiv:1103.2124 Full non-Gaussian analysis Power spectrum analysis with

26. What does an estimate of do for us? Probe : depends on geometry and matter power spectrum break degeneracies in the linear CMB power spectrum - Better constraints on neutrino mass, dark energy, , … Neutrino mass fraction with and without lensing (Planck only) Engelen et al, 1202.0546 Perotto et al. 2006 WMAP+SPT Planck forecast

27. Conclusions • CMB is still by far the cleanest probe of early-universe physics. Accurately constrain some combinations of cosmological parameters. • Linear power spectrum constraints subject to degeneracies, and miss information if the fluctuations not Gaussian, homogeneous and isotropic • Non-Gaussianities contain more information. Squeezed shapes can be studied by reconstructing modulations with quadratic estimators. - Primordial non-Gaussianity - Potentially powerful way to refute classes of simple inflation models- No detection as yet, may be very small - CMB Lensing – definitely there - Large trispectrum; equivalently reconstruct the lensing potential Break primary CMB degeneracies, improve parameters - Well-detected by ACT & SPT, already becoming useful - Planck and polarization will improve things significantly Future: digging out small B-mode signal may require removal of lensing B-modes

28. Why lensing is important • Known effect, small but significant amplitude () • Modifies the power spectra on small-scales ( • Lensing of E gives B-mode polarization (confusion for tensors/strings) • Anisotropy/non-Gaussianities….

29. e.g. CMB lensing CMB temperature Lensed CMB Lensing deflection angles Anisotropic (anisotropic easily distinguished from scalar primordial non-Gaussianity)

30. Deflection angle power spectrum Non-linear Linear Deflections O(10-3), but coherent on degree scales  important!