Neutrino Masses with Lensing of the Cosmic Microwave Background (Study of Experimental Probe of Inflationary Cosmology) Asantha Cooray University of California-Irvine (almost) uniform 2.726K blackbody (Penzias & Wilson) Universe at 400kyr: the microwave sky COBE (Mather & Smoot) O(10-5) perturbations (+galaxy) Dipole (local motion) WMAP Anisotropies Around 2013 with Planck Hu & Dodelson Amblard Hu Lensing distributes anisotropies from degree scales to damping tail and smooths acoustic peaks In temperature hard to see because of other secondaries In polarization lensing mixes E & B modes. Polarization secondaries are smaller. Non-Gaussianity of lensing Bad: decreases information content of lensing B-modes from the case of a simple Gaussian mode counting. (Beware of Gaussian Fisher predictions of B-modes) Good: allows a statistical mechanism to reconstruct foreground mass distribution responsible for lensing 4 FIG. 1: The correlation matrix [Eq. (25)] for temerature (left), E-mode (middle), and B-mode (right) power spectra between different l values. The color axis is on a log scale and each scale is different for each panel. As is clear from this figure, the off diagonal correlation is weak for both θ and E-mode power spectra, but is more than 0.1formostentriesfortheB-mode power spectrum. This clearly shows that the non-Gaussianities are most pronounced for the B-mode signal and will impact the information extraction from the angular power spectrum of B-modes than under the Gaussian variance alone. The B-mode covariance shown in the left panel agrees with Figure 5 of Ref.[14]. mm1m2 mm1m2m3 where the expressions for the mode coupling integrals +2Ill1l2 and +2Jll1l2l3 are described in Refs. [15, 16]. As for the covariance of E-mode powerspectrum, we write 1 1 ˜ ˜∗ ˜ ˜∗ ˜E ˜E CovEE El1m1 El1m1 El2m2 El2m2 Cl1 Cl2 = + +( + )δl1 l2 (14) ≡ 2l1 +12l2 +1 " #− H I J K m1m2 ! where 1 φ E 2 E 2 l1+l2+L = CL (2Fl1Ll2 Cl2 ) +(2Fl2Ll1 Cl1 ) (1 + ( 1) ) H (2l1 +1)(2l2 +1) − L ! " # 2 φ E E l1+L+l2 = CLCl1 Cl2 (1 + ( 1) )2Fl1Ll2 2Fl2Ll1 I (2l1 +1)(2l2 +1) − !L ! 2 φ E E l1+L+l 2 ! ! = 2 CLCl Cl1 (1 + ( 1) )(2Fl1Ll ) J (2l1 +1) ! − !L,l (l1(l1 +1) 4) φ E 2 = − CL(Cl1 ) L(L +1)(2L +1). (15) K − 2π(2l1 +1) !L The last two terms can be written in terms of the lensed power spectrum of E-mode anisotropies as 2 ˜E 2 + = (Cl1 ) , (16) J K 2l1 +1 where 1 ( F )2 C˜E =[1 (l2 + l 4)R]CE + Cφ 2 ll1 l2 CE(1 + ( 1)l+l1+l2 ) l − − l 2 l1 2l +1 l2 − !l1l2 1 R = l (l +1)(2l +1)Cφ 8π 1 1 1 l1 !l1 1 (2l +1)(2l1 +1)(2l2 +1) ll l F = [l (l +1)+l (l +1) l(l +1)] 1 2 . (17) 2 ll1 l2 2 1 1 2 2 − 4π 20 2 $ % − & ˜E Note that Cl is the power spectrum of the lensed E-modes. CMB lens reconstructionNon-Gaussianity of lensing Lensing weakly correlates CMB modes with l = l : T (l)T (l)∗ φ(l l). ∝ − Reconstructed field φ is quadratic in CMB temperature: a φ(n)= ∂ α(n)∂aβ(n) d2l 1 α(n)= T (l)eil n 2 TT TT · (2π) C + N b 2 TT d l C il n β(n)= 2 TT TT T (l)e · (2π) C + N b Second idea for detecting CMB lensing: look for extra power in φ. Compute C φφ: quadratic in φ, or four-point in CMB. WMAP3: statistical errors only give 1σ. (> 50 publications) In addition, systematics likely to be difficult. Pipeline PipelineHint of lensing in WMAP? Final result (including systematic errors) Start Cross-correlation3.4σ detection, as (step a cross-correlation 8): (1) ❄ Gaussian fieldsStartg , φ , aunlensedLens reconstructionInput: Lensing (step potential 6): and galaxy (1) m m m (2) ❄{ } fields (shown bandlimited to 20 ❄ unlensed Input: Maximum likelihood CMB Gaussian fields glensedm, φm, a(4)m ≤ Combine statistical errors with sys- Lensed(2) CMB{am } map 40): ❄(3) ≤ tematic errors considered previ- ❄lensed (4) ❄ Lensed CMB am (3) ously: ❄ ❄ WMAP beam effects φg Output: Cross correlation C , Galactic CMB foregrounds WMAP data NVSS data (5) Output:withReconstructed estimator normalization lensing po- and Point sources + SZ WMAP data❄ NVSS data(7) (5) ❄ tentialstatisticalφ (shown errors bandlimited computed to by Filtered❄ CMB am (7) (6) Filtered galaxy Filtered CMB❄am ❄ 20 Monte 40): Carlo (6) Filteredfield galaxygm ≤ ≤ Reconstructed❄ field✁gm 2 Toφg assess total statistical significance:7 fit to one large bandpower Reconstructedpotential φm ✁ ✁ C = (33.2 10.5) φg 10− potential φ ❅ in multiple of fiducial± C× . m ✁(8)✁ (20 40, stat.) ❅ (8)✁❅❅❘ ✁☛ φg Lensing❅❅❘ estimator✁☛ C Result: 1.15 0.≤34,≤ i.e. a 3.4σ detection, consistent with the φg ± Lensing estimator C fiducial model. Smith et al. 07 no detection limits on lensing-ISW and lensing-SZ Calabrese et al. 09 Next steps A detection of the lensing potential power spectrum with WMAP-7? Requires a computation of the 4 point function, work started, results out soon!!! (Joseph Smidt et al. in preparation) Existing estimators (Hu & Okamoto; Seljak & Hirata) are biased, need to properly account for the Gaussian part of the trispectrum and remove noise bias. Fast, optimized estimators for non-Gaussianity now developed in a series of papers by Munshi, Smidt et al. (we measured the primordial trispectrum for the first time ever in 1001.5026) Still requires a large number of Monte-Carlo simulations. Limited by computational resources. Out to ell of 900, ~25,000 CPU hours. Naive estimator scales as l4. Fast estimators scales as l3logl. CMB lensing CMB lensing vs. galaxy lensing Advantages: 1. A precisely known source 2. Linear fluctuations, there is really no need to model non- linearities down to sub-percent precision. 3. Community experience in analyses of complex CMB datasets Disadvantages: Finite information content! Experimental Probe of Inflationary Cosmology EPIC Selected by NASA in 2003 for a 2 to 3-year study, again in 2008-2009 In 2008-2009, EPIC was put forward as a general CMB community-supported mission concept for the CMBpol post-Planck mission. In Europe, B-POL study (but not selected; Euclid selected for dark energy as a Cosmic Visions M class mission). Jamie Bock (JPL), PI Bock et al. 0906.1188 Post-Planck Mission Effort in US The EPIC-IM Study Team PPPDT CMB Inflation Probe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participants O&**/6(9>%1/B( ,-. L/6=(4*M+6( E4?K Deca da l White Papers 8*&#(,>'6B>6( 23(8/*D/%/H –The Origin of the Universe as Revealed Through the Polarization of the CMB, Dodelson et al. 8*+&6(L/&=+6N( 23(?&6(7+/N> and 211 Co-signers, ArXiv 0903.3796 3'&>T.+6(L$> ?=&6Q>*#(2: –Observing the Evolution of the Universe, Page et al. and 168 Co-signers, ArXiv 0903.0902 !#*+&6(.//( 23(8/*D/%/H –A Program of Technology Development and Sub-Orbital Observations of CMB Polarization !6#*/M(.&6N/( 3&%=/<'G,-. Leadinggg to and Including a Satellite Mission,,y Meyer et al. and 141 Co-signers 3'&*%/B( .&M*/6</ ,-. CMB Community Reports ?=/5/(;/H/*( 2:(3'+<&N> E&=/(;+%%/*( 23(?&6(7+/N> –Theory and Foregrounds: 5 Papers with 135 Authors and Co-Authors 9+/6 EN$H/6( ,-. – Probing Inflation with CMB Polarization, Baumann et al. 2008, ArXiv 0811.3919 U%/6&(-+/*C&>%+ 2?3 – Gravitational Lensing, Smith et al. 2008, ArXiv 0811.3916 E+<>%&B(->6='+/$ 4!?@(A*&6</ – Reionization Science with the CMB, Zaldarriaga et al. 2008, ArXiv 0811.3918 ,/&6T.>$CCN(-$N/=( 4!?@(A*&6</ – PtfPlidFdRlProspects for Polarized Foreground Removal, Dkltl2008AXi08113915Dunkley et al. 2008, ArXiv 0811.3915 ,/QQ(R&&" EF!? -&$%(R+<'&*#B( 23(8/*D/%/H – Foreground Science Knowledge and Prospects, Fraisse et al. 2008, ArXiv 0811.3920 3/%/B=/(?&==/* ,-. –Systematic Error Control: 10 Papers with 68 Authors and Co-Authors ;+D/(?/+QQ/*= ,-. –CMB Technology Development: 22 Papers with 37 Authors and Co-Authors ;/+*(?'+1>6( 23?7 –Path to CMBPol: Conference on CMBPol mission in July with 104 participants 9$&6 K*&6( 23(8/*D/%/HG??.