Olivier Doré (Canadian Institute for Theoretical ... - cosmo 06

WMAP 3 years of observations:Methods and **cosmo**logical insights**Olivier** **Doré**CITA / Princeton Universityon behalf of the WMAP science team

WMAP Science TeamNASA - GSFCGODDARDPRINCETONC.Bennett (JHU)G. HinshawR. HillA. KogutM. LimonN. OdegardJ. WeilandE. WollackC. BarnesR. Bean (Cornell)O. **Doré** (CITA)M. Nolta (CITA)N. JarosikE. Komatsu (Texas)L. PageH. Peiris (Chicago)L. Verde (Penn)D. SpergelM. Halpern (UBC)S. Meyer (Chicago)G. Tucker (Brown)E. Wright (UCLA)

What has WMAP-1 done **for** us ?Color codes temperature (intensity), here ±100μKTemperature traces gravitational potential at the time of recombination, when the Universe was372 000 ±14000 years oldThe statistical analysis of this map entails detailed **cosmo**logical in**for**mationWMAP-1 has improved over COBE by a factor of 45 in sensitivity and 33 in angular resolutionDoing so, the mission met all its requirements after the first year...”Mission Accomplished!”... but...

What has WMAP-3 done **for** us?... the insights expected on Inflation theory (~10 -18 s after BB) and the Universe reionization (364+124/-74 Myr) from large scale CMB polarization measurements were too tempting to not be pursuedWMAP-3 has measured the CMB polarization on very large angular scalesTo do so required us to improve control the systematics at a level 50 times higher than originallyproposed!

OutlineRecap on WMAP and analysis improvements over the last 2 yearsA case **for** large scale polarized CMB detectionCosmological implicationsPhenomenological success of ΛCDM **cosmo**logyWMAP already addresses new set of questions risen by this successI can’t cover it all now. Please ask questions.

WMAP primerPrecession rate: 1rph22.5 o half angleA line of sightLagrangepoint L2EarthSUNSpin rate: 0.464rpmB line of sightL2 orbitConstant survey modeThermal stabilityPassive coolingRapid and complex sky scanObserve 30% of the sky every dayMost of pixels are observed with evenly distributedorientationsDifferential measurement onlyMost of the common modes cancelTwo radiometers per feedT 1 +T 2 IntensityT 1 -T 2 Polarization10 feeds, 20 DA total5 microwave frequencies to monitor **for**egroundsK, Ka, Q, V, W bands22, 33, 40, 60, 93 GHzAccurate calibration on the **cosmo**logical dipole and beammeasurements on JupiterDesign optimized **for** temperature measurements

Remarks on the analysis over the last 2 yearsDifferential measurement and interlocked scanning strategy suppressespolarization systematics as **for** temperature.No new systematics, but the weak nature of the spinorial polarized signalrequires extra-care to avoid any coupling to the much stronger T field (100times).Non-trivial interactions between the slow drift gain, non-uni**for**m weightingacross the sky, time series masking, 1/f noise, galactic **for**egrounds, band-passmismatch, off-set sensitivity and loss imbalance.The handling of these effect had to be propagated from the map-making till thepower-spectrum measurement.To understand them required numerous end-to-end simulations (enough to havegood statistics). Most of 2004-5 was spent running those and realizing that theprevious short-cuts did not work anymore.A new pipeline was eventually required and has been designed, written andoptimized.We rely heavily on null tests in map (various frequency) and C l space to assessthe quality of this processing

Q-bandTemperature mapsQ-bandV bandV-bandyear 1(pub) year 3 year 3 - year 1V-bandW-bandW bandW-band-200 +200-30 +30-200 +200-30 +30

Polarization mapsK bandV bandKa bandW bandQ bandColor code P=(Q 2 +U 2 ) 1/2 smoothed with a 2 o fwhmDirection shown **for** S/N > 1

K band - 23 GHz

Ka band - 33 GHz

Q band - 41 GHz

V band - 61 GHz

W band - 94 GHz

Uncleaned power spectraWMAP Year-3 Polarization Maps 21Foregrounds dominate over all l ofinterest and all frequencies unlike**for** temperatureOutside p**06** maskG. 17.— The absolute value of the EE (solid, violet through green) and BB (dashed, violet through green) polarization spectra **for** the region outside themask. The best fit ΛCDM model to TT, TE, and EE data with τ = 0.09 and an additional tensor contribution with r = 0.3 is shown in black. The crossctra have been combined into frequency bins according to Table 5 and into the following l bins: [2, 3, 4-5, 6-8, 9-15, 16-32, 33-101, 102-251, 252-502]. In

Foreground cleaned maps18 Page et al.pre-cleanedKa-bandcleanedQ-bandV-bandW-bandQ Stokes-2020Ka 10.65 1.20 6144 58**06**1FIG. 15.— The Ka, Q, V, and W band Q Stokes Parameter maps be**for**e and after **for**eground subtraction using the method outlined in §4.3. There is a possibleTABLE 4residual signal in W band though the noise is not yet sufficiently low to be certain. The U maps look similar. The cleaning **for** the **cosmo**logical analysis wasQ 3.91 1.09 6144 17326done outside the processing cut (Jarosik et al. 20**06**) and was based on the K-band maps and the starlight-based dust template. The over-subtracted dark regionsCOMPARISON OF χ 2 BETWEEN PRE-CLEANED AND CLEANEDon the galactic plane are inside the processing cut.Due to correlations between**for**egrounds, a map based cleaningis more powerful2 parameters/frequency fit onlyfollow Appendix A of Kogut et al. (2003). 19Fundamental symmetries in the production and growth ofthe polarized signal select the possible configurations **for** theCMB polarization. Scalar (density) perturbations to the matterpower spectrum give rise to T and E modes. Tensor perturbations(gravitational waves) give rise to T, E, and B modesprimarily at l 200 20 . Both scalar and tensor perturbations19 In this paper we do not use the rotationally invariant Q ′ and U ′ of Kogutet al. (2003).20 At l 70 primordial B modes are dominated by the gravitational lenscanproduce polarization patterns in both the decoupling andreionization epochs. Vector perturbations 21 (both inside andoutside the horizon) are redshifted away with the expansion ofthe universe, unless there are active sources creating the vectormodes, such as topological defects. We do not considerKa Band 2.142 χ 2 /ν Pre-cleaned χ 2 /ν 1.096 Cleaned ν4534 ∆χ 24743Q Ka 1.28910.65 1.018 1.20 6144 453458**06**1229VQ1.0483.91 1.0161.09 6144453417326145V 1.36 1.19 6144 1045W W 1.**06**11.38 1.050 1.58 6144 4534 -1229 50ing of E modes.21 Vector modes are produced by purely rotational fluid flow. Based onthe fit of the adiabatic ΛCDM model to WMAP TT data, the contribution ofsuch modes is not large (Spergel et al. 2003). However, a **for**mal search **for**them has not been done.WMAP Year-3 PolarizatiTABLE 4COMPARISON OF χ 2 BETWEEN PRE-CLEANED AND CLEANEDMAPSBand χ 2 /ν Pre-cleaned χ 2 /ν Cleaned ν ∆χ 2WMAP Year-3 Polarization MapsV 1.36 MAPS1.19 6144 1045W 1.38 1.58 6144 -1229RawCleanwherprovtweethis aspecthavedentwhere N Q , N Uprovided aswithtween Qces andfUthis as “N obs wspectra betweFohave the the adva ladent maps that coas there are foces **for** theto opvaFor l C< l . 23 T

Final CMB spectra30 Page et al.100.0010.00{ l(l+1) C l / 2! } 1/2 [µK]1.000.100.011 10 100 1000Multipole moment (l)

Cosmological Implications

Simple ΛCDM model fitsSimple flat ΛCDM model with 6 parameters (Ω cdm ,Ω b ,n s ,A s ,h,τ) still an excellent fitDespite smaller error bars, the χ 2 eff **for** TT improves from 1.09 (893 dof) to 1.**06**8 (982 dof) andfrom 1.**06**6 (1342 dof) to 1.041 **for** TT+TE (1410 dof)For T, Q, U maps, we have χ 2 eff=0.981 **for** 1838 pixels– 79 –Previously discrepant points get closer6000Angular Scale90° 2° 0.5° 0.2°500040003000TT200010000TE210TE–110 100 500 1000Multipole moment (l)

Improvement in parameter space– 10 –– 10 –– 10 –CDM Model Parameters Table 2: and Power 68% Law Confidence ΛCDM Model Intervals Parameters (A SZ = 0) andTable 68% Confidence 2: Power Law Intervals ΛCDM(A Model SZ = 0) Parameters and 68% Confidence Intervals (A SZ = 0Year WMAPext Parameter Three Year First First Year YearWMAPext Three Year Parameter First Year FirstWMAPext Year WMAPext Three Year Three Year First Year WMAPext Thn Mean Mean Mean ML Mean ML Mean ML ML MeanML MeanMLMean ML ML0.130.12 2.32 −0.11 +0.12 2.23 100Ω± 0.08 2.30 2.21 2.22 100Ω b h 2 2.380.0160.016 0.134 −0.0**06** +0.0**06**−0.12 +0.13 2.32 +0.12b h 2 2.38 −0.12 +0.13 2.32 −0.11 +0.12 2.23 ± 0.08 2.30 2.21 2.22−0.11 2.23 ± 0.08 2.30 2.210.126 Ω ± 0.009 0.145 0.138 0.128 Ω m h 2 0.144 +0.01655 73 +3−3 74 +3−0.016 0.134 −0.0**06** +0.0**06**m h 2 0.144 −0.016 +0.016 0.134 −0.0**06** +0.0**06** 0.126 ± 0.009 0.145 0.138 0.128 0.126 ± 0.009 0.145 0.138H −3 68 71 73 H 0 72 +50.080.07 0.15 −0.07 +0.07−5 73 +3−3 74 +30 72 +5−5 73 +3−3 74 +3−3 68 71 73−3 68 710.093 τ± 0.029 0.17 0.10 0.10 0.092 τ 0.17 +0.080.040.04 0.98 −0.03 +0.03−0.07 +0.08 0.15 −0.07 +0.07 0.093 ± 0.029 0.10 0.10−0.07 0.15 −0.07 +0.07 0.092 0.093 ± 0.029 0.10 0.100.961 n± 0.017 0.97 0.96 0.958 n s 0.99 +0.040.070.07 0.25 −0.03 +0.03−0.04 0.98 −0.03 +0.03s 0.99 −0.04 +0.04 0.98 −0.03 +0.03 0.961 ± 0.017 0.97 0.96 0.958 0.961 ± 0.017 0.97 0.960.234 Ω ± 0.035 0.32 0.27 0.24 Ω m 0.29 +0.070.10.1 0.84 −0.**06** +0.**06**−0.07 0.25 −0.03 +0.03m 0.29 −0.07 +0.07 0.25 −0.03 +0.03 0.234 ± 0.035 0.32 0.27 0.24 0.234 ± 0.035 0.32 0.270.76 σ± 0.05 0.88 0.82 0.77 σ 8 0.92 −0.1 +0.1 0.84 −0.**06** +0.**06**8 0.92 −0.1 +0.1 0.84 −0.**06** +0.**06** 0.76 ± 0.05 0.88 0.82 0.77 0.76 ± 0.05 0.88 0.821.0 1.01.0 1.01.01.200.8 0.80.8 0.80.81.150.6 0.60.6 0.60.61.10Driven by EE0.4 0.40.4 0.40.41.050.2 0.20.2 0.20.21.000.0 0.00.0 0.00.015 20 255 10 0.88 0.90 150.92 0.9420 0.96 0.98 25 1.00 1.02 0.88 5 0.90 0.92 10 0.94 150.96 0.9820 1.00 1.02 250.88 0.90 0.92 0.94 0.96 0.98z reion z reion n szn reion sn s0.95x ex e– 8 –1.25x enstraints on theFig. reionization 3.— WMAP history. constraints (Left) The on the 68% reionization and 95% Fig. joint history. 3.— WMAP (Left) constraints The 68% and on 95% the reionization joint history. (Left) The 68% andnfidence level contours 2-d marginalized **for** x 0 e − z confidence reion **for** a power level contours law Λ Cold **for**Dark0.902-dx 0 emarginalized − z reion **for** a confidence power law Λlevel Cold contours Dark **for** x 0 e − z reion **for** a power law Λ Codel with the reionization Matter (ΛCDM) historymodel described withby thequation reionization 3 andMatter history fit (ΛCDM) describedmodel by equation with the 3 and reionization fit to history described by equation 30.14 0.16 0.18 0.2ear data. In equation the WMAP 3 we assume three year that data. the universe In equation0.1was3partiallywe0.2 0.3 0.4 0.5theassume WMAPthat three theyear universe data. was In equation partially 3 we assume that the universe wasan ionization fraction reionized of xat 0 , zand reion then to anbecame ionization fully fraction ionizedof at xreionized 0 z , = and 7. then at became z to an fully ionization ionized at fraction z = 7. of x 0 , and then became fully ionizex e

32 Page et al.τ is robust vs **for**egrounds!TABLE 9OPTICAL DEPTH VS. DATA SELECTION95% CLCombination Exact EE Only Exact EE & TE Simple tau EE Simple tau, noKaQV 0.111 ± 0.022 0.111 ± 0.022 ··· ···Q 0.100 ± 0.044 0.082 ± 0.043 0.08 ± 0.03 0.085 ± 0QV 0.100 ± 0.029 0.092 ± 0.029 0.110 ± 0.027 0.085 +0.!0.QV+VV ··· ··· 0.145 ± 0.03 0.14 +0.!0.V 0.089 ± 0.048 0.094 ± 0.043 0.09 +0.03!0.07 0.10 +0.0!0.0QVW 0.110 ± 0.021 0.101 ± 0.023 0.090 ± 0.012 0.090 ± 0KaQVW 0.107 ± 0.018 0.1**06** ± 0.019 0.095 ± 0.015 0.095 ± 0The values of simple tau are computed **for** 2 ≤ l ≤ 11. The models are computed in steps of ∆τ = 0.005 and linearly intecolumn is computed with the errors on l = 5,7 multiplied by ten. The QV+VV is the QV combination without the QQ comexact likelihood is based on the Ka, Q, V, and W maps, there is no corresponding entry **for** QV+VV. Note that the maximumare independent of frequency combination indicating that **for**eground emission is not biasing the determination of τ.Formal marginalization give the same results

Cosmological contrasts... and yet concordance50001000100ACBARB03CBIMAXIMAVSA400 600 10002000WMAP “predicts” small scale CMB experiments

Cosmological contrasts... and yet concordancethe large-scale structure measurements will reduceWMAP “predicts” low z mass distributionFig. 6.— The prediction (same **for** 2dF) **for** the mass fluctu

Where are we now?The current strong “phenomenological” success means:The primordial inhomogeneities are mostly adiabatic with a nearly scale invariant powerspectrumWe have a successful GR based theory of linear perturbations to evolve themWe have a good description of the main components even if we do not know what theyareWe can now ask various sets of questions:Ask question within the modelWhat else can we learn about the components of themodel, eg neutrino?What is Dark Energy?What is Dark Matter?Did the Universe really undergo an Inflationaryphase?First stars and how did the Universe get reionized?Explore further the data and look **for** “anomalies”, iedeviations from this modelFundamentalPhysics we don’t know yetPhysics we don’t knowto compute

Constraining neutrino mass0.90.8WMAPWMAP+SDSS0.70.60.50.4– 48 –0.30.0 0.5 1.0 1.5 2.0Table 10: Constraints on Neutrino∑PropertiesData Set mν (95% limit **for** N ν = 3.02)WMAP2.0 eV(95% CL)WMAP + SDSS0.91 eV(95% CL)WMAP + 2dFGRS 0.87 eV(95% CL)CMB + LSS +SN 0.68 eV(95% CL)

Dark EnergyConstraints on constant – DE 52 – equation of state w=p/ρ0.0–0.5w–1.0–1.5WMAPWMAP+SDSSWMAPWMAP+2dF–2.00.0–0.5w–1.0–1.5–2.00.0WMAPWMAP+SN(HST/GOODS)WMAPWMAP+SN(SNLS)0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8– 46 –Table 9: Constraints on w in Flat Cosmologies With DifferentEnergy ClusteringData Set with perturbations no pertWMAP + SDSS −0.75 +0.18−0.16 −0.6WMAP + 2dFGRS −0.914 +0.193−0.099 −0.87WMAP + SNGold −0.944 +0.076−0.094 −0.94WMAP + SNLS −0.966 +0.070−0.090 −0.98CMB+ LSS+ SN −0.926 +0.051Fig. 16.— Constraints on w, the equation of state of dark energy, in a flat universe,Model M6 in Table 3, based on the combination of WMAP data and otherastronomical data. We assume that w is independent of time, but include densityand pressure fluctuations in dark energy with the speed of sound in the comovingframe equal to the speed of light, c 2 s = 1. In all of the figures, WMAP data onlyconstraints are shown in black solid lines and WMAP + astronomical data setin red. The contours show the joint 2-d marginalized contours (68% and 95%confidence levels) **for** Ω m and w. (Upper left) WMAP only and WMAP + SDSS.With DE perturbationsbut fixed c s2(cf Bean & **Doré** 03)−0.075 −0.91

Robustness of DE constraints–0.8w + curvature–1.0–1.2–1.4–0.08 –0.**06** –0.04 –0.02 0.00 0.02 0.04–0.8w + neutrino–1.0–1.2CMB + LSS + SN–1.4–1.60.0 0.5 1.0 1.5

What is Inflation?Inflation was introduced to solve the problems of the “standard Big Bang”model like flatness and the horizon problemKey feature: during an extended period of time, the universe is expandingexponentially. Fluctuations are generated during this phaseThis is achieved by introducing in the matter sector (a) new scalar field(s) Φwith a well chosen potential V(Φ)For a given V(Φ) there are relations between derivatives of V andobservables like n s , r and dn s /dlnkTesting Inflation is mostly testing these consistency relationsGuth 81, Sato 81, Linde 82, Albrecht & Steinhardt 82Guth & Pi 82, Starobinsky 82, Mukhanov & Chibisov 81, Hawking 82, Bardeen et al. 83Linde 05, Lyth & Riotto 99 **for** reviews

What are Inflation predictions?Most of Inflation predictions, in the 80s, when there were few evidences **for** any of those ideaFlatness TOCO, MAXIMA, BOOMERANG, WMAP...Primordial perturbations nearly scale invariant COBE (n s = 1.2±0.3 - Gorski et al. 96)Gaussianity of fluctuations WMAP-1Adiabatic initial perturbations WMAP-1Super-Horizon perturbations WMAP-1 (TE at l~100)Deviation from scale invariance WMAP-3Tensor perturbations, i.e. Gravity Wave Background WMAP-8 ?, Planck?, Spider?, Biceps?

Spectral index, tensor modes and InflationV (φ) ∝ φ αConsistency relationsr ≃ 4α N1 − n s = α + 22Nwhere∆ 2 R(k) =( kk 0) ns −11.00.8WMAPWMAP + SDSS50 6050 60r 0.0020.60.40.2These models predictalmost no running0.01.00.8WMAP + 2dFWMAP + CBI + VSA50 6050 60r 0.0020.60.40.20.00.90 0.95 1.00 1.05n s0.90 0.95 1.00 1.05n sSimilarconstraints **for**B03+ACBARRemarks: Eriksen et al. **06** pointed out an inaccuracy around l~20-30.It shifts n s from 0.951 to 0.96±0.016 (WMAP only) or from 0.938 to 0.947±0.015 (WMAP+all)including a slightly revised point source amplitude, but still higher than Huffenberger et al. **06**)

Do we see a running spectral index?d ln∆ 2 R (k)d lnk= n s (k 0 ) − 1 + dn sd lnk ln(k/k 0)2.0WMAP2.0WMAP1.51.5r 0.0021.0r 0.0021.00.50.50.00.9 1.0 1.1 1.2 1.3 1.4 1.5n s 0.0020.0–0.20 –0.15 –0.10 –0.05 0.00 0.05dn s /d lnk2.0WMAP + SDSS2.0WMAP + SDSS1.51.5r 0.0021.0r 0.0021.00.50.50.00.9 1.0 1.1 1.2 1.3 1.4 1.5n s 0.0020.0–0.20 –0.15 –0.10 –0.05 0.00 0.05dn s /d lnk2.0WMAP + CBI + VSA2.0WMAP + CBI + VSA1.51.5r 0.0021.00.50.00.9 1.0 1.1 1.2 1.3 1.4 1.5n s 0.0020.0–0.20 –0.15 –0.10 –0.05 0.00 0.05dn s /d lnkConsistent trend but weak signal so farWMAP and LSS probe almost the same scales currentlyThe trends come ~equally from the low l points and the high l pointsr 0.0021.00.5Similarconstraints **for**B03+ACBAR

Where do this constraints come from?5000WMAPCBIVSA10001000500Text Half100 2005 10 1540**06**0010002000The constraints come almost equally from the lowest l and the highest l

ConclusionsWMAP has now produced well characterized temperature and polarization mapsAfter removing the galactic **for**egrounds, WMAP has detected EE and TE signatures ofreionization with optical depth of 0.09Simple flat ΛCDM **cosmo**logical model has survived its most rigorous test andchallenges fundamental physicsData favors red spectral index (with values consistent with simple inflationary models)over Harrison-Zeldovich Peebles spectrumThe combination of WMAP data and other astronomical data now places evenstronger constraints on the density of dark matter and dark energy, the properties ofneutrinos, the properties of dark energy and the geometry of the UniverseAll the data and the derived products (time ordered data, maps, noise covariancematrices, likelihood codes, Markov chains) are all available on Lambda http://lambda.gsfc.nasa.gov . We are looking **for**ward your analysis!

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