The Cosmic Microwave Background : Extracting Cosmological Information from Acoustic Oscillations
Olivier Doré
JPL/Caltech (Cahill 305)
1 Outline
• A cosmology primer
• A CMB primer: ‣ The microwave sky ‣ Baryon acoustic oscillations in the sky... ‣ ... at multiple redshifts.
• Guiding question: ‣ How can we measure cosmological parameters with acoustic oscillations?
Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 2 Useful References • Reference books: ‣ Scott Dodelson, Modern Cosmology ‣ James Peebles, Lyman Page, Bruce Partridge, Finding the Big Bang ‣ Durrer, The Cosmic Microwave Background ‣ Bruce Partridge, 3K: The Cosmic Microwave Background • Many online resources: ‣ Wayne Hu’s CMB tutorial ‣ Matias Zaldarriaga CMB lectures ‣ CMBSimple by Baumann and Pajer ‣ Lecture notes by Daniel Baumann • Codes: ‣ CAMB, CLASS, CosmoMC, HEALPix • Data: ‣ WMAP, Planck data and data products are all public as well as associated softwares
Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 3 Planck Collaboration: Cosmological parameters
2.1.2. Ionization history galactic nuclei. We approximate reionization as being relatively sharp, with the mid-point parameterized by a redshift z (where To make accurate predictions for the CMB power spectra, the re xe = f /2) and width parameter zre = 0.5. Hydrogen reion- background ionization history has to be calculated to high ac- ization and the first reionization of helium are assumed to oc- curacy. Although the main processes that lead to recombina- cur simultaneously, so that when reionization is complete xe = tion at z 1090 are well understood, cosmological param- f 1 + f 1.08 (Lewis 2008), where f is the helium- ⇡ ↵ He He eters from Planck can be sensitive to sub-percent di erences to-hydrogen⌘ ratio⇡ by number. In this parameterization, the opti- in the ionization fraction xe (Hu et al. 1995; Lewis et al. 2006; cal depth is almost independent of zre and the only impact of Rubino-Martin et al. 2009; Shaw & Chluba 2011). The process the specific functional form on cosmological parameters comes of recombination takes the Universe from a state of fully ion- from very small changes to the shape of the polarization power ized hydrogen and helium in the early Universe, through to the 4 spectrum on large angular scales. The second reionization of he- completion of recombination with residual fraction x 10 . + ++ e ⇠ lium (i.e., He He ) produces very small changes to the Sensitivity of the CMB power spectrum to xe enters through power spectra ( !⌧ 0.001, where ⌧ is the optical depth to changes to the sound horizon at recombination, from changes Thomson scattering)⇠ and does not need to be modelled in detail. in the timing of recombination, and to the detailed shape of the We include the second reionization of helium at a fixed redshift ↵ recombination transition, which a ects the thickness of the last- of z = 3.5 (consistent with observations of Lyman-↵ forest lines ↵ scattering surface and hence the amount of small-scale di usion in quasar spectra, e.g., Becker et al. 2011), which is su ciently (Silk) damping, polarization, and line-of-sight averaging of the accurate for the parameter analyses described in this paper. perturbations. Since the pioneering work of Peebles (1968) and Zeldovich et al. (1969), which identified the main physical 2.1.3. Initial conditions processes involved in recombination, therePlanck has Collaboration: been signif- Cosmological parameters icant progress in numerically modelling the many relevant In our baseline model we assume purely adiabatic scalar per- atomic2.1.2. transitionsIonization history and processes that can a↵ect the details of galacticturbations nuclei. at very We early approximate times, with reionization a (dimensionless) as being relatively curvature power spectrum parameterized by the recombination process (Hu et al. 1995; Seager et al. 2000; sharp, with the mid-point parameterized by a redshift zre (where To make accurate predictions for the CMB power spectra, the Wong et al. 2008; Hirata & Switzer 2008; Switzer & Hirata xe = f /2) and width parameter zre = 0.5. Hydrogen reion- background ionization history has to be calculated to high ac- ns 1+(1/2)(dns/d ln k) ln(k/k0) 2008; Rubino-Martin et al. 2009; Chluba & Thomas 2011; ization and thek first reionization of helium are assumed to oc- curacy. Although the main processes that lead to recombina- (k) = As , (2) Ali-Haimoud & Hirata 2011). In recent years a consen- curPR simultaneously,k0 so that when reionization is complete xe = tion at z 1090 are well understood, cosmological param- f 1 + f ! 1.08 (Lewis 2008), where f is the helium- suseters has from emerged⇡Planck betweencan be sensitive the results to sub-percent of two di multi-level↵erences ⌘ He ⇡ He atom codes HyRec5 (Switzer & Hirata 2008; Hirata 2008; to-hydrogenwith ns and ratiodns/ byd ln number.k taken In to this be parameterization, constant. For most the opti-of this in the ionization fraction xe (Hu et al. 1995; Lewis et al. 2006; CosmoRec6 calpaper depth we is shall almost assume independent no “running”, of zre and i.e., the a power-law only impact spec- of Ali-HaimoudRubino-Martin & etHirata al. 20092011; Shaw), and & Chluba 2011).(Chluba The process et al. 2010; Chluba & Thomas 2011), demonstrating agreement at a thetrum specific with dn functionals/d ln k = form0. on The cosmological pivot scale, parametersk0, is chosen comes to be of recombination takes the Universe from a state of fully ion- 1 level better than that required for Planck (di↵erences less that fromk0 = very0.05 Mpcsmall changes, roughly to in the the shape middle of the of the polarization logarithmic power range ized hydrogen4 and helium in the early Universe, through to the 4 10 in the predicted temperature power spectra on small4 spectrumof scales on probed large by angularPlanck scales.. With The this second choice, reionizationns is not strongly of he- completion⇥ of recombination with residual fraction xe 10 . + ++ scales). ⇠ liumdegenerate (i.e., He with theHe amplitude) produces parameter very smallAs. changes to the Sensitivity of the CMB power spectrum to xe enters through ! These recombination codes are remarkably fast, given the powerThe spectra amplitude ( ⌧ of the0.001, small-scale where ⌧ linearis the CMB optical power depth spec- to changes to the sound horizon at recombination, from changes Cosmological⇠ Parameters2⌧ complexity of the calculation. However, the recombination his- Thomsontrum is proportional scattering) and to doese A nots. Because need to bePlanck modelledmeasures in detail. this in the timing of recombination, and to the detailed shape of the We include the second reionization of helium at a fixed redshift tory can be computed even more rapidly by using the sim- •amplitudeUniverse content: very accurately Ω , Ω , f , Ω there w(z) is a tight linear constraint be- recombination transition, which a↵ects the thickness of the last- = . b DM ν Λ, ↵ ↵ oftweenz 3⌧5and (consistent ln As (see with Sect. observations3.4). For this of Lyman- reason weforest usually lines use plescattering e ective surface three-level and hence atom the model amount developed of small-scale by Seager di↵usion et al. Universe dynamics: H 7 •in quasar spectra, e.g.,0 Becker et al. 2011), which is su ciently (2000) and implemented in the recfast code , with appropri- ln As as a base parameter with a flat prior, which has a signifi- (Silk) damping, polarization, and line-of-sight averaging of the accurate for the parameter analyses described in this paper. atelyperturbations. chosen small correction functions calibrated to the full •cantlyInitial perturbations more Gaussian (clumpiness): posterior As than, σ8, nAs(k)s. A linear parameter re- definition then also allows the degeneracy between ⌧ and A to be numerical results (Wong et al. 2008; Rubino-Martin et al. 2009; Primordial gravity waves: r=At/As, A , n s Since the pioneering work of Peebles (1968) and • t t ShawZeldovich & Chluba et al.2011(1969).), We which use recfast identifiedin our the baseline main physical param- 2.1.3.explored Initial e conditionsciently. (The degeneracy between ⌧ and AsPlanckis Collaboration: broken Cosmological parameters When the first stars formed: z Table 1. Cosmological parameters used in our analysis. For each, we give the symbol, prior range, value taken in the base ⇤CDM •by the relative amplitudes ofre , large-scaleτ cosmology temperature (where appropriate), and summary and definition polar- (see text for details). The top block contains parameters with uniform eterprocesses analysis, involved with correction in recombination, functions adjusted there has so been that the signif- pre- priors that are varied in the MCMC chains. The ranges of these priors are listed in square brackets. The lower blocks define various derived parameters. dicted power spectra C` agree with those from the latest ver- •InizationOther: our baseline CMBWDM, isocurvature, anisotropies model we non-Gaussianity... assume and by thepurely non-linear adiabatic e↵ scalarect of per- CMB icant progress in numerically modelling the many relevant Parameter Prior range Baseline Definition turbations at very early times, with a (dimensionless)! ⌦ 2 . , . curvature... HyRec CosmoRec lensing.) b bh ...... [0 005 0 1] Baryon density today sionsatomic of transitions(January and processes2012) and that can a↵(v2)ect the to better details than of ! ⌘ ⌦ h2 ...... [0.001, 0.99] ... Cold dark matter density today c ⌘ c 100✓MC ...... [0.5, 10.0] ... 100 approximation to r /DA (CosmoMC) 8 ⇤ powerWe spectrum shall also parameterized consider extended by models⌧ ...... with . . [0.01, 0. a8] significant... Thomson⇥ scattering optical depth due to reionization 0.the05% recombination. We have confirmed, process (Hu using et al. importance1995; Seager sampling, et al. 2000 that; ⌦ ...... [ 0.3, 0.3] 0 Curvature parameter today with ⌦ = 1 ⌦ K tot K m⌫ ...... [0, 5] 0.06 The sum of neutrino masses in eV Varied me↵ ...... [0, 3] 0 E↵ective mass of sterile neutrino in eV amplitude of primordial gravitational waves⌫, sterile (tensor modes). cosmologicalWong et al. 2008 parameter; Hirata constraints & Switzer using2008recfast; Switzerare & consis- Hirata P . , . a = + n 1+(1/2)(dn /d ln k) ln(k/k ) w0 ...... [ 3 0 0 3] 1 Dark energy equation of state , w(a) w0 (1 a)wa s s 0 w ...... [ 2, 2] 0 As above (perturbations modelled using PPF) a Throughoutk this paper, the (dimensionless)Ne↵ ...... tensor . . . . [0.05, 10.0] mode 3.046 spec- E↵ective number of neutrino-like relativistic degrees of freedom (see text) tent2008 with; Rubino-Martin those using CosmoRec et al. 2009at the; Chluba 0.05 level. & Thomas Since the2011 re-; . , . = , YP ...... [0 1 0 5] BBN Fraction of baryonic mass in helium (k) As AL . . .9 ...... [0, 10] 1 Amplitude(2) of the lensing power relative to the physical value 1 R ns ...... [0.9, 1.1] ... Scalar spectrum power-law index (k0 = 0.05Mpc ) sultsAli-Haimoud of the Planck & Hirataparameter2011 analysis). In recentare crucially years dependent a consen- on Ptrum is parameterizedk as a power-law with 1 0 n ...... n = r . /8 Inflation Tensor spectrum power-law index (k = 0.05Mpc ) t t 0 05 0 ! dns/d ln k ...... [ 1, 1] 0 Running of the spectral index 10 1 ln(10 As) ...... [2.7, 4.0] ... Log power of the primordial curvature perturbations (k0 = 0.05 Mpc ) thesus accuracy has emerged of the recombination between the history, results we of have two also multi-level checked, , . 1 nt r0.05 ...... [0 2] 0 Ratio of tensor primordial power to curvature power at k0 = 0 05 Mpc 5 ⌦⇤ ...... Dark energy density divided by the critical density today with ns and dnk s/d ln k taken to be constant. For most of... this followingatom codesLewisHyRec et al. (2006(Switzer), that & there Hirata is no2008 strong; Hirata evidence2008 for; t0 ...... Age of the Universe today (in Gyr) ⌦m ...... Matter density (inc. massive neutrinos) today divided by the critical density t(k) = At . ... (3) 6 paper we shall assume no “running”, i.e.,8 ...... a power-law spec-RMS matter fluctuations today in linear theory simpleAli-Haimoud deviations & Hirata from the2011 assumed), and history.CosmoRec However,(Chluba we et note al. zre ...... Redshift at which Universe is half reionized P k 1 1 0 H0 ...... [20,100] ... Current expansion rate in km s Mpc 1 ! r0.002 ...... 0 Ratio of tensor primordial power to curvature power at k0 = 0.002 Mpc trum with dns/d ln k = 0. The pivot scale,9 k0, is chosen to be9 1 that2010 any; Chluba deviation & Thomas from the2011 assumed), demonstrating history could agreement significantly at a 10 As ...... 10 dimensionless curvature power spectrum at k0 = 0.05 Mpc ! ⌦ h2 ...... Total⇥ matter density today (inc. massive neutrinos) 1 m ⌘ m k = 0.05 Mpc , roughly in the middle ofz the...... logarithmic... rangeRedshift for which the optical depth equals unity (see text) level better than that required for Planck (di↵erences less that We0 define r . A /A , the primordial tensor-to-scalar⇤ ratio at shift parameters compared to the results presented here and we 0 05 t s r = rs(z )...... Comoving size of the sound horizon at z = z ⇤ ⇤ ⇤ 100✓ ...... 100 angular size of sound horizon at z = z (r /DA) 4 ⌘ ⇤ ⇥ ⇤ ⇤ Derived 4 10 in the predicted temperature power spectra on small ofk = scalesk . Our probed constraints by Planck are. With only this weakly choice,zdrag sensitive...... ns is not to strongly the... tensorRedshift at which baryon-drag optical depth equals unity (see text) have not performed a detailed sensitivity analysis. 0 rdrag = rs(zdrag)...... Comoving size of the sound horizon at z = zdrag 1 ⇥ kD ...... Characteristic damping comoving wavenumber (Mpc ) degenerate with the amplitude parameter A100✓ ...... 100 angular extent of photon di↵usion at last scattering (see text) sD scales).The background recombination model should accurately spectral index, nt (which is assumed toz ...... be close to zero),... Redshift⇥ and of matter-radiation equality (massless neutrinos) eq 100✓ ...... 100 angular size of the comoving horizon at matter-radiation equality eq ⇥ These recombination codes are remarkably fast, given the e.g.,we PlanckThe adopt amplitude 2013. the XVI. theoretically Cosmological of the small-scale motivated Parameters linear single-fieldrdrag/DV(0 CMB.57) . . . . power inflation... spec-BAO con- distance ratio at z = 0.57 (see Sect. 5.2) capture the ionization history until the Universe is reionized a 2⌧ For dynamical dark energy models with constant equation of state, we denote the equation of state by w and adopt the same prior as for w0. atcomplexity late times of via the ultra-violet calculation. photons However, from the starsrecombination and/or active his- trumsistency is proportional relation nt = to er 0.05A/s8,. Because rather thanPlanck varyingmeasuresnt indepen- this The photon temperature today is well measured to be T0 = current cosmological data as a single massive eigenstate with Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 20172 amplitude very accurately there is a tight2.7255 0 linear.0006 K (Fixsen constraint2009); we adopt T0 = 2.7255 be- K as m⌫ = 0.06 eV (⌦⌫h m⌫/93.04 eV 0.0006; corrections tory can be computed even more rapidly by using the sim- dently. We put a flat prior on r0.05, butour also fiducial± value. report We assume full the thermal constraintequilibrium prior to and uncertainties at the⇡ meV level are well⇡ below the accuracy 5http://www.sns.ias.edu/ yacine/hyrec/hyrec.html tween ⌧ and ln A (see1 Sect. 3.4). For thisneutrino reason decoupling. The we decoupling usually of the neutrinos is use nearly, required here). This is consistentP with global fits to recent os- ple e↵ective three-level atom model˜ developed by Seager et al. at k = 0.002 Mpcs (denoted r0.002), whichbut not entirely, is complete closer by the time of to electron-positron the scale anni- cillation and other data (Forero et al. 2012), but is not the only 6 hilation. This leads to a slight heating of the neutrinos in addition possibility. We discuss more general neutrino mass constraints http://www.chluba.de/CosmoRec/ 7 A to that expected for the photons and hence to a small departure in Sect. 6.3. (2000) and implemented in the recfast code , with appropri- ln s as a base parameter with a flat prior, which has a= signifi-/ 1/3 from the thermal equilibrium prediction T (11 4) T⌫ be- 7 9 tween the photon temperature T and the neutrino temperature http://www.astro.ubc.ca/people/scott/recfast.html cantly more Gaussian posterior than AsT.⌫. We A account linear for the additional parameter energy density in neutrinos re- by ately chosen small correction functions calibrated to the full For a transverse-traceless spatial tensorassumingH thatij they, the have a thermal tensor distribution part with an e of↵ective the 8 recfast definition then2 also2 allows2 the degeneracyi energyj between density ⌧ and A to be We shall also consider the possibility of extra radiation, numericalThe updated results (Wongused et al. here2008 in; theRubino-Martin baseline model et is al. publicly2009; metric is ds = a [d⌘ ( ij + 2Hij)dx dx ], and4/3 t is defineds so thatbeyond that included in the Standard Model. We model this 7 4 N ⇢⌫ = N ↵ ⇢ , (1) as additional massless neutrinos contributing to the total e↵ ij e 8 11 P camb explored= @ e ciently. (The degeneracy between ! ⌧ and A is broken determining the radiation density as in Eq. (1). We keep the availableShaw & as Chluba version2011 1.5.2). and We is use therecfast default in in ouras baseline of October param- 2012. t(k) ln k 2Hij2H . s mass model and heating consistent with the baseline model at with Ne↵ = 3.046 in the baseline model (Mangano et al. 2002, P h i = . (massive) = 2005). This density is divided equally between three neutrino Ne↵ 3 046, so there is one massive neutrino with Ne↵ by the relative amplitudes of large-scale temperature and polar- (massless) eter analysis, with correction functions adjusted so that the pre- species while they remain relativistic. 3.046/3 1.015, and massless neutrinos with Ne↵ = In our baseline model we assume a minimal-mass normal N 1.015.⇡ In the case where N < 1.015 we use one mas- e↵ e↵ dicted power spectra C` agree with those from the latest ver- ization CMB anisotropies and by the non-linearhierarchy for the neutrino e masses,↵ect accurately of approximated CMB for sive eigenstate with reduced temperature. 6 sions of HyRec (January 2012) and CosmoRec (v2) to better than lensing.) 5 0.05%8. We have confirmed, using importance sampling, that We shall also consider extended models with a significant cosmological parameter constraints using recfast are consis- amplitude of primordial gravitational waves (tensor modes). tent with those using CosmoRec at the 0.05 level. Since the re- Throughout this paper, the (dimensionless) tensor mode spec- sults of the Planck parameter analysis are crucially dependent on trum is parameterized as a power-law with9 the accuracy of the recombination history, we have also checked, nt following Lewis et al. (2006), that there is no strong evidence for k t(k) = At . (3) simple deviations from the assumed history. However, we note P k0 that any deviation from the assumed history could significantly ! shift parameters compared to the results presented here and we We define r0.05 At/As, the primordial tensor-to-scalar ratio at ⌘ have not performed a detailed sensitivity analysis. k = k0. Our constraints are only weakly sensitive to the tensor The background recombination model should accurately spectral index, nt (which is assumed to be close to zero), and capture the ionization history until the Universe is reionized we adopt the theoretically motivated single-field inflation con- at late times via ultra-violet photons from stars and/or active sistency relation nt = r0.05/8, rather than varying nt indepen- dently. We put a flat prior on r0.05, but also report the constraint 5http://www.sns.ias.edu/ yacine/hyrec/hyrec.html 1 ˜ at k = 0.002 Mpc (denoted r0.002), which is closer to the scale 6http://www.chluba.de/CosmoRec/ 7 9 http://www.astro.ubc.ca/people/scott/recfast.html For a transverse-traceless spatial tensor Hij, the tensor part of the 8 2 2 2 i j The updated recfast used here in the baseline model is publicly metric is ds = a [d⌘ ( ij + 2Hij)dx dx ], and t is defined so that available as version 1.5.2 and is the default in camb as of October 2012. (k) = @ 2H 2Hij . P Pt ln kh ij i
6 Cosmic Camembert *
* J. Lesgourgues Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 5 CMB is a leftover from when the Universe was 380,000 yrs old Time Temperature • The Universe is expanding and cooling
• Once it is cool enough for Hydrogen to form, (T~3000K, t~3.8 CMB 105 yrs), the photons start to comes from propagate freely (the Thomson mean t = 380,000 yrs free path is greater than the horizon after Big Bang scale) Reionization • This radiation has the imprint of the small anisotropies that grew by gravitational instability into the large
structures we see today TODAY: t = 13.7 BILLION yrs after Big Bang Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 CMB Fun Facts
• Universe was ~ 3000° K at 380,000 yr • Full of visible light (~1μm) • Universe is expanding: • Causes light to change wavelength. • Visible light becomes microwaves (~1cm).
• 400 photons per cubic cm today.
• Universe in equilibrium ⇒ Black body.
• Observe perfect black body at 2.73K
• Can relate present day # photons, protons, 13.6eV to get Trecombimation.
• From TCMB today, we get zrecombination
Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 7 Discovery of the Cosmic Microwave Background
Penzias & Wilson 1965 Nobel Prize in Physics 1978 Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 COBE
WMAP
Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 Units'
• Spectra'in'the'microwave'band'is'measured'in' several'ways.'
• Spectral'intensity'Iν'(units:'MJy/sr)' • Blackbody'temperature'or'thermodynamic'
temperature'TB(ν)'(units:'K)' 2hν 3 1 Iν = 2 c exp[hν /kTB(ν)]−1
• Antenna'temperature'or'brightness'temperature'TA (ν)'(units:'K)' € 2kν 2 I T ( ) ν = 2 A ν 5' c Slides from Chris Hirata
Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 10
€ Units,'Part'II'
• All'three'funcCons'−'Iν,'TB(ν),'and'TA(ν)'−'contain'the' same'informaCon.' • IdenCCes:'
– For'a'blackbody,'TB(ν)=constant.''Blackbody'temperature'is' most'useful'for'CMB.'
– At'low'frequencies,'hν< its'perturbaCon'ΔTB(ν).' 6' Slides from Chris Hirata Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 11 CMB Frequency Spectrum COBE FIRAS, Maher++94 Nobel Prize in Physics 2006 Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 What Planck saw Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 Zooming the color scale… 1 in 1000 Conventional explanation due to our motion with v/c = 0.0012 in direction of the constellation Crater Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 Galactic coordinates 30 GHz Caltech Obscos 11 April 2013 B. P. Crill 15 44 GHz Caltech Obscos 11 April 2013 B. P. Crill 16 70 GHz Caltech Obscos 11 April 2013 B. P. Crill 17 100 GHz Caltech Obscos 11 April 2013 B. P. Crill 18 143 GHz Caltech Obscos 11 April 2013 B. P. Crill 19 217 GHz Caltech Obscos 11 April 2013 B. P. Crill 20 353 GHz Caltech Obscos 11 April 2013 B. P. Crill 21 545 GHz Caltech Obscos 11 April 2013 B. P. Crill 22 857 GHz Caltech Obscos 11 April 2013 B. P. Crill 23 Consistency between instruments: 100GHz – 70GHz GalacCc'Emission,'Part'VI' [SchemaAc%representaAon%of%medium.laAtude%sky.% There%may%be%other%models%that%work!]% %%L%%%%%%S%%%%%%%%C%%%%%X%%%Ku%%K%%Ka%Q%%V%%W% 10000' 1000' CMB'anisotropy' Synchrotron' 100' FreeFfree' Thermal'dust' 10' Spinning'dust?' Antenna%temperature%(μK)% 1' 1' 10' 100' 1000' ν%(GHz)% 49' Slides from Chris Hirata Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 25 Cosmic Microwave Background The Same, but Fancier... thecmb.org Planck Cosmic Microwave Background • Summary: • Color codes temperature (intensity), here ±100μK • Temperature traces gravitational potential at the time of recombination, when the Universe was 372 000 ±14000 years old • Planck has improved over WMAP by a factor of 10 in sensitivity and 2.5 in angular resolution • The statistical analysis of this map entails detailed cosmological information • Several remarks come to mind: • Clearly random • But not white, i.e., you clearly see a distinctive scale • Looks statistically isotropic, e.g., the same characteristic size is visible everywhere • All these statements needs to be quantified but are highly non-trivial and have important consequences! StaCsCcs' • CMB'anisotropy'is'a'staCsCcal'field'and'one'can' define'correlaCon'funcCons'and'power'spectra'on'it.' • This'is'similar'to'the'density'field'case'except'that' CMB'anisotropy'lives'on'the'unit'sphere.' • The'correlaCon'funcCon'is:' C(θ) = ΔT(nˆ ) ΔT(nˆ $ ) , nˆ ⋅ nˆ $ = cosθ (Depends'on'angular'separaCon'θ.)' • To'define'the'power'spectrum,'we'need'to'go'to' € “Fourier”'(i.e.'spherical'harmonic)'space.' 7' Slides from Chris Hirata Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 29 PDF of a Noise Normalized Map (WMAP V band) Various bands V band at various resolution 4o 1o 13’ • Very Gaussian • The CMB follow a multi-variate Gaussian distribution (up to 0.025% in power) Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 30 Angular Power Spectrum 2` +1 T (ˆn )T (ˆn ) = C P (cos ✓ )B2 h 1 2 i 4⇡ ` ` 12 ` X • For a Gaussian random field, all statistical information is contained in the power spectrum, i.e., no information in phase. • Isotropy implies no m dependence • The angular power spectrum Cl is thus the right place to confront theory and measurements. Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 31 Cosmic'Variance' • LimitaCon:'since'there'are'only'2l+1'mulCpoles'alm' for'each'l,'can'only'measure'their'variance'with' accuracy' σ(C ) 2 l = Cl 2l +1 even'with'a'perfect'instrument.' € • This'limitaCon'is'known'as'cosmic'variance.' • WMAP'is'at/near'cosmic'variance'limitaCon'at'l<530.'' FronCer'has'moved'to'high'l'and'polarizaCon.' 41' Slides from Chris Hirata Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 32 Planck CMB Angular Power Spectrum Angular scale 90 18 1 0.2 0.1 6000 Planck 2013. 5000 ] 4000 2 K µ [ 3000 ` D 2000 1000 0 2 10 50 500 1000 1500 2000 Multipole moment, ` (log,lin scale) A clear characteristic angular scale Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 33 Power Spectrum Review Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 34 The Use of Standard Ruler in Cosmology • Suppose we had an object whose length is known (in meters) and we knew it as a function of cosmic epoch • By measuring the angle (θ) subtended by this ruler (r=ΔD) as a function of redshift we map out the angular diameter distance DA r DL z dz = DA(z)= 2 DA(z) (1+z) 0 H(z ) • By measuring the redshift interval (Δz) associated with this distance, we map out the Hubble parameter H(z) c z = H(z) D • Measuring DA allows to probe the constituents of the Universe using the Friedmann’s equation 2 H 4 3 2 2 = ⌦Ra + ⌦ma + ⌦ka + ⌦⇤ H0 Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 35 The CMB as a Cosmological Standard Ruler • At early times, the Universe was hot, dense and ionized. Photons and baryons were tightly coupled by Thomson scattering. • The mean free path of photons is much smaller than the horizon and allows fluid approximation • Initial fluctuations in density and gravitational potential drive acoustic waves in the fluid: compressions and rarefactions with δphotons ∝ δb • These perturbations show up at temperature fluctuations in the CMB • Since ρ∝T4 a harmonic wave will be for one comoving mode k 1/4 T ⇥ A(k)cos(kc t) s • Plus a component due to the velocity of the fluid (Doppler effect) Courtesy M. White Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 36 The CMB as a Standard Ruler • A sudden recombination decouplesThe cartoon the radiation and matter giving us a snapshot of the fluid at last scattering • A sudden “recombination” decouples the radiation and matter, giving us a snapshot of the fluid at “last scattering”. • These fluctuations are then projected on the sky with !~rls" or l~k rls • The fluctuations are projected on the sky as λ~DA(lsound)θ or l~krecombination lsound Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 37 Acoustic Scales Seen in the CMB Angular scale 90 18 1 0.2 0.1 6000 First “compression” at kcstls = π. Density max, vel=0 5000 First “rarefaction” ] 4000 2 peak at kcstls = 2π K µ [ 3000 ` D Etc... But clear “Silk” 2000 damping 1000 Vel maximum 0 2 10 50 500 1000 1500 2000 Multipole moment, ` Acoustic scale is set by the sound horizon at last scattering, s = cstls Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 38 LCDM Predictions are VERY Accurate LCDM makes a very precise prediction 68% confidence prediction of LCDM given WMAP9 data Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 39 LCDM Predictions are VERY Accurate Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 40 LCDM Predictions are VERY Accurate Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 41 LCDM Predictions are VERY Accurate Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 42 LCDM Predictions are VERY Accurate This accuracy demonstrates the power of CMB where accurate linear predictions are possible Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 43 – 56 – The Angular Diameter Degeneracy WMAP 3 yrs 1.0 H0 (km s–1Mpc–1) 0.8 30 40 50 0.6 60 70 80 0.4 90 Flat 100 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Planck Collaboration: Cosmological parameters Fig. 20.— Range of non-flat cosmology models consistent with the WMAP data only. The models in the figure are all power-law CDM models with dark energy 141 and dark matter, but without the constraint that Ωm + ΩΛ = 1 (model M10 in 71 Table 3). The different colors correspond to values of the Hubble constant as 2.28 indicated in the figu146re. While models with ΩΛ = 0 are not disfavored by the 2 2.26 70 WMAP data only (∆χeff = 0; Model M4 in Table 3), the combination of WMAP 140 data plus measurements of the Hubble constant strongly constrain the geometry 2.24 and composition of the universe within the framework of these models. The 100 69 dashed line shows an approximation to the degeneracy track: ΩK = −0.3040 + 145 2.22 H 0.4067ΩΛ. 68 139 0 r 100 [Mpc] 2.20 b / h ) 67 2 2.18 144 z ( 66 2.16 A 138 D 2.14 65 143 2.12 64 137 0.136 0.140 0.144 0.148 0.136 0.140 0.144 0.148 2 2 mh mh 2 Planck 2013. XVI.2 Cosmological Parameters Fig. 17. MCMC samples and contours in the r –⌦mh plane (left) and the DA(z )–⌦mh plane (right) for ⇤CDM models analysed with PlanckOlivier+ WPDoré+highL.Cosmic The lines Microwave in these plots⇤ Background show the expected Anisotropies degeneracy - I⇤ directions- Caltech, in January the base ⇤201CDM7 cosmology. Samples44 2 are colour-coded by the values of ⌦bh (left) and H0 (right). therefore to compare with astrophysical measurements of H0, Eq. (53) and is also discordant with the Planck value (Eq. 16) since any discrepancies could be a pointer to new physics. at about the 2.5 level. The error analysis in Eq. (54) does not There have been remarkable improvements in the preci- include a number of known sources of systematic error and is sion of the cosmic distance scale in the last decade or so. very likely an underestimate. For this reason, and because of the The final results of the Hubble Space Telescope (HST)Key relatively good agreement between Eqs. (53) and (54), we do not Project (Freedman et al. 2001), which used Cepheid calibrations use the estimate in Eq. (54) in the likelihood analyses described of secondary distance indicators, resulted in a Hubble constant in Sect. 6. 1 1 of H0 = (72 8) km s Mpc (where the error includes esti- The dominant source of error in the estimate in Eq. (53) ± mates of both 1 random and systematic errors). This estimate comes from the first rung in the distance ladder. Using the has been used widely in combination with CMB observations megamaser-based distance to NGC4258, Riess et al. (2011) find 1 1 and other cosmological datasets to constrain cosmological pa- (74.8 3.1) km s Mpc . Using parallax measurements for 10 ± 1 1 rameters (e.g., Spergel et al. 2003, 2007). It has also been recog- Milky Way Cepheids, they find (75.7 2.6) km s Mpc , and ± nized that an accurate measurement of H0 with around 1% pre- using Cepheid observations and a revised distance to the Large 1 1 cision, when combined with CMB and other cosmological data, Magellanic Cloud, they find (71.3 3.8) km s Mpc . These has the potential to reveal exotic new physics, for example, a estimates are consistent with each other,± and the combined esti- time-varying dark energy equation of state, additional relativistic mate in Eq. (53) uses all three calibrations. The fact that the er- particles, or neutrino masses (see e.g., Suyu et al. 2012b, and ref- ror budget of measurement (53) is dominated by the “first-rung” erences therein). Establishing a more accurate cosmic distance calibrators is a point of concern. A mild underestimate of the scale is, of course, an important problem in its own right. The distance errors to these calibrators could eliminate the tension possibility of uncovering new fundamental physics provides an with Planck. additional incentive. Figure 16 includes three estimates of H0 based on “geomet- Two recent analyses have greatly improved the precision of rical” methods20. The estimate labelled “UGC 3789” shows the 1 1 the cosmic distance scale. Riess et al. (2011) use HST observa- result H0 = (71.6 5.7) km s Mpc from VLBI observations tions of Cepheid variables in the host galaxies of eight SNe Ia to of water masers orbiting± within the accretion disc of UCG 3789 calibrate the supernova magnitude-redshift relation. Their “best (Reid et al. 2012). The point labelled “RXJ1131-1231” shows estimate” of the Hubble constant, from fitting the calibrated SNe +4.3 1 1 the estimate H0 = 78.7 4.5 km s Mpc derived from gravita- magnitude-redshift relation, is tional lensing time delay measurements of the system RXJ1131- 1 1 1231, observed as part of the “COSmological MOnitoring of H = (73.8 2.4) km s Mpc (Cepheids+SNe Ia), (53) 0 ± GRAvitational Lenses” (COSMOGRAIL) project (Suyu et al. where the error is 1 and includes known sources of systematic 2012a). Finally, the point labelled SZ clusters shows the value +10.7 1 1 errors. At face value, this measurement is discrepant with the H0 = 76.9 8.7 km s Mpc (Bonamente et al. 2006), derived Planck estimate in Eq. (51) at about the 2.5 level. by combining tSZ and X-ray measurements of rich clusters Freedman et al. (2012), as part of the Carnegie Hubble of galaxies (see Carlstrom et al. 2002, and references therein). Program, use Spitzer Space Telescope mid-infrared observations These geometrical methods bypass the need for local distance to recalibrate secondary distance methods used in the HST Key calibrators, but each has its own sources of systematic error Project. These authors find that need to be controlled. The geometrical methods are con- sistent with the Cepheid-based methods, but at present, the er- 1 1 H = [74.3 1.5 (statistical) 2.1 (systematic)] km s Mpc rors on these methods are quite large. The COSMOGRAIL mea- 0 ± ± (Carnegie HP). (54) surement (which involved a “blind” analysis to prevent experi- We have added the two sources of error in quadrature in the 20Note that each of these estimates is weakly dependent on the as- error range shown in Fig. 16. This estimate agrees well with sumed background cosmology. 31 The Key Number • Not coincidentally, the sound horizon is extremely well determined by the structure of the acoustic peaks in the CMB • Planck: θs(a=9.166 x 10-4) = (0.59672 ± 0.00038) deg (0.1% at 1σ! ) • SDSS-BOSS: θs(a=0.64) = (4.19 ± 0.07) deg (1.7%) Courtesy M. White Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 45 Planck + Baryon Acoustic OscillationsPlanck Collaboration: Cosmological parameters 0.00 0.04 • Measuring explicitly Da as K 0.08 a function of z allows to 0.12 break the intrinsic “Da- 1.6 1.2 degeneracy” [eV] 0.8 2 m H 4 3 2 = ⌦ a + ⌦ a + ⌦ a + ⌦ 0.4 H2 R m k ⇤ 0 4.8 4.0 e N 3.2 • Here, constraining single 2.4 parameter extension of 0.32 P 0.28 Y LCDM model 0.24 • The use a compilation of 0.015 k 0.000 ln d / 0.015 current BAO data s dn 0.030 illustrates clearly the power of this 0.24 0.18 0.002 0.12 combination. r 0.06 0.5 1.0 Red: Planck alone w 1.5 Blue: Planck + BAO 2.0 0.021 0.022 0.023 0.11 0.12 0.13 0.14 0.93 0.96 0.99 1.02 45 60 75 90 0.60 0.75 0.90 1.05 2 2 ns 8 bh ch H0 Fig. 21. 68% and 95% confidence regions on one-parameter extensions of the base ⇤CDM model for Planck+WP (red) and Olivier Doré Cosmic Microwave BackgroundPlanck Anisotropies+WP+BAO (blue). Horizontal - I - Caltech, dashed lines correspond January to the fixed 201 base7 model parameter value, and vertical46 dashed lines show the mean posterior value in the base model for Planck+WP. 36 More than Acoustic Scales Seen in the CMB Horizon at decoupling Angular scale 90 18 1 0.2 0.1 6000 First “compression” at kcstls = π. Density max, vel=0 5000 First “rarefaction” ] 4000 2 Sachs-Wolfplateau peak at kcstls = 2π K µ [ 3000 ` D 2000 1000 Silk damping Vel maximum 0 2 10 50 500 1000 1500 2000 Multipole moment, ` Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 47 Flat ! Open: Peak shifts to the right Wayne Hu’s page Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 Varying Matter Density Wayne Hu’s page Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 Varying Baryon Density Wayne Hu’s page Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 CMB Phenomenology Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 CMB Cheat Sheet 2 ↓Ωmh ←Age of Universe ↑Ω h2 ← ← Ωm+ΩΛ b ↓zre ↑ns Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 Conclusions • Acoustic oscillations in the sky enable cosmological standard rulers across cosmic times. • The linear physics at play at the time of recombination makes the CMB the perfect cosmological probe (“How can you study anything else?!”, C. Lawrence). • It points us towards a “standard” LCDM model • And there is more to it: ‣ The CMB is polarized • Probe of reionization and Inflation. ‣ The CMB could be mildly non-Gaussian • Probe of Inflation and low-z Universe. ‣ The microwave sky contains other cosmological signatures: • The Sunyaev-Zel’dovich signal. • The lensing of the CMB. • The potential mild CMB non-Gaussianity. • The Cosmic Infrared Background (tomorrow). • Anomalies (?) • What you will find! Olivier Doré Cosmic Microwave Background Anisotropies - I - Caltech, January 2017 53 FIN 54