Cosmology(from(the( microwave( background(
Jo(Dunkley( University(of(Oxford(
Jo Dunkley History of early universe
Inflation? T ∼ 1015 GeV t ∼ 10-35 s CDM decoupling? T ∼ 10 GeV? t ∼ 10-8 s
Neutrino decoupling T ∼ 1 MeV t ∼ 1s
Big Bang Nucleosynthesis T ∼ 100 keV t ∼ 10 min Matter-Radiation Equality T ∼ 0.8 eV t ∼ 60,000 yr Recombination T ∼ 0.3 eV t ∼ 380,000 yr
Later: Neutrinos become ‘cold’ < t~100,000,000 yr z=1000, 380 000 yrs t Seeds of structure
1. Inflation (?) imprints quantum fluctuations.
2. Space expands, regions enter into causal contact and start to evolve.
3. Coupled baryons and photons produce oscillations in plasma.
After 380,000 years the fluctuations have evolved, and we see a snapshot of them as anisotropies in CMB.
Linearity means we can use the anisotropies to infer the initial fluctuations and the contents of the Universe.
Planck Collaboration: The Planck mission
Planck(Collaboration(2015
Fig. 7. Maximum posterior CMB intensity map at 50 resolution derived from the joint baseline analysis of Planck, WMAP, and 408 MHz observations. A small strip of the Galactic plane, 1.6 % of the sky, is filled in by a constrained realization that has the same statistical properties as the rest of the sky.
Fig. 8. Maximum posterior amplitude Stokes Q (left) and U (right) maps derived from Planck observations between 30 and 353 GHz. These mapS have been highpass-filtered with a cosine-apodized filter between ` = 20 and 40, and the a 17 % region of the Galactic plane has been replaced with a constrained Gaussian realization (Planck Collaboration IX 2015). From Planck Collaboration X (2015).
viewed as work in progress. Nonetheless, we find a high level of 8.2.2. Number of modes consistency in results between the TT and the full TT+TE+EE likelihoods. Furthermore, the cosmological parameters (which One way of assessing the constraining power contained in a par- do not depend strongly on ⌧) derived from the TE spectra have ticular measurement of CMB anisotropies is to determine the comparable errors to the TT-derived parameters, and they are e↵ective number of a`m modes that have been measured. This consistent to within typically 0.5 or better. is equivalent to estimating 2 times the square of the total S/N in the power spectra, a measure that contains all the available
16 100 GHz
143 GHz
217 GHz
Plus(6(other(wavelengths Planck Collaboration: The Planck mission
Planck Collaboration: The Planck mission
Fig. 7. Maximum posterior CMB intensity map at 50 resolution derived from the joint baseline analysis of Planck, WMAP, and 408 MHz observations. A small strip of the Galactic plane, 1.6 % of the sky, is filled in by a constrained realization that has the same statistical properties as the rest of the sky.
Q Stokes(vectors Acmb
Fig. 7. Maximum posterior CMB intensity map at 50 resolution derived from the joint baseline analysis of Planck, WMAP, and 408 MHz observations. A small strip of the Galactic plane, 1.6 % of the sky, is filled in by a constrained realization that has the same statistical properties as the rest of the sky.
U Acmb
Fig. 8. Maximum posterior amplitude Stokes Q (left) and U (right) maps derived from Planck observations between 30 and 353 GHz. These mapS have been highpass-filtered with a cosine-apodized filter between ` = 20 and 40, and the a 17 % region of the Galactic plane has been replaced with a constrained Gaussian realization (Planck Collaboration IX 2015). From Planck Collaboration X (2015).
viewed as work in progress. Nonetheless, we find alargest(scales(removed high level of 8.2.2. Number of modes + + consistency in results3 between the0 TT and the full3 Planck(Collaboration(2015 TT TE EE likelihoods. Furthermore, the cosmological parameters (which One way of assessing the constraining power contained in a par- do not depend strongly on ⌧) derivedµK from the TE spectra have ticular measurement of CMB anisotropies is to determine the comparable errors to the TT-derived parameters, and they are e↵ective number of a`m modes that have been measured. This Fig. 8. Maximum posterior amplitude Stokes Q (left) and U (right) maps derived from Planck observations between 30 and 353 GHz. consistent to within typically 0.5 or better. is equivalent to estimating 2 times the square of the total S/N These mapS have been highpass-filtered with a cosine-apodized filter between ` = 20 and 40, and the a 17 % region of the Galacticin the power spectra, a measure that contains all the available plane has been replaced with a constrained Gaussian realization (Planck Collaboration IX 2015). From Planck Collaboration X (2015). 16 viewed as work in progress. Nonetheless, we find a high level of 8.2.2. Number of modes consistency in results between the TT and the full TT+TE+EE likelihoods. Furthermore, the cosmological parameters (which One way of assessing the constraining power contained in a par- do not depend strongly on ⌧) derived from the TE spectra have ticular measurement of CMB anisotropies is to determine the comparable errors to the TT-derived parameters, and they are e↵ective number of a`m modes that have been measured. This consistent to within typically 0.5 or better. is equivalent to estimating 2 times the square of the total S/N in the power spectra, a measure that contains all the available
16 Q
E U
B ACTPol maps, scale 15 uK, 10 degrees, Naess et al 2014 Planck Collaboration: Gravitational lensing by large-scale structures with Planck Lensing(potential,(phi Planck at the expected level. In Sect. 3.3, we cross-correlate the reconstructed lensing potential with the large-angle temperature T anisotropies to measure the CL correlation sourced by the ISW e↵ect. Finally, the power spectrum of the lensing potential is pre- sented in Sect. 3.4. We use the associated likelihood alone, and in combination with that constructed from the Planck temper- ature and polarization power spectra (Planck Collaboration XI 2015), to constrain cosmological parameters in Sect. 3.5.
3.1. Lensing potential ˆWF (Data) In Fig. 2 we plot the Wiener-filtered minimum-variance lensing Planck(Collaboration(2015 estimate, given by T(nFig.) = T 2(nT Lensing+(nd))==TT((n potentialn++d∇)φ=)T( estimatedn + ∇φ) from the SMICA full-mission C , fid CMB maps using the MV estimator. The power spectrum of ˆWF = L ˆMV, LM , fid LM (5) this map forms the basis of our lensing likelihood. The estimate CL + NL has been Wiener filtered following Eq. (5), and band-limited to , fid 8 L 2048. where CL is the lensing potential power spectrum in our fidu- cial model and NL is the noise power spectrum of the recon- struction. As we shall discuss in Sect. 4.5, the lensing potential estimate is unstable for L < 8, and so we have excluded those modes for all analyses in this paper, as well as in the MV lensing map. As a visual illustration of the signal-to-noise level in the lens- ing potential estimate, in Fig. 3 we plot a simulation of the MV reconstruction, as well as the input realization used. The re- construction and input are clearly correlated, although the recon- struction has considerable additional power due to noise. As can be seen in Fig. 1, even the MV reconstruction only has S/N 1 ˆWF (Sim.) for a few modes around L 50. ⇡ The MV lensing estimate⇡ in Fig. 2 forms the basis for a public lensing map that we provide to the community (Planck Collaboration I 2015). The raw lensing potential estimate has a very red power spectrum, with most of its power on large angular scales. This can cause leakage issues when cutting the map (for example to cross-correlate with an additional mass tracer over a small portion of the sky). The lensing convergence defined by L(L + 1) = , (6) LM 2 LM has a much whiter power spectrum, particularly on large angular Input (Sim.) scales. The reconstruction noise on is approximately white as well (Bucher et al. 2012). For this reason, we provide a map Fig. 3 Simulation of a Wiener-filtered MV lensing reconstruc- of the estimated lensing convergence rather than the lensing tion (upper) and the input realization (lower), filtered in the potential . same way as the MV lensing estimate. The reconstruction and input are clearly correlated, although the reconstruction has con- siderable additional power due to noise. 3.2. Lensing B-mode power spectrum The odd-parity B-mode component of the CMB polarization is of great importance for early-universe cosmology. At first order in perturbation theory it is not sourced by the scalar fluctuations that dominate the temperature and polarization anisotropies, and so the observation of primordial B-modes can be used as a uniquely powerful probe of tensor (gravitational wave) or vec- analysis gives no statistically-significant evidence for primor- tor perturbations in the early Universe. A detection of B-mode dial gravitational waves, and establishes a 95 % upper limit fluctuations on degree angular scales, where the signal from r0.05 < 0.12. This still represents an important milestone for gravitational waves is expected to peak, has recently been re- B-mode measurements, since the direct constraint from the B- ported at 150 GHz by the BICEP2 collaboration (Ade et al. mode power spectrum is now as constraining as indirect, and 2014). Following the joint analysis of BICEP2 and Keck Array model-dependent, constraints from the TT spectrum (Planck data (also at 150 GHz) and the Planck polarization data, primar- Collaboration XIII 2015). ily at 353 GHz (BICEP2/Keck Array and Planck Collaborations In addition to primordial sources, the e↵ect of gravitational 2015), it is now understood that the B-mode signal detected lensing also generates B-mode polarization. The displacement of by BICEP2 is dominated by Galactic dust emission. The joint lensing mixes E-mode polarization into B-mode as (Smith et al.
4 What(are(the(geometry,(contents,(and(initial(conditions( of(the(Universe?( What(happened(to(start(the(expansion?(Why?( What(are(the(properties(of(the(dark(sector?( Rough(description(of(CMB(analysis(process:(
‘Data’(((((=(maps(of(the(blackbody(sky((temp,(pol,(lensing)( Statistic(=(angular(power(spectrum(of(maps( Output(((=(cosmological(parameters((reliable(codes( (((((((((((((((((((((((((((((predict(their(theory(power(spectra) CMB(temperature Angular scale 90 18 1 0.2 0.1 0.07 0.05 104 Planck ACT SPT 103 ] 2 K µ [ ` 102 D
101
Planck(Collaboration(2015 2 10 30 1000 2000 3000 4000 Multipole moment, `
6Rparameter(LCDM(fits(extremely(well:(constraints(on(baryon,(CDM(and(Lambda(fractions,(and(size( 2 of(initial(fluctuations.(Relic(DM(density(Ωch = 0.120 ± 0.003( Planck Collaboration: The Planck mission
6000
5000 Planck Collaboration: The Planck mission
6000
] 4000 2 K µ [ 30005000 TT D ] 20004000 2 K µ [ 10003000 TT D 20000 600 60 1000300 30 TT 0 0 D
0 -300 -30 600 60 -600 -60 300 30 TT 2 10 30 500 1000 1500 2000 2500 0 0 D -300 -30 Fig. 9. The Planck 2015 temperature-600 power spectrum. At multipoles ` 30 we show the maximum likelihood-60 frequency averaged Plik temperature spectrum computed2 from the10 cross-half-mission30 500 likelihood1000 with1500 foreground2000 and other2500 nuisance parameters deter- mined from the MCMC analysis of the base ⇤CDM cosmology. In the multipole range 2 ` 29, we plot the power spectrum estimates from the Commander component-separation algorithm computed over 94 % of the sky. The best-fit base ⇤CDM theoretical Fig.spectrum 9. The fittedPlanck to the2015Planck temperatureTT+lowP power likelihood spectrum. is plotted At multipoles in the upper` 30 panel. we show Residuals the maximum with respect likelihood to this model frequency are shown averaged in temperaturethe lower panel. spectrum The error computed bars show from the1 Plikuncertainties.cross-half-mission From Planck likelihood Collaboration with foreground XIII (2015 and). other nuisance parameters deter- ± mined from the MCMC analysis of the base ⇤CDM cosmology. In the multipole range 2 ` 29, we plot the power spectrum estimates from the Commander component-separation algorithm computed over 94 % of the sky. The best-fit base ⇤CDM theoretical spectrum fitted to the Planck TT+lowP likelihood is plotted in the upper panel. Residuals with respect to this model are shown in the lower panel. The error bars show 1 uncertainties. From Planck Collaboration XIII (2015). ± CMB(polarization((ERmode)
100 Planck(Collaboration(2015 ] 2 80 K µ
5 60
[10 40 EE ` 20 C -40 2000 30 500 1000 1500 2000
Fig. 10. Frequency-averaged TE (left) and EE (right) spectra (withoutGreatly(limits(vast(zoo(of(alternatives(to(LCDM,(e.g.( fitting for T–P leakage). The theoretical TE and EE spectra plotted in the upper panel of each plot are computed from the best-fit• modeldifferent(contents:( of Fig. 9.extra(relativistic(species,(early(dark(energy( Residuals with respect to this theoretical model are shown in the lower panel in each plot. The error bars show 1• different(initial(fluctuations:(errors. The green linesscale5dependent(power,(tensor(or(isocurvature(fluctuations in the lower panels show the best-fit ( temperature-to-polarization leakage model, fitted separately to the± TE• extra(components:(and EE spectra.cosmic(defects,(magnetic(fields( From Planck Collaboration XIII (2015). • Fig. 10. Frequency-averaged TE (left) and EE (right) spectra (withoutnon5standard(BBN(or(recombination(history,(dark(matter(annihilation fitting for T–P leakage). The theoretical TE and EE spectra plotted in the upper panel of each plot are computed from the best-fit model of Fig. 9. Residuals with respect to this theoretical model are shown in the lower panel in each plot. The error bars show 1 errors. The green lines in the4 lower panels show the best-fit temperature-to-polarizationcosmological information if leakage we assume model, that fitted the anisotropies separately to are the± TEandand 96 000EE modes,spectra. respectively. From PlanckFrom Collaboration this perspective XIII (2015 the 2015). purely Gaussian (and hence ignore all non-Gaussian informa- Planck data constrain approximately 55 % more modes than in tion coming from lensing, the CIB, cross-correlations with other the 2013 release. Of course this is not the whole story, since probes, etc.). Carrying out this procedure for the Planck 2013 some pieces of information are more valuable than others, and cosmologicalTT power spectrum information data provided if we assume in Planck that the Collaboration anisotropies XV are inand fact 96Planck 000 modes,is able respectively. to place considerably4 From this tighter perspective constraints the 2015 on (purely2014) and GaussianPlanck (and Collaboration hence ignore XVI all(2014 non-Gaussian), yields the informa- number particularPlanck data parameters constrain (e.g., approximately reionization 55 optical % more depth modes or than certain in 826tion 000 coming (which from includes lensing, the the e CIB,↵ects cross-correlations of instrumental noise, with other cos- the 2013 release. Of course this is not the whole story, since micprobes, variance etc.). and Carrying masking). out this The procedure 2015 TT fordata the havePlanck increased2013 some4Here pieces we have of information used the basic are (and more conservative) valuable than likelihood; others, more and thisTT power value to spectrum 1 114 000, data with providedTE and inEEPlanckadding Collaboration a further 60 000 XV modesin fact arePlanck e↵ectivelyis able probed to place by Planck considerablyif one includes tighter constraints larger sky frac- on (2014) and Planck Collaboration XVI (2014), yields the number tions.particular parameters (e.g., reionization optical depth or certain 826 000 (which includes the e↵ects of instrumental noise, cos- mic variance and masking). The 2015 TT data have increased 4Here we have used the basic (and conservative) likelihood; more this value to 1 114 000, with TE and EE adding a further 60 000 modes are e↵ectively probed by Planck if one includes larger sky frac-17 tions.
17 Planck Collaboration: Cosmological parameters
Dark(Matter( 1.025 23 Planck TT,TE,EE+lowP annihilation 10 WMAP9 CVL 1.000 24 Possible interpretations for: ] 1 10 AMS-02/Fermi/Pamela
Planck Collaboration: Cosmological parameters s Fermi GC s 3 n CMB 25 0.975If we allow Y to vary as an additional parameter to base The way in which DM annihilations heat and ionize the P Planck TT,TE,EE+lowP [cm 10 ⇤CDM, we find the following constraints (at 95 % CL): gaseous background depends on the nature of the cascade of par- Planck TE+lowP v
ticles produced following annihilation and, in particular, on the Planck EE+lowP 26 Thermal relic
+0.041 production 10 of e± pairs and photons that couple to the gaseous 0.950 0.253 Planck TTPlanck+lowPTT+lowP ; e
0.042 f background. The fraction of the rest mass energy that is injected . +0.036 WMAP9+ + BBN 8 0 255 0.038 Planck TT lowP BAO ; into the gaseous background can be modelled by an “e ciency YP = > 27 0> . +0.0262 4 + 6 8 factor”,10f ( z), which is typically in the range f = 0.01–1 and > 0 251 0.027 Planck TT,TE,EE lowP ; 27 > 27 3 1 1 depends on redshift . Computations of f (z) for various annihi- < . +0p.025ann [10Planck cm s GeV+ ] + > 0 253 0.026 TT,TE,EE lowP BAO . lation channels can be found in Slatyer et al. (2009), Hutsi¨ et al. > 1 10 100 1000 10000 > (79) (2009) and Evoli et al. (2013). The rate of energy release per unit > BBN Fig.Joint 40. constraints2-dimensional: on (YP marginal, !b) are distributions shown in Fig. in38 the. Thepann ad-–ns volume by annihilating DM can thereforem [GeV] be written as planedition for ofPlanckPlanckTTpolarization+lowP (red), measurements EE+lowP (yellow), results in TE a+ sub-lowP dE 2 2 2 6 (green),stantial or reductionPlanck TT,TE,EE in the uncertainty+lowP (blue) on the data helium combinations. fraction. Fig. 41. Constraints(z) = on2 g the⇢ self-annihilationc ⌦ (1 + z) pann(z cross-section), (81) at re- BBN dtdV crit c WeIn also fact, show the thestandard constraints deviation obtained on YP usingin WMAP9 the case of dataPlanck (light combination, 3 z , times the e ciency parameter, fe↵ (Eq. 82). h i ⇤ blue).TT,TE,EE+lowP is only 30 % larger than the observational error whereThe bluepann areais defined shows as the parameter space excluded by the Planck quoted by Aver et al. (2013). As emphasized throughout this pa- TT,TE,EE+lowP data at 95 % CL. The3 yellow line indicates the per, the systematics in the Planck polarization spectra, although pann(z) f (z)h i, (82) constraint using WMAP9 data.⌘ Them dashed green line delineates 16 at low levels, have not been accurately characterized at this time. the region ultimately accessible by a cosmic variance limited ex- Readers should therefore treat the polarization constraints with ⇢critperimentthe critical with density angular of resolution the Universe comparable today, m is to the that mass of Planck of . some caution. Nevertheless, as shown in Fig. 38, all three data the DM particle, and 3 is the thermally-averaged annihilation We then add pann as an additional parameter to those of the base The horizontal red band includes the values of the thermal-relic combinations agree well with the observed helium abundance cross-section times (Møller)h i velocity (we will refer to this quan- ⇤CDM cosmology. Table 6 shows the constraints for various cross-section multiplied by the appropriate f for di↵erent DM measurements and with the predictions of standard BBN. tity loosely as the “cross-section” hereafter). In Eq.e↵ (81), g is a data combinations. annihilation channels. The dark grey circles show the best-fit There is a well-known parameter degeneracy between YP degeneracy factor that is equal to 1/2 for Majorana particles and and the radiation density (see the discussion in PCP13). Helium 1/DM4 for models Dirac particles. for the PAMELA In this paper,/AMS-02 the constraints/Fermi cosmic-ray will refer ex- cesses, as calculated in Cholis & Hooper (2013) (caption of their abundance predictions from the CMB are3 therefore1 particularly1 to Majorana particles. Note that to produce the observed dark Table 6. Constraints on pann in units of cm s GeV . sensitive to the addition of the parameter Ne↵ to base ⇤CDM. matterfigure density 6). The from light thermal grey stars DM relics show requires the best-fit an s-wave DM models anni- for BBN the Fermi Galactic centre gamma-ray26 excess,3 1 as calculated by Allowing both YP and Ne↵ to vary we find the following con- hilation cross-section of 3 3 10 cm s at the time of straints (at 95 % CL): freeze-outCalore et (see al. e.g.,(2014 the) (their reviewh i⇡ tables by ⇥Profumo I, II,2013 and). III), with the light Data combinations pann (95 % upper limits) greyBoth area the indicating amplitude the and astrophysical redshift dependence uncertainties of the on e the - best- 27 TT+lowP . . . . .+ .0. 058 ...... < 5.7 10 ciencyfit cross-sections. factor f (z) depend on the details of the annihilation pro- 0.252 0.065 Planck TT+lowP ; ⇥ 27 EE+lowP . . . . . ...... < 1.4 10 cess (e.g., Slatyer et al. 2009). The functional shape of f (z) + . +0.058 + < +. ⇥ 28 TEBBNlowP8 .0 .251 . . . .0. 064 . . . .Planck ...... TT lowP5 9BAO10 ; can be taken into account using generalized parameterizations Y = ⇥ 27 TTP +lowP>+lensing. +0. 034 ...... < 4+.4 10 orimprovement principal components if other astrophysical (Finkbeiner et data, al. or2012Planck; Hutsilensing, et al. are > 0 263 0.037 Planck TT,TE,EE lowP⇥ ; > 28 2011), similar29 to the analysis of the recombination history pre- TT,TE,EE<>+0lowP.262+ .0. 035 . . . .Planck ...... TT,TE,EE< 4+.1lowP10+ BAO . added. > 0.037 ⇥ 28 sented in Sect. 6.7.4. However, as shown in Galli et al. (2011), TT,TE,EE>+lowP+ lensing ...... < 3.4 10 We verified the robustness of the Planck TT,TE,EE+lowP > ⇥ 28 (80) Giesen et al. (2012), and Finkbeiner et al. (2012), to a first ap- TT,TE,EE>+lowP+BBNext ...... < 3.5 10 constraint by also allowing other extensions of ⇤CDM (Ne↵, Contours in: the (Y , Ne↵) space are shown in⇥ Fig. 39. Here proximation the redshift dependence of f (z) can be ignored, P dn /d ln k, or Y ) to vary together with p . We found that the again, the impact of Planck polarization data is important, and sinces current CMBP data (including Planck) areann sensitive to en- helps to reduce substantially the degeneracy between these two ergyconstraint injection is weakened over a relatively by up to narrow 20 %. range Furthermore, of redshift, we typi- have ver- parameters. Note that the Planck TT,TE,EE+lowP contours are callyifiedz that1000–600. we obtain The consistent e↵ects of results DM annihilation when relaxing can there- the priors The constraints on pann from the Planck TT+lowP spec- ⇡ in very good agreement with standard BBN and Ne↵ = 3.046. foreon thebe reasonably amplitudes well of the parameterized Galactic dust by templates a single constant or if we pa- use the tra are about 3 times weaker than the 95 % limit of pann < CamSpec Plik However,27 even3 if1 we relax1 the assumption of standard BBN, the rameter, pannlikelihood, (with f (z instead) set to of a constant the baselinefe↵) that encodeslikelihood. the 2.1 10 cm s GeV derived from WMAP9, which in- CMB does not allow high values of Ne↵. It is therefore di cult dependenceFigure on41 theshows properties the constraints of the DM particles. from WMAP9, In the fol-Planck cludes⇥ WMAP polarization data at low multipoles. However, the to accommodate an extra thermalized relativistic species, even if lowing,TT,TE,EE we calculate+lowP, and constraints a forecast on the forp aann cosmicparameter, variance assum- limited Planckthe standard T E or BBNEE spectra prior on improve the helium the fraction constraints is relaxed. on pann by ingexperiment that it is constant, with similar and angular then project resolution these constraints to Planck30 on. The to hor- about an order of magnitude compared to those from Planck TT aizontal particular red dark band matter includes model the assuming values off thee↵ = thermal-relicf (z = 600), cross- ↵ alone. This is because the main e ect of dark matter annihila- sincesection the e multiplied↵ect of dark by matter the appropriate annihilationf peaksfor atdi↵z erent600 DM (see anni- 6.6. Dark matter annihilation e↵ ⇡ tion is to increase the width of last scattering, leading to a sup- Finkbeinerhilation channels. et al. 2012 For). The example,f (z) functions the upper used red line here corresponds are those to pression of the amplitude of the peaks both in temperature and Energy injection from dark matter (DM) annihilation can calculatedfe↵ = 0.67, in Slatyer which is et appropriate al. (2009), with for thea DM updates particle described of mass inm = polarization. As a result, the e↵ects of DM annihilation on the + alter the recombination history, leading to changes in the Galli10 GeV et al. annihilating(2013) and Madhavacheril into e e , while et al. the(2014 lower). Finally, red line we corre- powertemperature spectra at and high polarization multipole are power degenerate spectra with of other the param- CMB estimatesponds the to f fractions= 0.13, of for injected a DM energy particle that annihilating a↵ect the gaseous into 2⇡+⇡ ⇤ e↵ eters(e.g., ofChen base &CDM, Kamionkowski such as n2004s and; PadmanabhanAs (Chen & Kamionkowski & Finkbeiner background,through an fromintermediate heating, mediator ionizations, (see or e.g., Ly↵Arkani-Hamedexcitations us- et al. 20042005; Padmanabhan). As demonstrated & Finkbeiner in several2005 papers). At(e.g., largeGalli angular et al. 2009 scales; ing2009 the). updated The Planck calculationsdata exclude described at 95 in %Galli confidence et al. (2013 level) and a ther- (` Slatyer. 200), et al. however,2009; Finkbeiner dark matter et al. annihilation2012), CMB can anisotropies produce an Valdes et al. (2010), following Shull & van Steenberg (1985). We compute the theoretical angular power in the pres- enhancemento↵er the opportunityin polarization to caused constrain by the the increased nature ionization of DM. 29It is interesting to note that the constraint derived from Planck fractionFurthermore, in the freeze-out CMB experiments tail following such recombination. as Planck can achieve As a re- ence of DM annihilations by modifying the recfast routine TT,TE,EE+lowP is consistent with the forecast given in Galli28 et al. limits on the annihilation cross-section that are relevant to (Seager et al. 1999) in28 the camb3 1 code1 as in Galli et al. (2011). sult, large-angle polarization information is crucial in breaking (2009), pann < 3 10 cm s GeV . thethe degeneracies interpretation between of the parameters,rise in the cosmic-ray as illustrated positron in Fig. frac-40. 2730 ⇥ > ToWe maintain assumed consistency that the with cosmic other variance papers on limited dark matter experiment annihila- would Thetion strongest at energies constraints10 GeV on observedpann therefore by PAMELA, come fromFermi the, and full tion,measure we retain the the angular notation powerf (z) for spectra the e upciency to a factor maximum in this section. multipole of AMS (Adriani et⇠ al. 2009; Ackermann et al. 2012; Aguilar et al. Planck temperature and polarization likelihood and there is little It` shouldmax = 2500, not be observing confused with a sky the fraction growth ratefsky factor= 0.65. introduced in Equ. 2014). The CMB constraints are complementary to those de- (32). termined from other astrophysical probes, such as the gamma- 28We checked that we obtain similar results using either the HyRec ray observations of dwarf galaxies by the Fermi satellite code (Ali-Haimoud & Hirata 2011), as detailed in Giesen et al. (2012), 51 (Ackermann et al. 2014). or CosmoRec (Chluba & Thomas 2011), instead of recfast.
50 CMB(lensing Planck Collaboration: Cosmological parameters ] 7 1.6 T only 10
[ T + P 1.2 2 / 0.8 C 2 0.4 + 1)] ( [
0.0 50 100 150 200 250 300 350 400 ] 2 Planck(Collaboration(2015
Lensing(limits(curvature(to(2%,(and(neutrino(mass(sum(to(0.7(eV.
Fig. 11. Planck measurements of the lensing power spectrum compared to the prediction for the best-fitting base ⇤CDM model to the Planck TT+lowP data. Left: the conservative cut of the Planck lensing data used throughout this paper, covering the multipole range 40 ` 400. Right: lensing data over the range 8 ` 2048, demonstrating the general consistency with the ⇤CDM prediction over this extended multipole range. In both cases, green points are the power from lensing reconstructions using only temperature data, while blue points combine temperature and polarization. They are o↵set in ` for clarity. Error bars are 1 . In the top panels the solid lines are the best-fitting base ⇤CDM model to the Planck TT+lowP data with no renormalization or ±N(1) correction applied (see text). The bottom panels show the di↵erence between the data and the renormalized and N(1)-corrected theory bandpowers, which enter the likelihood. The mild preference of the lensing measurements for lower lensing power around ` = 200 pulls the theoretical prediction for C` downwards at the best-fitting parameters of a fit to the combined Planck TT+lowP+lensing data, shown by the dashed blue lines (always for the conservative cut of the lensing data, including polarization).
Beam uncertainties are no longer included in the covariance The Planck measurements of C` , based on the temperature • and polarization 4-point functions, are plotted in Fig. 11 (with matrix of the C` , since, with the improved knowledge of the beams, the estimated uncertainties are negligible for the lens- results of a temperature-only reconstruction included for com- ing analysis. The only inter-bandpower correlations included parison). The measured C` are compared with the predicted lensing power from the best-fitting base ⇤CDM model to the in the C` bandpower covariance matrix are from the uncer- tainty in the correction applied for the point-source 4-point Planck TT+lowP data in this figure. The bandpowers that are function. used in the conservative lensing likelihood adopted in this pa- per are shown in the left-hand plot, while bandpowers over the As in the 2013 analysis, we approximate the lensing likelihood range 8 ` 2048 are shown in the right-hand plot, to demon- as Gaussian in the estimated bandpowers, with a fiducial co- strate the general consistency with the ⇤CDM prediction over variance matrix. Following the arguments in Schmittfull et al. the full multipole range. The di↵erence between the measured (2013), it is a good approximation to ignore correlations between bandpowers and the best-fit prediction are shown in the bottom the 2- and 4-point functions; so, when combining the Planck panels. Here, the theory predictions are corrected in the same power spectra with Planck lensing, we simply multiply their re- way as they are in the likelihood15. spective likelihoods. Figure 11 suggests that the Planck measurements of C are It is also worth noting that the changes in absolute calibra- ` ⇤ tion of the Planck power spectra (around 2 % between the 2013 mildly in tension with the prediction of the best-fitting CDM and 2015 releases) do not directly a↵ect the lensing results. The model. In particular, for the conservative multipole range 40 ` 400, the temperature+polarization reconstruction has 2 = CMB 4-point functions do, of course, respond to any recalibra- 15.4 (for eight degrees of freedom), with a PTE of 5.2 %. For tion of the data, but in estimating C` this dependence is re- reference, over the full multipole range 2 = 40.81 for 19 de- moved by normalizing with theory spectra fit to the observed 2 grees of freedom (PTE of 0.3 %); the large is driven by a CMB spectra. The measured C` bandpowers from the 2013 and single bandpower (638 ` 762), and excluding this gives an current Planck releases can therefore be directly compared, and acceptable 2 = 26.8 (PTE of 8 %). We caution the reader that are in good agreement (Planck Collaboration XV 2015). Care is this multipole range is where the lensing reconstruction shows a needed, however, in comparing consistency of the lensing mea- mild excess of curl-modes (Planck Collaboration XV 2015), and surements across data releases with the best-fitting model pre- dictions. Changes in calibration translate directly into changes in A e 2⌧, which, along with any change in the best-fitting opti- s 15In detail, the theory spectrum is binned in the same way as the cal depth, alter As, and hence the predicted lensing power. These data, renormalized to account for the (very small) di↵erence between changes from 2013 to the current release go in opposite direc- the CMB spectra in the best-fit model and the fiducial spectra used in the tions leading to a net decrease in As of 0.6 %. This, combined lensing analysis, and corrected for the di↵erence in N(1), calculated for (1) with a small (0.15 %) increase in ✓eq, reduces the expected C the best-fit and fiducial models (around a 4 % change in N , since the ` by approximately 1.5 % for multipoles ` > 60. fiducial-model C` is higher by this amount than in the best-fit model).
22 Planck Collaboration: Cosmological parameters
photon density ⇢ at T 1 MeV by ⌧ / Planck Collaboration: Cosmological parameters 7 4 4 3 ⇢ = N ↵ ⇢ . (59) e 8 11 Planck Collaboration: Cosmological parameters photon density ⇢ at T 1 MeV by! Planck Collaboration: Cosmological parameters ⌧ The numerical factors in this equation4/3 are included so that Ne↵ = 3 for three standard model7 4 neutrinos that were thermal- photon density ⇢ at T⇢ = N1e MeV↵ by ⇢ . (59) ized in the early Universe⌧ and8 decoupled11 well before electron- positron annihilation. The standard ! cosmological prediction is 4/3 Theactually numericalNe↵ = factors3.046, since in this7 neutrinos equation4 are are not included completely so that de- ⇢ = Ne↵ ⇢ . (59) coupledNe↵ = 3 at for electron-positron three standard model8 annihilation11 neutrinos and that are were subsequently thermal- izedslightly in the heated early (Mangano Universe et and al. decoupled2002! ). well before electron- ThepositronIn numerical this annihilation. section factors we The focus in this standard on equation additional cosmological are density included prediction from so mass- that is Nactuallylesse↵ = particles.3N fore↵ three= In3 addition. standard046, since to model massless neutrinos neutrinos sterile are not neutrinos, that completely were thermal- a variety de- izedcoupledof other in the at particles early electron-positron Universe could contribute and annihilation decoupled to Ne↵ well.and We are before assume subsequently electron- that the positronslightlyadditional heated annihilation. massless (Mangano particles The et standard al. are2002 produced cosmological). well before prediction recombi- is actuallynation,In this andNe↵ section neither= 3.046, we interact focus since nor onneutrinos decay, additional so are that notdensity their completely energy from mass- den- de- coupledlesssity particles.scales at electron-positron with In the addition expansion to massless annihilation exactly sterile like and massless neutrinos, are subsequently neutrinos. a variety Fig. 31. Samples from Planck TT+lowP chains in the Ne↵–H0 slightlyofAn other additional heated particles ( ManganoNe could↵ = 1 contribute et could al. 2002 correspond to). N . We to a assume fully thermal- that the e↵ < plane, colour-coded by 8. The grey bands show the constraint additionalizedIn sterile this massless section neutrino we particles that focus decoupled areon additional produced at T well density100 before MeV; from recombi- for mass- ex- 1 1 ⇠ H0 = (70.6 3.3) km s Mpc of Eq. (30). Note that higher lessnation,ample particles. any and sterile neither In addition neutrino interact to with normassless decay, mixing sterile so angles that neutrinos, their large energy enough a variety den- to ± provide a potential resolution to short-baseline reactor neutrino Ne↵ brings H0 into better consistency with direct measurements, ofsity other scales particles with the could expansion contribute exactly to N likee↵. We massless assume neutrinos. that the but increases . Solid black contours show the constraints from oscillation anomalies would most likely thermalize rapidly in the Fig. 31. Samples8 from Planck TT+lowP chains in the Ne↵–H0Fig.additionalAn 29. additionalSamples massless from Ne↵ the particles= Planck1 could areTT produced correspond+lowP posterior well to before a fully in the recombi- thermal- Planck TT,TE,EE+lowP+BAO. Models with Ne↵ < 3.046 (left early Universe. However, this solution to the< neutrino oscillation plane, colour-coded by 8. The grey bands show the constraint mnation,ized⌫–H0 sterileplane, and neither neutrino colour-coded interact that decoupled norby decay,8. Higher at soT that100 theirm⌫ MeV;damps energy for den-Fig. ex- 30. Constraints on m⌫ for various data combinations. of the solid vertical line)1 require1 photon heating after neutrino anomalies requires approximately 1 eV sterile⇠ neutrinos, rather H0 = (70.6 3.3) km s Mpc of Eq. (30). Note that higherthesityample matter scales any fluctuation with sterile the neutrino amplitude expansion with exactly8, mixing but also like angles decreases massless large neutrinos. enoughH0 to decoupling or± incomplete thermalization. Dashed vertical linesP than the massless case considered in this section;P exploration of Fig.Ne↵ 31.bringsSamplesH0 into from betterPlanck consistencyTT+lowP with chains direct in measurements, the Ne↵–H0(greyAnprovide bands additional a show potential theNe↵ resolution direct= 1 could measurement to correspond short-baselineH0 to= a reactor(70 fully.6 thermal- neutrino P correspond to specific fully-thermalized particle models, for ex- . the two1 parameters1 Ne↵ and m⌫ is reported< in Sect. 6.4.3± .Adding For the polarization spectra improves this constraint slightly plane,but increases colour-coded 8. Solid by black 8. The contours grey bands show show the constraints the constraint from3 3)izedoscillation km steriles Mpc anomalies neutrino , Eq. 30 that). would Solid decoupled most black likely contours at T thermalize show100 the MeV; rapidly con- for in ex- the ample one additional massless1 boson1 that decoupled around thestrainta review from Planck of sterileTT neutrinos+lowP+lensing see Abazajian (which⇠ mildlyet al. (2012 prefers). to HPlanck0 = (70TT,TE,EE.6 3.3)+lowP km s +BAO.Mpc Modelsof Eq. with (30).N Notee↵ < that3.046 higher (left ampleearly Universe. any sterile However, neutrino this withP solution mixing to angles the neutrino large enough oscillation to same time as± the neutrinos ( Ne↵ 0.57), or before muonlarger masses),More generally and filled the contours additional show radiation the constraints does not from need to be Nof thebrings solidH verticalinto better line) consistency require photon with heating direct measurements, after neutrino provideanomalies a potential requires resolution approximately to short-baseline 1 eV sterile neutrinos,reactor neutrino rather m⌫ < 0.59 eV (95%, Planck TT,TE,EE+lowP+lensing). annihilatione↵ 0 ( N 0.39), or an additional⇡ sterile neutrinoPlanckfullyTT thermalized,+lowP+lensing for+BAO. example there are many possible models butdecoupling increases or incomplete. Solide↵ black thermalization. contours show Dashed the constraints vertical from lines oscillationthan the massless anomalies case would considered most likely in this thermalize section; exploration rapidly in the of (56) that decoupled8 around⇡ the same time as the active neutrinos of non-thermal radiation production via particle decays (see e.g.,X PlanckcorrespondTT,TE,EE to specific+lowP fully-thermalized+BAO. Models with particleNe↵ models,< 3.046 for (left ex- earlythe two Universe. parameters However,Ne↵ and this solutionm⌫ is reported to the neutrino in Sect. oscillation6.4.3.We For take the combined constraint further including BAO, JLA, ( Ne↵ 1). Hasenkamp & Kersten 2013; Conlon & Marsh 2013). The radi- ofample the solid one⇡ additional vertical line) massless require boson photon that heating decoupled after around neutrino the anomaliesa review of requires sterile neutrinos approximately see Abazajian 1 eV sterile et al. neutrinos,(2012). ratherand H0 (“ext”) as our best limit ation could also be producedP at temperatures T > 100 MeV, decouplingsame time or as incomplete the neutrinos thermalization. ( Ne↵ 0. Dashed57), or vertical before muon lines thanMore the massless generally case the considered additional in radiation this section; does explorationnot need to of be ⇡ in which case typically Ne↵ < 1 for each additional species, m < 0.23 eV . thefully two thermalized, parameters forN ↵ exampleand m there⌫ is reported are many in possible Sect. 6.4.3 models. For ⌫ correspondannihilation to ( specificNe↵ fully-thermalized0 39), or an additional particle models,sterile neutrino for ex-highsince multipoles heating produces by photon ae relatively production small improvement at muon annihilation to the (at 95%, Planck TT+lowP+lensing+ext. ⇡ Planckaof review non-thermalTT+lowP of sterile+BAO radiation neutrinos constraint production see (andAbazajian the via improvement particle et al. decays(2012 is even). (see e.g., 2 amplethatA decoupled larger one additional range around of neutrino massless the same masses boson time wasthat as founddecoupled the active by Beutler around neutrinos et the al. T 100 MeV) decreases the fractional importance of the ad-X⌦⌫h < 0.0025 9 smaller with the alternative CamSpecP likelihood) so we consider > same(2014 Ne↵ time) using1). as thea combination neutrinos ( ofNe RSD,↵ 0 BAO,.57), or and before weak muon lens- ditionalHasenkamp⇡More component generally & Kersten the at the additional2013 later; Conlon times radiation relevant & Marsh does for2013 not the). need CMB. The to radi- For be = (57) ⇡ ⇡ Planck Collaboration: Cosmologicalthe TT results parameters to be our most reliable constraints. > > annihilationing information. ( Ne↵ The0 tension.39), or between an additional the RSD sterile results neutrino and fullyparticlesation thermalized, could produced also be for at produced exampleT 100 at there MeV temperatures are the many density possibleT would100 models be MeV,This di- is slightly weaker; than the constraint from Planck ⇡ + + + thatbase decoupled⇤CDM was around subsequently the same reduced time as following the active the neutrinos analysis ofThelutedin non-thermal which constraint even case more of radiationtypically by Eq. numerous (54b production ) N ise consistent↵ phase< 1 viatransitions for with particle each the additional and 95 decays % particle limit (see species, anni- e.g.,TT,TE,EE lowP lensing BAO, (which is tighter in both the < . + CamSpec and Plik likelihoods) but is immune to low level sys- (of NSamushiae↵ 1). et al. (2014), as shown in Fig. 17. Galaxy weakof Hasenkamphilations,sincem⌫ heating0 23 and & eV give Kersten by reported photon N 2013 in productionPCP13;1.Conlon Furthermore,for & atPlanck Marsh muon if theBAO.2013 annihilation particle). The The is radi- not (at ⇡ limits are similar because thee↵ linear CMB is insensitive to the tematics that might a↵ect the constraints from the Planck polar- lensingA larger and some range cluster of neutrino constraints masses remain was found in tension by Beutler with et base al. ationfermionic,T could100 MeV) the also factors decreasesbe produced entering⌧ the the at fractional temperatures entropy importance conservationT > 100 of equation the MeV, ad- massP of⇡ neutrinos that are relativistic at recombination. There is ization spectra. Equation (57) is therefore a conservative limit. ⇤(2014CDM,) using and we a combination discuss possible of RSD, neutrino BAO, resolutions and weak of these lens- inareditional which di↵erent, component case and typically even at the thermalized N latere↵ < times1 for particles relevant each additional could for the give CMB. species, specific For ing information. The tension between the RSD results andlittlesinceparticles to be heating gained produced from by photon improved at T production measurement100 MeV at the of muon density the CMB annihilation would tem- beMarginalizing (at di- over the range of neutrino masses, the Planck con- problems in Sect. 6.4.4. fractional values of Ne↵. For example Weinberg (2013) consid- 23 baseA⇤ largerCDM range was of subsequently neutrino masses reduced was foundfollowing by Beutler the analysis et al.peratureTluted power100 even MeV) more spectra, by decreases though numerous improved the phase fractional transitions external importance data and can particle help of the anni-straints ad- on the late-time parameters are Another way of potentially improving neutrino mass con-to breakers⇡ the the case geometric of a thermalized degeneracy massless to higher boson, precision. which CMB contributes (of2014Samushia) using et a al. combination(2014), as of shown RSD, in BAO, Fig. 17 and. Galaxy weak lens-weak ditional hilations,= component/ and give. atN thee↵ later1. Furthermore, times relevant if for the. the particle CMB.< is For not< H0 = 67.7 0.6 straints is to use measurements of the Ly↵ flux power spectrumlensingNe can↵ also4 7 provide0 57 if additional it decouples⌧ information in the range at lower 0 5 MeV red- T ± ing information. The tension between the RSD results and ⇡ T + . Planck TT+lowP+lensing+ext. (58) lensing and some cluster constraints remain in tension with base particles100fermionic, MeV produced like the factors the neutrinos,at entering100 or the MeV entropyNe↵ the0 conservation density.39 if it would decouples equation be di- at 0 015 of high-redshift quasars. Palanque-Delabrouille et al. (2014)shifts, and future high-resolution CMB polarization measure- 8 = 0.810 0.012 base⇤CDM,⇤CDM and was we discuss subsequently possible reduced neutrino following resolutions the analysis of these lutedare di even↵erent, more and by even numerous thermalized phase transitions particles⇡ could and particle give specific anni- 9 have recently reported an analysis of a large sample of quasarmentsT that> 100 accurately MeV (before reconstruct the photon the lensing production potential at can muon probe annihila- => ofspectraproblemsSamushia from in Sect. et the al. SDSSIII6.4.4(2014. ),/BOSS as shown survey. in Fig. When17 combining. Galaxy weak theirmuchhilations,tion,fractional smaller hence and masses values undergoing give (seeof NN e.g.e↵e fractional↵.Abazajian For1. exampleFurthermore, dilution). et al.Weinberg2015b if the). ( particle2013) consid- isFor not this restricted range;> of neutrino masses, the impact on the lensing and some cluster constraints remain in tension with base fermionic,ers the case the of factors a thermalized entering⌧ massless the entropy boson, conservation which contributes equationother cosmological parameters is small and, in particular, low resultsAnother with 2013 way Planck of potentially data, these improving authors find neutrino a bound massm con-⌫ < As discussedIn this paper in detail we in followPCP13 theand usual Sect. phenomenological5.1, the Planck ap- ⇤ ↵= / . . < values< of 8 will remain in tension with the parameter space 0straints.CDM,15 eV is and(95 to % use we CL), measurementsdiscuss compatible possible ofwith neutrino the the Ly results↵ flux resolutions presented power spectrum of in these this areproachNe di↵ erent, where4 7 and we0 57 even constrain if it thermalized decouplesNe↵ as ain particles free the parameterrange could 0 5 give MeV with specific a wideT CMB power spectra⇡ prefer somewhat more lensing smoothing preferred by Planck. problemssection.of high-redshift in Sect. 6.4.4 quasars.. Palanque-Delabrouille et al. P(2014)thanfractionalflat100 predicted prior, MeV valuesthough in like⇤CDM the of we neutrinos, (allowing commentNe↵. For theor example on lensing aN fewe↵ Weinberg discrete amplitude0.39 if cases( it2013 to decouples vary separately) consid- at ersT > the100 case MeV of a (before thermalized the photon massless production boson,⇡ which at muon contributes annihila-The constraint of Eq. (57) is weaker than the constraint of haveAnotherAn recently exciting way reported future of potentially prospect an analysis improving is the of a possible large neutrino sample direct mass of detection quasar con-givesbelow.AL > Values1 at just of N overe↵ < 23 .046). The are neutrino less well mass motivated, constraint since they = / . . < Eq.< (54b) excluding lensing, but there is no good reason to disre- straintsofspectra non-relativistic is from to use the measurements SDSSIII cosmic/BOSS neutrinos of survey. the by Ly↵ capture Whenflux power combining on tritium, spectrum their forfromwouldtion,N thee↵ hence power require4 7 undergoing spectra the0 57 standard if is it therefore fractional decouples neutrinos quite dilution). in to the tight, be range incompletely since 0 5 increas- MeV thermal-T 100 MeV like⇡ the neutrinos, or N 0.39 if it decouplesgard at the Planck lensing information while retaining other astro- ofexampleresults high-redshift with with 2013 theNeutrino(properties(from(cosmology Planck quasars. PTOLEMY data,Palanque-Delabrouille these experiment authors find (Cocco a bound et et al. al.(20142007m⌫ <)ing; theized neutrinoIn or this additional paper mass lowers photonwe follow the production predicted the usuale↵ smoothing after phenomenological neutrino even decoupling, fur- physical ap- data. The CMB lensing signal probes very-nearly lin- > ⇤ ⇡ haveBetts0.15 recently eV et al. (952013 % reported CL),; Long compatible an et al. analysis2014 with). of Unfortunately, the a large results sample presented for of the quasar in mass thistherTbutproach compared we100 include where MeV to base we (before this constrain rangeCDM. the for photon OnN completeness.e↵ theas production othera free hand parameter at the muon lensing with annihila- a wideear scales and passes many consistency checks over the multi- Planck Collaboration: Cosmologicalreconstruction parameters data, which directly probes the lensing power, spectrarangesection. fromm < the0. SDSSIII23 eV preferred/BOSSPlanck(Collaboration(2015 survey. by Planck When, detection combining withP their the tion,flatFigure prior, hence though31 undergoingshows we comment that fractionalPlanck on dilution). ais few entirely discrete consistent cases separately withpole the range used in the Planck lensing likelihood (see Sect. 5.1 ⌫ prefers lensing amplitudes slightly below (but consistent with) results with 20138 Planck data, these authors+ find a bound m < standardbelow.In this Values value paper of⇤NN↵ wee↵=< follow33.046..046 theare However, less usual well aphenomenological significant motivated, density since they ap- of Fig.firstAn 29. generation excitingSamples experiment future from the prospectPlanck will be isTT di the cult.lowP possible posterior direct indetection the⌫(1)ofNumber(of(species:( extensions to base CDMe the largest degradation of the error and Planck Collaboration XV 2015). The situation with galaxy Planck TT+lowP thein ! baseis in⇤ modelsCDM prediction that allow N (Eq.to vary.18). InThe thesePlanck models,+lensing the con- 0of.15m non-relativistic⌫– eVHP0 (95plane, % CL), colour-coded cosmic compatible neutrinos by with the8 by. Higher results capture presented onm⌫ tritium,damps in this forFig.proachadditionalwouldb 30. Constraints require where radiation we the on constrain standard ism still⌫e↵for allowed,neutrinosN variouse↵ as a data with free to be combinations. theparameter incompletely (68 %) with constraints thermal- a wideweak lensing is rather di↵erent, as discussed in Sect. 5.5.2. In 7 Planck TT+lowP+BAO straintmean value therefore of ! is pulls almost the identical constraints to that slightly for base away⇤CDM, from but zero to- thesection.example matter with fluctuation the PTOLEMY amplitude experiment 8, but also (Cocco decreases et al.PH20070 ; flatized prior, or additional thoughb we photon comment production on a few after discrete neutrino cases decoupling, separatelyaddition to possible observational systematics, the weak lensing Planck TT,TE,EE+lowP wardsthe error higher on !b neutrinoincreases masses, by about as 30 shown %. The invalue Fig. of30!b.is Although sta- the
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48 In(next(decade:(measure(neutrino(mass?
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Inflation(status(from(Planck
Universe(is(flat(to(0.5%,(fluctuations(are(super5horizon,(Gaussian(and(adiabatic Planck Collaboration: Cosmological parameters
1.0 CDM n = 0.96 +running+tensors 1500 s 0.8 ns = 1.00 ]
2 0.6 max
1000 P / [mK
P 0.4 D 2 500 0.2
0.0 n<1 0.94 0.96 0.98 1.00 0 ns 100 500 1000 2000 0.03 Multipole moment Planck(Collaboration(2014,(2015( CDM+running CDM+running+tensors 2 Fig. 22. The Planck power spectrum of Fig. 10 plotted as ` ` D against multipole, compared to the best-fit base ⇤CDM model 0.00 with n = 0.96 (red dashed line). The best-fit base ⇤CDM model k s ln
with ns constrained to unity is shown by the blue line. d / s
dn 0.03 Our extensive grid of models allows us to investigate cor- relations of the spectral index with a number of cosmological parameters beyond those of the base ⇤CDM model (see Figs. 0.06 21 and 24). As expected, ns is uncorrelated with parameters de- 0.94 0.96 0.98 1.00 scribing late-time physics, including the neutrino mass, geom- n etry, and the equation of state of dark energy. The remaining s correlations are with parameters that a↵ect the evolution of the early Universe, including the number of relativistic species, or the helium fraction. This is illustrated in Fig. 24: modifying the standard model by increasing the number of neutrinos species, 0.4 CDM+tensors or the helium fraction, has the e↵ect of damping the small-scale CDM+running+tensors power spectrum. This can be partially compensated by an in- crease in the spectral index. However, an increase in the neu- 0.3 trino species must be accompanied by an increased matter den- sity to maintain the peak positions. A measurement of the matter
0.002 N = 40
density from the BAO measurements helps to break this degen- r 0.2 N = 50 eracy. This is clearly seen in the upper panel of Fig. 24, which N = 60 shows the improvement in the constraints when BAO measure- 0.1 ments are added to the Planck+WP+highL likelihood. With the m 2 addition of BAO measurements we find more than a 3 devi- 2 ation from ns = 1 even in this extended model, with a best-fit 0.0 value of ns = 0.969 0.010 for varying relativistic species. As 0.94 0.96 0.98 1.00 discussed in Sect. 6.3±, we see no evidence from the Planck data ns for non-standard neutrino physics. The simplest single-field inflationary models predict that the running of the spectral index should be of second order in infla- tionary slow-roll parameters and therefore small [dns/d ln k Fig. 23. Upper: Posterior distribution for ns for the base ⇤CDM 2 ⇠ (ns 1) ], typically about an order of magnitude below the model (black) compared to the posterior when a tensor compo- sensitivity limit of Planck (see e.g., Kosowsky & Turner 1995; nent and running scalar spectral index are added to the model Baumann et al. 2009). Nevertheless, it is easy to construct in- (red) Middle: Constraints (68% and 95%) in the ns–dns/d ln k flationary models that have a larger scale dependence (e.g., by plane for ⇤CDM models with running (blue) and additionally adjusting the third derivative of the inflaton potential) and so it with tensors (red). Lower: Constraints (68% and 95%) on ns and is instructive to use the Planck data to constrain dns/d ln k.A the tensor-to-scalar ratio r0.002 for ⇤CDM models with tensors test for dns/d ln k is of particularly interest given the results from (blue) and additionally with running of the spectral index (red). previous CMB experiments. The dotted line show the expected relation between r and ns for Early results from WMAP suggested a preference for a nega- a V( ) 2 inflationary potential (Eqs. 66a and 66b); here N is tive running at the 1–2 level. In the final 9-year WMAP analy- the number/ of inflationary e-foldings as defined in the text. The sis no significant running was seen using WMAP data alone, with dotted line should be compared to the blue contours, since this dns/d ln k = 0.019 0.025 (68% confidence; Hinshaw et al. model predicts negligible running. All of these results use the 2012. Combining WMAP± data with the first data releases from Planck+WP+highL data combination.
38 Gravitational(waves
From(K(Story
a˙ h˙˙ + 2 h˙ − k 2h = 0 k a k k
δT00 = 0
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0.6 0.6 ] 2 K µ
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0 0 BB l(l+1)C 0.01 0 0.2 0.4 0 5 10 15 Planck TT+lowP+BKP 2 N=60 r A @ l=80 & 353GHz [µK ] +lensing+ext d 0 N=50 0.20
FIG. 10. Likelihoods for r and Ad,usingBICEP2/Keck −0.01 and Planck,asplottedinFig.6, overplotted on constraints 0 50 100 150 200 250 300 Multipole obtained from realizations of a lensed-⇤CDM+noise+dust 2 Planck/BICEP2(Collaborations(2015 0.15 model with dust power similar to that favored by the real Convex 2 data (Ad =3.6 µK ). Half of the r curves peak at zero as 0.002 Concave r expected. 1 Fiducial analysis 0.10 Cleaning analysis 1 1 0.8 0.8 0.8 0.05 0.6 0.6 0.6 peak L/L 0.4 0.4 0.4 0.00 0.95 0.96 0.97 0.98 0.99 1.00 0.2 0.2 ns Planck(Collaboration(2015 0.2 0 0 0 0.2 0.4 0 5 10 15 2 Fig. 21. Left: Constraints on the tensor-to-scalar ratio r0.002 in the ⇤CDM model, using Planck TT+lowP and Planck r A @ l=80 & 353GHz [µK ] 0 d TT+lowP+lensing+BAO0 +JLA+H0.10 (red and blue,0.2 respectively)0.3 assuming negligible running and the inflationary consistency rela- tion. The result is model-dependent; for example,r the grey contours show how the results change if there were additional relativistic FIG. 11. Constraints obtained when adding dust realizationsdegrees of freedom with Ne↵ = 0.39 (disfavoured, but not excluded, by Planck). Dotted lines show loci of approximately con- p from the Planck Sky Model version 1.7.8 to the base lensed-stant FIG.e-folding 12. numberUpper: NBB, assumingspectrum simple of theV BICEP2/( /mPl) Kecksingle-fieldmaps inflation. Solid lines show the approximate ns–r relation for / ⇤CDM+noise simulations. (Curves for 139 regions with peakquadraticbefore and and linear after potentials subtraction to first of order the in dust slow contribution, roll; red lines esti- show the approximate allowed range assuming 50 < N < 60 and 2 Ad < 20 µK are plotted). We see that the results for ra power-lawmated frompotential the for cross-spectrum the duration of with inflation.Planck The353 solid GHz. black The line (corresponding to a linear potential) separates concave and are unbiased in the presence of dust realizations which doconvexerror potentials. bars areRight the: standard Equivalent deviations constraints of in simulations, the ⇤CDM model which, when adding B-mode polarization results corresponding to the 0.42 not necessarily follow the ` power law or have Gaussiandefaultin configuration the latter case, of have the BICEP2 been scaled/Keck and Array combined+Planck in (BKP) the same likelihood. These exclude the quadratic potential at a higher level fluctuations about it. of significanceway. The compared inner error to bars the Planck are from-alone lensed- constraints.⇤CDM+noise sim- ulations as in the previous plots, while the outer error bars are from the lensed-⇤CDM+noise+dust simulations. Lower: as the level of Ad increases, and we should therefore notlimitedconstraint by cosmic on variancer derived of from the dominant the cleaned scalar spectrum anisotropies, comparedfrom tensor modes. The constraints shown by the blue contours be surprised if the fraction of realizations peaking at aand itto is the also fiducial model dependent. analysis shown In polarization, in Fig. 6. in addition to B- in Fig. 21, which add Planck lensing, BAO, and other astrophys- value higher than the real data is increased compared tomodes, the EE and TE spectra also contain a signal from tensor ical data, are therefore tighter in the ns direction and shifted to the simulations with mean A =3.6 µK2. However wemodes coming from reionization and last scattering. However, slightly higher values, but marginally weaker in the r-direction. d in this release the addition of Planck polarization constraints at The 95 % limits on r are still expect that on average 50% will peak above zero and B. Subtraction of scaled spectra 0.002 ` 30 do not significantly change the results from temperature approximately 8% will have an L /L ratio less than 0 peak and low-` polarization (see Table 5). r0.002 < 0.10, Planck TT+lowP, (39a) the 0.38 observed in the real data. In fact we find 57% FigureAs21 previouslyshows the 2015 mentioned,Planck constraint the modified in the ns–r blackbodyplane, r0.002 < 0.11, Planck TT+lowP+lensing+ext, (39b) and 7%, respectively, consistent with the expected val-addingmodelr as a predicts one-parameter that extension dust emission to base is⇤ 4%CDM. as Note bright that in the ues. There is one realization which has a nominal (false)for baseBICEP2⇤CDM band (r = 0), as it the is value in the ofPlanckns is 353 GHz band. There-consistent with the results reported in PCP13. Note that we as- detection of non-zero r of 3.3 , although this turns out to fore, taking the auto- and cross-spectra of the combinedsume the second-order slow-roll consistency relation for the ten- also have one of the lowest L /L ratios in the Gaus- n = 0.9655 0.0062, Planck TT+lowP. (38) sor spectral index. The result in Eqs. (39a) and (39b) are mildly 0 peak BICEP2/s Keck±maps and the Planck 353 GHz maps, as sian simulations shown in Fig. 10 (with which it shares shown in the bottom row of Fig. 2, and evaluatingscale dependent, with equivalent limits on r0.05 being weaker by the CMB and noise components), so this is apparentlyWe highlight this number here since ns, a key parameter for in- about 5 %. (BK BK ↵BK P)/(1 ↵), at ↵ = ↵fid cleans out the just a relatively unlikely fluctuation. flationary cosmology,⇥ shows⇥ one of the largest shifts of any pa- PCP13 noted a mismatch between the best-fit base ⇤CDM rameterdust in contribution base ⇤CDM between (where the↵fidPlanck=0.04).2013 The and upperPlanck panelmodel and the temperature power spectrum at multipoles ` < 40, 2015of analyses Fig. 12 (aboutshows 0.7 the ). result. As explained in Sect. 3.1, part of partly driven by the dip in the multipole range 20 < ` < 30.⇠ If this shiftAs was an caused alternative by the ` to1800 the systematicfull likelihood in the analysis nominal- pre-this mismatch is simply a statistical fluctuation of⇠ the ⇠⇤CDM missionsented 217 in217 Sec. spectrumIII B, used we⇡ can in PCP13 instead. work with the dif-model (and there is no compelling evidence to think otherwise), Theferenced red contours⇥ spectra in Fig. from21 show above, the constraintsa method from we denotePlanck thethe strong Planck limit (compared to forecasts) is the result of TT+lowP.“cleaning” These are approach. similar to If the↵fid constraintswere the shown true value,in Fig. 23the ex-chance low levels of scalar mode confusion. On the other hand if of PCP13, but with ns shifted to slightly higher values. The ad- the dip represents a failure of the ⇤CDM model, the 95 % limits dition of BAO or the Planck lensing data to Planck TT+lowP of Eqs. (39a) and (39b) may be underestimates. These issues are 2 lowers the value of ⌦ch , which at fixed ✓ increases the small- considered at greater length in Planck Collaboration XX (2015) scale CMB power. To maintain the fit to⇤ the Planck tempera- and will not be discussed further in this paper. ture power spectrum for models with r = 0, these parameter As mentioned above, the Planck temperature constraints on shifts are compensated by a change in amplitude As and the tilt r are model-dependent and extensions to ⇤CDM can give sig- ns (by about 0.4 ). The increase in ns to match the observed nificantly di↵erent results. For example, extra relativistic de- power on small scales leads to a decrease in the scalar power grees of freedom increase the small-scale damping of the CMB on large scales, allowing room for a slightly larger contribution anisotropies at a fixed angular scale, which can be compensated
34 Planck Collaboration: The Planck mission
Fig. 15. Maximum posterior amplitude polarization maps derived from the Planck observations between 30 and 353 GHz (Planck Collaboration X 2015). The left and right columns show the Stokes Q and U parameters, respectively. Rows show, from top to bottom: CMB; synchrotron polarization at 30 GHz; and thermal dust polarization at 353 GHz. The CMB map has been highpass- filtered with a cosine-apodized filter between ` = 20 and 40, andPlanck(gave(us(new(view(of(the(Galaxy the Galactic plane (defined by the 17 % CPM83 mask) has been replaced with a constrained Gaussian realization (Planck Collaboration IX 2015).
30 44 70 100 143 217 353 545 857 30 44 70 100 143 217 353 Sum fg Synchrotron K) K) 2 2 µ µ
10 Thermal dust 10 Until(Planck,(dust(level( CMB uncertain(to(order%of%
1 1 magnitude% 10 10 Thermal dust Sum fg Free-free 0 Spinning dust 0 Planck Collaboration: The Planck mission
10 CO 1-0 10 CMB AP Synchrotron d -1 -1 RMS brightness temperature ( RMS brightness temperature ( 10 10
10 30 100 300 1000 10 30 100 300 1000 Frequency (GHz) Frequency (GHz) Planck(Collaboration(2015 (level(over(70R90%(of(sky) Fig. 16. Brightness temperature rms as a function of frequency and astrophysical component for temperature (left) and polarization (right). For temperature, each component is smoothed to an angular resolution of 1 FWHM, and the lower and upper edges of each line are defined by masks covering 81 and 93 % of the sky, respectively. For polarization, the corresponding smoothing scale0 is 400, 20 200 and the sky fractions are 73 and 93 %. µKRJ @ 353 GHz 2 2 Fig. 21. Dust polarization amplitude map, P = Q + U , at 353 GHz, smoothed to an angular resolution of 100, produced by the di↵use component separation process described in (Planck Collaboration X 2015) using Planck and WMAP data. p 10. Planck 2015 cosmology results lent agreement with this paradigm, and continue to tighten the constraints on deviations and reduce the uncertainty on the key Since their discovery, anisotropies in the CMB have contributed cosmological parameters. significantly to defining our cosmological model and measuring The major methodological changes in the steps going its key parameters. The standard model of cosmology is based from sky maps to cosmological parameters are discussed upon a spatially flat, expanding Universe whose dynamics are in Planck Collaboration XII (2015); Planck Collaboration XIII governed by General Relativity and dominated by cold dark mat- (2015). These include the use of Planck polarization data in- ter and a cosmological constant (⇤). The seeds of structure have stead of WMAP, changes to the foreground masks to include Fig. 22. All-sky view of the magnetic field and total intensity of dust emission measured by Planck. The colours represent intensity. The “drapery” pattern, produced using the line integral convolution (LIC, Cabral & Leedom 1993), indicates the orientation of Gaussian statistics and form an almost scale-invariant spectrum more sky and dramatically reduce the numbermagnetic field projected of point on the plane of source the sky, orthogonal to the observed polarization. Where the field varies significantly along of adiabatic fluctuations. The 2015 Planck data remain in excel- “holes,” minor changes to the foregroundthe line ofmodels, sight, the orientation pattern improve- is irregular and di cult to interpret.
29 23 Path(ahead
Now:(’StageR3’(CMB:(Spider,(PolarBear,(BICEP3,(Keck,(CLASS,(SPTR3G,(GroundBird(
My(project((led(in(Princeton):(AdvACT(( Targeting(r=0.01(with(five(wavelengths(2016R18.
Next:(CMBRS4(campaign(from(~2020R25( Cosmic(microwave(background(data(continue(to(demand( LCDM(cosmological(model.(It(holds(up(very(well(to(new(lensing( and(polarization(measurements(from(the(Planck(satellite.(
• If(inflation(is(not(correct(scenario,(it(has(to(look(a(lot(like( it.(Gravitational(wave(search(still(firmly(on.(
• Neutrino(sector(holds(questions(that(cosmology(can(help( answer(in(coming(decade.(