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The Cosmic Microwave Background (CMB)

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The Cosmic Microwave Background (CMB) The critical role of statistics in CMB studies V(φ) φ Hiranya Peiris University College London Wednesday, 30 September 2009 Outline Wednesday, 30 September 2009 Outline • Non-technical introductions – The Cosmic Microwave Background – Inflation - a theory for the origin of primordial fluctuations Wednesday, 30 September 2009 Outline • Non-technical introductions – The Cosmic Microwave Background – Inflation - a theory for the origin of primordial fluctuations • The primordial power spectrum – Inferences from the CMB with inflationary priors Wednesday, 30 September 2009 Outline • Non-technical introductions – The Cosmic Microwave Background – Inflation - a theory for the origin of primordial fluctuations • The primordial power spectrum – Inferences from the CMB with inflationary priors • The primordial power spectrum – Minimally parametric reconstruction using cross-validation Wednesday, 30 September 2009 Outline • Non-technical introductions – The Cosmic Microwave Background – Inflation - a theory for the origin of primordial fluctuations • The primordial power spectrum – Inferences from the CMB with inflationary priors • The primordial power spectrum – Minimally parametric reconstruction using cross-validation • CMB temperature anomalies – Beyond a posteriori statistics using consistency tests Wednesday, 30 September 2009 Outline • Non-technical introductions – The Cosmic Microwave Background – Inflation - a theory for the origin of primordial fluctuations • The primordial power spectrum – Inferences from the CMB with inflationary priors • The primordial power spectrum – Minimally parametric reconstruction using cross-validation • CMB temperature anomalies – Beyond a posteriori statistics using consistency tests Wednesday, 30 September 2009 The Cosmic Microwave Background (CMB) 60 K Credit: NASA/WMAP Science Team Wednesday, 30 September 2009 #OMPOSITIONOFAND+ECosmic HistoryY%VENTS$ UR/ INGTHE%CosmicVOLUTIONOFTHE5 MysteryNIVERSE presentpresent energy energy Y density Ω7totTOT = 1(k=0)K density DAR RADIATION KENER dark energy YDENSIT DARK G (73%) DARKMATTER Y G ENERGY dark matter DARK MA(23.6%)TTER TIONOFENER WHITEWELLUNDERSTOOD DARKNESSPROPORTIONALTOPOORUNDERSTANDING BARYONS BARbaryons(4.YONS AC 4%) FR −42 −33 −22 −16 −12 Fractional Energy Density 10 s 10 s 10 s 10 s 10 s 1 sec 380 kyr 14 Gyr ~1015 GeV SCALEFACTimeTOR ~1 MeV ~0.2 eV 4IME TS TS TS TS TS TSEC TKYR T'YR Y Y Planck GUT Y T=100 TeV nucleosynthesis Y IES TION TS EOUT DIAL ORS TIONS G TION TION Z T Energy THESIS symmetry (ILC XA 100) MA EN EE WNOF ESTHESIS V IMOR GENERATEOBSERVABLE IT OR ELER ALTHEOR TIONS EF SIGNATURESINTHE#-" EAKSYMMETR EIONIZA INOFR Y% OMBINA R E6 EAKDO #X ONASYMMETR SIC W '54SYMMETR IMELINEOF EFFWR Y Y EC TUR O NUCLEOSYN ), * +E R 4 PLANCKENER Generation BR TR TURBA UC PH Cosmic Microwave NEUTR OUSTICOSCILLA BAR TIONOFPR ER A AC STR of primordial ELEC non-linear growth of P 44 LIMITOFACC Background Emitted perturbations perturbations: GENER ES carries signature of signature on CMB TUR GENERATIONOFGRAVITYWAVES INITIALDENSITYPERTURBATIONS acoustic#-"%MITT oscillationsED NON LINEARSTR andUCTUR EIMPARTS #!0-!0OBSERVES#-" ANDINITIALDENSITYPERTURBATIONS GROWIMPARTINGFLUCTUATIONS CARIESSIGNATUREOFACOUSTIC SIGNATUREON#-"THROUGH *throughEFFWRITESUPANDGR weakADUATES WHICHSEEDSTRUCTUREFORMATION TO#-" OSCILLATIONSANDPpotentiallyOTENTIALLYPR IMORprimordialDIAL GRAVITATIONALLENSING IGNA 3 GRAVITYWAVES INTHE#-" gravitational waves gravitational lensing Figure: J. McMahon, adapted by HVP Wednesday, 30 September 2009 ΛCDM: The “Standard Model” of Cosmology Homogeneous background Perturbations 60 K Ωb, Ωc, ΩΛ,H0,τ As,ns,r •atoms 4% •nearly scale-invariant •cold dark matter 23% •adiabatic •dark energy 73% •Gaussian Λ? CDM? ORIGIN?? Wednesday, 30 September 2009 History of CMB temperature measurements 60 K 2.725 K TOCO (1998) BOOMERANG (1998, 2003) MAXIMA (2000) ARCHEOPS (2002) CBI (2002) ACBAR (2002) VSA (2002) Wednesday, 30 September 2009 History of CMB temperature measurements 60 K 2.725 K TOCO (1998) BOOMERANG (1998, 2003) MAXIMA (2000) ARCHEOPS (2002) CBI (2002) ACBAR (2002) VSA (2002) Wednesday, 30 September 2009 Planck: 7 deg 15 arcmin 5 arcmin Wednesday, 30 September 2009 ThermalTHERMAL History HISTORY CMB and matter plausibly produced during reheating at end of inflation • CMB decouples around recombination, 300 kyr later • Universe starts to reionize once first stars (?) form (somewhere in range • z = 10–20) and 10% of CMB re-scatters 28 13 10 10 K 10 K 10 K 3000 K Recombination Nucleosynthesis Quarks -> Hadrons -34 -6 10 s 10 Sec 2 Wednesday, 30 September 2009 Space-time and CMB Physics (NOT to scale) time past light cone Universe transparent COBE resolution WMAP resolution Last scattering 379,000 yrs Universe opaque Big Bang space Wednesday, 30 September 2009 Compress the CMB map to study cosmology Express sky as: δT (θ,φ)=! almYlm(θ,φ) l,m If the anisotropy is a Gaussian random field (real and imaginary parts of each alm independent normal deviates, not correlated) all the statistical information is contained in the angular power spectrum. 0.06% of map 5 deg 1 2 Cl = |alm| X 1 deg 2! +1! m ANGULAR POWER SPECTRUM Raw 94 GHz +/- 32 uK Raw 61 GHz near NEP near NEP Wednesday, 30 September 2009 WMAP temperature power spectrum Hinshaw et al. (2003) Wednesday, 30 September 2009 A simplified CMB likelihood function theory noise bias Cth + N C 2 ln = (2! + 1) ln ! ! + ! 1 . − L Cth + N − ! " C! ! ! & ! # % $ estimator$ for sky Cls •Logarithmic at large scales; more likely to scatter low. •Approaches Gaussian at small scales. •Cosmic variance: even ideal experiment can only measure (2l+1) modes. Wednesday, 30 September 2009 Radical data compression Time-ordered data (e.g. WMAP 5 years 60-100 GB) mostly experimental characteristics map (12-50 million pixels) physically motivated statistics angular power spectrum - O(1000) to O(10000) numbers experiment, physics, statistics model - O(10) parameters Wednesday, 30 September 2009 State of the art: temperature 4 10 Figure: M. Brown !CDM 3 10 ] 2 K [µ " WMAP5 /2 l QUaD ACBAR l(l+1)C 2 10 QUaD 150 GHz QUaD 100 GHz SZA 30 GHz CBI 1 10 500 1000 1500 2000 2500 3000 3500 4000 4500 Multipole Moment l ‣Sachs-Wolfe plateau and the late time Integrated Sachs-Wolfe effect ‣Acoustic peaks at “adiabatic” locations ‣Damping tail and photon diffusion ‣Weak gravitational lensing (detected in cross-correlation, Smith et al. 2007) Wednesday, 30 September 2009 Types of CMB polarization CMB polarization can be decomposed into two orthogonal modes. E- mode is the curl-free mode (“Electric”). B-mode is the divergence- free mode (“Magnetic”). E-mode B-mode Wednesday, 30 September 2009 Types of CMB polarization CMB polarization can be decomposed into two orthogonal modes. E- mode is the curl-free mode (“Electric”). B-mode is the divergence- free mode (“Magnetic”). E-mode B-mode B mode discriminates between scalar and tensor perturbations Wednesday, 30 September 2009 Generation of CMB polarization • Temperature quadrupole at the surface of last scatter generates polarization. electron isotropic no net polarization Thomson Scattering anisotropic net polarization Quadrupole generated by velocity gradients at Last Scattering Surface Wednesday, 30 September 2009 Temperature-Polarization Correlation Temperature quadrupole at Radial pattern around cold spots z~1089 generates polarization Tangential pattern around hot spots Figure: E. Komatsu Wednesday, 30 September 2009 Source of CMB polarization Signal from Reionization (NOT to scale) time Scattered light is polarized if incident light is anisotropic: low-l signal from secondary past light cone scattering Universe partially transparent “Real” last scattering high-l signal from primary scattering Universe transparent COBE resolution WMAP resolution 2nd-to-last scattering 379,000 yrs Universe opaque Big Bang space Wednesday, 30 September 2009 State of the art: polarization ‣Acoustic peaks at “adiabatic” locations ‣E-mode polarization and cross-correlation with T ‣Large angle polarization from reionization ‣BICEP limit from BB- alone: T/S < 0.73 (95% CL) Figure: Chiang et al. (2009) Wednesday, 30 September 2009 Coupled Einstein-Boltzmann Equations Neutrinos Dark Photons Matter Metric Thomson scattering Electrons Protons Coulomb scattering Wednesday, 30 September 2009 CMB as a sound wave (graphic by W. Hu) Last scattering surface : snapshot of the photon-baryon fluid On large scales : primordial ripples, purely GR Effects Forced damped harmonic oscillator Photons radiation pressure On smaller scales: { } Sound waves Gravity compression Stop oscillating at recombination Smaller than photon mean free path: Exponentially damped by photon diffusion Horizon size at last scattering surface is fundamental mode Peebles & Yu (1970), Sunyaev & Zel’dovich (1970), Sachs and Wolfe (1968), Silk (1968) Wednesday, 30 September 2009 SHO analogy I Consider simple harmonic oscillator with mass m, force constant k driven by external force F0. k F x¨ + x = 0 m m F0 Assuming oscillator is initially at rest, F0 x = A cos(ωt)+ 2 mω k nπ ω = Peaks at t = . !m ω unforced: peak heights equal forced: odd (even) peaks higher (lower) forcing disparity greater for lower Even peaks correspond to negative x Figure from Dodelson, “Modern Cosmology” Wednesday, 30 September 2009 SHO analogy II Cartoon gravitational instability: δ¨ + [Pressure Gravity]δ =0 − Oscillator analogy: F0 ¨ 2 2 Θ0 + k csΘ0 = F 2 F is force due to gravity, c s is sound speed of entire photon- baryon fluid. k ω = Add more baryons; sound speed m (frequency)
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