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The Cosmic Microwave Background : Extracting Cosmological Information from Acoustic Oscillations

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The Cosmic Microwave Background : Extracting Cosmological Information from Acoustic Oscillations The Cosmic Microwave Background : Extracting Cosmological Information from Acoustic Oscillations Olivier Doré JPL/Caltech (Cahill 305) [email protected] 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 sufficiently (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 sufficiently (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 effi 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).
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