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Extracting Cosmology from High Resolution CMB Data *Focused on ACT and SO

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Extracting Cosmology from High Resolution CMB Data *Focused on ACT and SO Extracting cosmology from high resolution CMB data *focused on ACT and SO Jo Dunkley, Princeton University May 23, 2018 Jo Dunkley Cosmic Microwave Background T=2.7K ∆T/T ~0.00001 Also polarization: Rep.Two-point statistics: Prog. Phys. 81 (2018) 044901 Report on Progress TxT TxE BxB ExE Staggs, JD, Page 2018 review Figure 3. Example of recent CMB power spectra from [50–54]. Left. TT (top) and EE (bottom) data and power spectra plotted with logarithmic y axes. The TT and EE oscillations are out of phase by ∼π/2 as expected for acoustic oscillations (see section 1.4) since TT and EE trace density and velocity, respectively. The TT spectrum at low ℓ, corresponding to superhorizon scales at decoupling (see section 2.1), has post-decoupling contributions from gravitational redshifting of the photons as they pass through evolving potential wells, known as the integrated Sachs-Wolfe (ISW) effect [55, 56]. The EE spectrum peaks at higher ℓ than TT both because it lacks the ISW effect, and because the acoustic oscillation velocity gradients sourcing the polarization grow with k and thus with ℓ. The spectra are suppressed at large ℓ due to photon diffusion from smaller regions of space, also called Silk damping [57], and to geometric effects from compressing the 3d structure to 2d spectra. Right. TE with linear y axis. Since the ISW effect does not change the polarization, the negative peak at ℓ = 150 in TE confrmed that some of the largest scale features in the CMB are primordial, and not just late-time effects [58–60]. Right. BB detections plotted with a linear y axis, along with theoretical expectations for gravitational lensing for comparison (see sections 2.4 and 2.1). Rotational invariance allows averaging over the azimuthal We use a shorthand notation so that XY refers to TT XY depend ence to generate the angular power spectrum Cℓ : Cℓ . Section 1.4 defnes the polarization spectra EE and BB. m=ℓ Figure 3 shows recent TT, EE and BB data. T TT 1 2 δT(nˆ)= aℓmYℓm(nˆ); Cℓ = aℓm . 2 ℓ + 1 | | 1.2. Foregrounds ℓ m= ℓ m ! !− ! (1) The CMB anisotropies are seen through foreground light For a Gaussian random feld, the amplitude of each complex emitted from the Galaxy and from extragalactic radio and coeffcient a is drawn from a Gaussian distribution with ℓm dusty sources. The Galactic signals dominate at large scales, zero mean, and the phase is drawn from a fat distribution 2 0.4 dropping approximately as ℓ C ℓ− for dust and synchro- between 0 and 2π. Thus, the modes are completely uncor- ℓ ∝ tron [61], while for angular scales ! 10′ (ℓ ! 1000) the extra- related: aℓma∗ =(δℓℓ δmm ) Cℓ. Then, Cℓ carries all the ℓ′m′ ′ ′ galactic emission is increasingly important. In intensity the information⟨ about⟩ the feld. CMB exceeds the Galactic foreground emission over much Cross-spectra are also possible. For example, TE is con- of the sky, at the foreground minimum of 30 200 GHz. In structed from the expansion coeffcients for the T and E maps, – polarization the E-mode CMB signal dominates only at high T E TE 1 T E a and a , as C = a (a )∗ . Section 2.4 ℓm ℓm ℓ 2 ℓ+1 m | ℓm ℓm | latitudes, and the CMB B-mode is everywhere smaller than describes how subsequent gravitational lensing of the CMB ! foregrounds at degree scales [63, 64]. introduces mode correlations, and defnes the lensing power The Galactic component is dominated by four emission φφ spectrum, Cℓ . mechanisms: synchrotron radiation from electrons spiraling in 5 Rep. Prog. Phys. 81 (2018) 044901 Report on Progress Rep. Prog. Phys. 81 (2018) 044901 Report on Progress T(n) = T(nT+(nd))==TT((nn++d∇)φ=)T(n + ∇φ) Planck Collab 2015 Lensing of the CMB (four-point statistic) Staggs, JD, Page 2018 review Figure 13. On the top is a full-sky map of the Wiener-fltered lensing potential, φ, from Planck [226]. The map traces the projected mass density in the universe. Note that the largest size in the map is set by the WienerFigure fltering. 13. Bottom On the left .top The is lensing a full-sky power map spectrum of the data Wiener- fltered lensing potential, φ, from Planck [226]. The map traces the projected mass from Planck [226], ACT [227], SPT [225, 228], Bicep2/Keck [229], and Polarbeardensity [230 in ].the Bottom universe. right. TheNote lensing that thepower largest spectrum size’s in the map is set by the Wiener fltering. Bottom left. The lensing power spectrum data dependence on different cosmological parameters. See text for more information. Reproduced with permission from Alex Van Engelen. from Planck [226], ACT [227], SPT [225, 228], Bicep2/Keck [229], and Polarbear [230]. Bottom right. The lensing power spectrum’s on the matter spectrum and its evolution under gravitational that correlatesdependence the phases on different and alters cosmological the distribution parameters. away from See text for more information. Reproduced with permission from Alex Van Engelen. collapse in the expanding universe, the CMB lensing is a being purely Gaussian. The difference between a map with powerful new cosmological observable. Because the CMB is lensingon and the one matter without spectrum has an rms and of roughly its evolution 20 µK. under gravitational that correlates the phases and alters the distribution away from a diffuse source and each defection is small, the interpreta- Thecollapse distortion inis quanti the fexpandinged as follows. universe, The temperature the CMB feld lensing is a being purely Gaussian. The difference between a map with tion of its lensed image is subtle. We describe it quantitatively T observedpowerful on the celestialnew cosmological sphere today in observable. a direction nˆ is Because related the CMB is lensing and one without has an rms of roughly 20 µK. below. The effect was predicted by Blanchard and Schneider to the aprimordial diffuse distributionsource and T byeach T(nˆ )=defTection(nˆ + d (isnˆ)) small,, where the interpreta- The distortion is quantifed as follows. The temperature feld in 1987 [216] and frst observed directly in a CMB map in d! is calledtion theof itsde flensedection f imageeld. Similarly, is subtle. the Weobserved describe polari it- quantitatively T observed on the celestial sphere today in a direction nˆ is related 2011 by Das et al [217] but was also seen though cross cor- zation is remapped as [Q iU](!nˆ)=[Q iU](nˆ + d(nˆ)). below. The effect was± predicted ±by Blanchard and Schneider to the primordial distribution T by T(nˆ)=T(nˆ + d(nˆ)), where relation [218, 219] and the smearing of the power spectrum The defection feld can be written as the gradient of the lens- in 1987 [216] and frst observed directly in a CMB map in ! is called the defection feld. Similarly, the observed polari- before that [220, 221]. Reviews of CMB lensing include ing potential φ: d = φ. !Maps! of φ show the location of d ∇ [222–224]. mass 2011concentrations. by Das etThe al convergence, [217] but wasκ = alsod /seen2, meas though- cross cor- zation is remapped as [Q iU](!nˆ)=[Q iU](nˆ + d(nˆ)). ∇ · ± ± On its way to us, a typical CMB photon experiences about ures therelation change [ 218in surface, 219] brightnessand the smearing due to lensing. of the The power spectrum The defection feld can be written as the gradient of the lens- ffty defections, primarily from mass concentrations in the angularbefore power thatspectra [220 of ,the 221 three]. Reviewsquantities areof relatedCMB aslensing include ing potential φ: d = φ. !Maps! of φ show the location of range z 0.5–4. The net defection is roughly 3′ and is coher- [L(L +[2221)]2C224φφ/4].= L(L + 1)Cdd/4 = Cκκ. Note that we ∇ ent over ∼several degrees, corresponding to the angular extents – mass concentrations. The convergence, κ = d/2, meas- use L = Onℓ itsℓ′ wayrather to than us, ℓa totypical highlight CMB that photon these spec experiences- about ∇ · of typical lenses, which are those at the peak of the matter tra probe |the− coherence| size of the lensing, rather than the ures the change in surface brightness due to lensing. The power spectrum, with size ∼300 Mpc. Thus, measuring lens- smallerf ftyscales, def ℓections, and ℓ′, that primarily the lensing from correlates. mass (Seeconcentrations also in the angular power spectra of the three quantities are related as ing from a map of the CMB requires arcminute resolution sectionsrange 2.1.2 z and0.5 4.5–).4. FigureThe net 13 deshowsfection a map is roughlytracing the 3 ′ and is coher- [L(L + 1)]2Cφφ/4 = L(L + 1)Cdd/4 = Cκκ. Note that we over degree angular scales. The lensing weakly magnifes ∼ distributionent over of dark several matter degrees, (or φ) derived corresponding from Planck to thelens -angular extents use L = ℓ ℓ′ rather than ℓ to highlight that these spec- (enlarges) some CMB spatial features while demagnifying ing measurements;of typical lenses, see also which [225]. Figureare those 13 also at showsthe peak the of the matter tra probe |the− coherence| size of the lensing, rather than the others. The net effect is to take a Gaussian random feld with Planck lensing power spectrum, augmented with results from power spectrum, with size Mpc. Thus, measuring lens- random phases, the unlensed CMB, and distort it in a manner ACT, SPT, Planck and Polarbear. See∼300 also [225]. smaller scales, ℓ and ℓ′, that the lensing correlates. (See also ing from a map of the CMB requires arcminute resolution sections 2.1.2 and 4.5). Figure 13 shows a map tracing the 18 over degree angular scales.
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