Measuring Primordial Non-Gaussianity using CMB T & E data Amit Yadav University of illinois at Urbana-Champaign GLCW8, Ohio, June 1, 2007
Outline Motivation for measuring non-gaussianity Do we expect primordial perturbations to be non-gaussian What is the extent of non-gaussianity? Current Status with CMB T data Poor reconstruction of primordial perturbations What will E Polarization do? Complementarity of T and E data Reconstructing primordial perturbations Fast estimator measuring non-gaussianity
Are primordial perturbations really Gaussian? Although current data suggest that primordial perturbations are very close to Gaussian but NO primordial perturbations should not be exactly Gaussian. No detection of NG will be a problem for standard model! nd Even the 2 order GR perturbations produce some NG (fnl~ 1) Different inflationary model predict different amount of NG so detection of NG helps distinguishing them.
Are primordial perturbations really Gaussian? Any modification to a simplest picture enhances non-gaussianity - modifying lagrangian ghost inflation, DBI inflation, higher derivative terms... - multiple scaler fields curvaton models, variable decay width,... Sensitivity goal: ΔfNL~ 1-2nd order GR produces fnl~ 1 so that sets the lower limit on NG one may hope to detect.
Simplified model of NG 2 G x = G x f NL x Komatsu and Spergel 2001 Characterizes the amplitude of non-gaussianity Non-Gaussianity from Inflation fnl ~ 0.05 canonical inflation (single field, couple of derivatives) (Maldacena 2003, Acquaviva etal 2003 ) fnl ~ 0.1--100 higher order derivatives DBI inflation (Alishahiha, Silverstein and Tong 2004) UV cutoff fnl >10 curvaton models fnl ~100 ghost inflation (Craminelli and Cosmol, 2003) (Lyth, Ungarelli and Wands, 2003) (Arkani-Hamed et al., Cosmol, 2004)
f NL =0 In collaboration with: Hansen, Liguori, Matarrese, Komatsu, and Wandelt
f =10 NL 1 In collaboration with: Hansen, Liguori, Matarrese, Komatsu, and Wandelt
f =10 NL 2 In collaboration with: Hansen, Liguori, Matarrese, Komatsu, and Wandelt
f =10 NL 3 In collaboration with: Hansen, Liguori, Matarrese, Komatsu, and Wandelt
f =10 NL 4 In collaboration with: Hansen, Liguori, Matarrese, Komatsu, and Wandelt
Non-Gaussianity using Bispectrum Physical non-gaussianity is generated in real space so our statistic should be sensitive to real space NG The Central Limit Theorem makes alm coefficients more Gaussian. Cubic Statistics: Komatsu, Spergel and Wandelt 2005 S prim= B r A r r dr f NL 2 2 B(r) is a reconstructed primordial perturbations A(r) picks out relevant configurations of the bispectrum Above statistics combine combine all configurations of bispectrum such that it most sensitive to the primordial non-gaussianity i.e fnl
Reconstructed Primordial Perturbations CMB DATA alm Φlm=Ol alm On large scales 1 T = 3 T Reconstructed Primordial perturbations with T alone Weiner filter Ol r =r dec Operator goes to zero => reconstruction fails S prim= B r A r r dr 2 2 B(r) is a reconstructed primordial perturbations
Current Status WMAP -58< fnl <137 (95%) WMAP 1yr -54< fnl <114 (95%) WMAP 3yr -30< fnl <100 (95%) Creminelli et. al. 2006 using WMAP 3yr data Non-Gaussianity from Inflation fnl ~ 0.05 canonical inflation (single field, couple of derivatives) (Maldacena 2003, Acquaviva etal 2003) fnl ~ 0.1--100 higher order derivatives DBI inflation (Alishahiha, Silverstein and Tong 2004) UV cutoff ΔfNL ~ 70 fnl >10 curvaton models fnl ~100 ghost inflation (Craminelli and Cosmol, 2003) (Lyth, Ungarelli and Wands, 2003) (Arkani-Hamed et al., Cosmol, 2004) We are far from ΔfNL ~ 1 but can already start putting constraints on some models like DBI inflation, ghost inflation etc.
Temperature and polarization are complementary S prim= B r A r r dr 2 2 Out of phase B(r) is a reconstructed primordial perturbations Weiner filter Ol CMB T CMB E Yadav, and Wandelt, PRD (2005)
Yadav, and Wandelt, PRD (2005)
Yadav, and Wandelt, PRD (2005)
Reconstructed perturbations at different radii S prim= B 2 r A r r 2 dr Yadav, and Wandelt, PRD (2005) Decoupling
Non-Gaussianity parameter Minimum detectable non-gaussianity as we go to smaller scales Temperature Temperature E Polarization E Polarization Combined Combined Smaller scales For and Ideal CMB experiment and using both temperature and polarization we can get down to ΔfNL ~ 1 For Planck we get down to ΔfNL ~3 Yadav, Komatsu and Wandelt, ApJ (in press)
Fast estimator of fnl using combined T and E polarization data Our estimator scales as N3/2 as compared to N5/2 scaling of the brute force bispectrum evaluation. For Planck this translates to speed-up by factors of millions Allows us to study the properties of estimator Estimator is optimal for homogeneous noise Yadav, Komatsu, and Wandelt, ApJ (in press)
Yadav, Komatsu, and Wandelt, ApJ (in press)
Estimator is tested against non-gaussian simulations Example: input non-gaussioan map with fnl=100 (lmax=500) Using our estimator fnl=102 ± 6.9 In collaboration with: Hansen, Liguori, Matarrese, Komatsu, and Wandelt (in preparation)
SUMMARY Detection of non-gaussianity will give huge information about the early universe (class of inflationary models) Sensitivity goal ΔfNL~ 1 Current status: ΔfNL ~ 70 (using CMB T ) T and E polarization are complimentary With CMB T and E polarization: ΔfNL ~3 (withing 5-10 yrs) Fast estimator exists! Estimator Tested against non-gaussian simulations
...and the search for non-gaussianity continues The End