the planck satellite and the cosmic microwave background

The Cosmic Microwave Background, Dark Matter

and Dark Energy Anthony Lasenby, Astrophysics Group,

Cavendish Laboratory and Kavli Institute for Cosmology, Cambridge

Overview

The Cosmic MicrowaveBackground — exciting new resultsfrom the Planck SatelliteContext of the CMB =⇒addressing key questions about theBig Bang and the Universe,including Dark Matter and DarkEnergyPlanck Satellite and planning for itsobservations have been a longtime in preparation — firstmeetings in 1993!Two instruments — the LFI (LowFrequency Instrument) and the HFI(High Frequency Instrument)

UK has been intimately involved— e.g. Cambridge is thescientific data processingcentre for the HFI— RAL provided the 4K Cooler

The Cosmic Microwave Background (CMB)

So what is the CMB?Anywhere in empty space at themoment there is radiation presentcorresponding to what ablackbody would emit at atemperature of ∼ 2.74K

(‘Blackbody’ being a perfectemitter/absorber — furnace witha small opening is a goodexample - needs perfectthermodynamic equilibrium)CMB spectrum is incrediblyaccurately black body — bestknown in nature!COBE result on this showed CMBbetter than its own reference b.b.within about 9 minutes of data!

Universe History

Radiation was emitted in the earlyuniverse (hot, dense conditions)Hot means matter was ionisedTherefore photons scattered frequentlyoff the free electronsAs universe expands it cools —eventually not enough energy to keepthe protons and electrons apart — they‘recombine’ to form atoms of HydrogenSuddenly the photons are able tofree-stream away crossing the entireuniverse without interruption

History of the Universe:superluminal inflation,particle plasma, atomic plasma,recombination,structure formation

Universe History


Universe History

Can see directly today the imprintspresent at recombinationGood evidence these were created byamplification of quantum-generatedirregularities during period of inflation,taking place about 10−35 s after theBig-Bang!


http://www.sdss3.org/surveys/boss.php (Chris Blake and Sam Moorfield)

Development of these (initially quantum) fluctuations from inflation untilrecombination, imprints characteristic scales on the universe (basically howfar ‘sound’ could have travelled by then) — should see this in both matter andCMB

The Power Spectrum

Look at power in fluctuations as afunction of angular scale on the skyShown is a theoretical curveSeries of coherent peaks is crucial— if can observe them, thenfluctuations must have been ‘phasedup’Inflation is only known mechanismfor achieving this!Details of peak location and heightdepend on the cosmologicalparameters such as density and ageof the UniverseThe ‘Omegas’ refer to densities invarious components, and H0 isHubble’s constant (linked to age)

Dark Matter and Dark Energy

THE TWO FURTHER INGREDIENTS:

We know there are bigproblems with understandingthe dynamics of galaxies andclusters of galaxiesThere appears to be a largeamount of ‘missing mass’ —i.e. inferred dynamically, butnot visibleVery obvious in the ‘rotationcurves’ of galaxiesFrom

mv2

r=

GMmr2

expect v ∝√

1/r outsidegalaxy

Instead rotational velocity isflat or even increasing withdistance!

Dark Matter (contd.)

For clusters of galaxies, thevisible matter is only about 1/10thof that needed to explain thedynamics we see(First pointed out by Fritz Zwicky in1933 — so this problem has beenround a long time!)

General consensus is that the‘missing mass’ is provided by ahitherto undetected particle,which only interactsgravitationally(Though particularly for thegalactic rotation curve problem,many attempts also to explain interms of modifications to the lawsof gravity, e.g. MOND theories.)

A cluster showing lensing

Fritz Zwicky

Dark Energy

On the largest scales in theuniverse we see not extraattraction, but ‘repulsion’The universe is accelerating, asmeasured by the brightness ofdistant supernovaeIs this Λ?Einstein introduced this into hisfield equations for GeneralRelativity to try to get a staticuniverseWhen he realised the universewas expanding, he discarded thisterm — we finally knew that itwas necessary in about 1998

A source term or geometry?

Schematically, Einstein’s equations are:

a geometrical object derivedfrom the metric g of spacetime

G = 8πT

the stress-energy tensor ofsources of matter and radiation

Where does the cosmological constant enter?

G − Λg = 8πT Modifies gravity itself

orG = 8πT + Λg A new source of energy

More generally, should we interpret the late-time acceleration of theuniverse in terms of a modified gravity theory?— or as the action of e.g. a new form of matter, such as a new scalarfield (like the Higgs, recently discovered)?

Lambda CDM

Putting the two together, we get ΛCDM

This is now the ‘standard model of cosmology’ (in analogywith the Standard Model of particle physics)Here dark matter particle is ‘cold’ — basically movingslowly and non-relativistically todaySuitable candidates could be e.g. large mass WIMPSAnd what provides the repulsion for the acceleratinguniverse is a simple cosmological constant Λ

This has a constant ratio of pressure to energy density= −1Other possibilities like scalar fields, this changes with timeKey tests come from the CMB power spectrum

The Planck Satellite

Planck has been called ‘thecoolest spacecraft ever built’!Certainly payload is one of themost complex scientific missionever put into spaceCost 700M euros, and mass atlaunch 1.9 tonnesIt flew out to the SecondLagrangian point (L2) of theEarth/Sun systemSemi-stable — flies in a Lissajousorbit about L2

5For more information, visit us on www.arianespace.com

The launcher’s attitude and trajectory are totally controlled by the two onboard computers, located in theAriane 5 vehicle equipment bay (VEB).7.05 seconds after ignition of the main stage cryogenic engine at T-0, the two solid-propellant boosters areignited, enabling liftoff. The launcher first climbs vertically for 6 seconds, then rotates towards the East. Itmaintains an attitude that ensures the axis of the launcher remains parallel to its velocity vector, in order tominimize aerodynamic loads throughout the entire atmospheric phase, until the solid boosters are jettisoned.Once this first part of the flight is completed, the onboard computers optimize the trajectory in real time,minimizing propellant consumption to bring the launcher first to the intermediate orbit targeted at the end of the main stage propulsion phase, and then the final orbit at the end of the flight of the cryogenic upper stage.The main stage falls back off the coast of Africa in the Atlantic Ocean (in the Gulf of Guinea).On orbital injection, the launcher will have attained a velocity of approximately 9967 meters/second, and willbe at an altitude of about 852 kilometers.The fairing protecting the HERSCHEL, PLANCK spacecraft is jettisoned shortly after the boosters are jettisonedat about T+243 seconds.

4. Flight traj e c to ry of HERSCHEl & PLANCK

Scanning strategy (1 rpm,plus 1 degree advance perday) leads to 2× 7 monthsurveys, each coveringentire sky once

Planck Science

So what did Planck see, and why is it such abig advance?The key is much improved resolution andsensitivity compared to the previousmissionsAt the higher frequencies, each Planck skymap gives about 50 million pixels at eachfrequency — compare ∼ 3 million for WMAPSensitivity about 10 times higher per beamFrequency coverage much improvedcompared to previously as well — canbetter discriminate the CMB from Galacticand other foregrounds

Planck Cosmology Results

28 papers plus associateddata products released Mar21Made headlines around theworld, including front page ofthe NY TimesRelease based on first 15months of datarest of data (another 15months) + crucial polarisationdata, due in 1 yearHFI cryogens ran out in early2012 — LFI observationsfinished recently and Plancknow ‘de-orbited’


Broad overview of results would be:Spectacular overall agreement withΛCMD cosmologyBut with some hints of departures inplacesAnd some tensions with other resultsFor example rate of universeexpansion (H0) from CMB nowdiscrepant with recent optical and IRdeterminations at about 2.5σ level(Universe has got slightly olderPlanck about 40 Myr > WMAP9value.)

Planck Collaboration: Cosmological parameters

Table 8. Approximate constraints with 68% errors on Ωm andH0 (in units of km s−1 Mpc−1) from BAO, with ωm and ωb fixedto the best-fit Planck+WP+highL values for the base ΛCDMcosmology.

Sample Ωm H0

6dF . . . . . . . . . . . . . . . . . . . . . . . . . 0.305+0.032−0.026 68.3+3.2

−3.2SDSS . . . . . . . . . . . . . . . . . . . . . . . 0.295+0.019

−0.017 69.5+2.2−2.1

SDSS(R) . . . . . . . . . . . . . . . . . . . . . 0.293+0.015−0.013 69.6+1.7

−1.5WiggleZ . . . . . . . . . . . . . . . . . . . . . 0.309+0.041

−0.035 67.8+4.1−2.8

BOSS . . . . . . . . . . . . . . . . . . . . . . . 0.315+0.015−0.015 67.2+1.6

−1.56dF+SDSS+BOSS+WiggleZ . . . . . . 0.307+0.010

−0.011 68.1+1.1−1.1

6dF+SDSS(R)+BOSS . . . . . . . . . . . 0.305+0.009−0.010 68.4+1.0

−1.06dF+SDSS(R)+BOSS+WiggleZ . . . . 0.305+0.009

−0.008 68.4+1.0−1.0

surements constrain parameters in the base ΛCDM model, weform χ2,

χ2BAO = (x − xΛCDM)T C−1

BAO(x − xΛCDM), (50)

where x is the data vector, xΛCDM denotes the theoretical pre-diction for the ΛCDM model and C−1

BAO is the inverse covari-ance matrix for the data vector x. The data vector is as fol-lows: DV(0.106) = (457 ± 27) Mpc (6dF); rs/DV(0.20) =0.1905 ± 0.0061, rs/DV(0.35) = 0.1097 ± 0.0036 (SDSS);A(0.44) = 0.474 ± 0.034, A(0.60) = 0.442 ± 0.020, A(0.73) =0.424±0.021 (WiggleZ); DV(0.35)/rs = 8.88±0.17 (SDSS(R));and DV(0.57)/rs = 13.67±0.22, (BOSS). The off-diagonal com-ponents of C−1

BAO for the SDSS and WiggleZ results are givenin Percival et al. (2010) and Blake et al. (2011). We ignore anycovariances between surveys. Since the SDSS and SDSS(R) re-sults are based on the same survey, we include either one set ofresults or the other in the analysis described below, but not bothtogether.

The Eisenstein-Hu values of rs for the Planck and WMAP-9base ΛCDM parameters differ by only 0.9%, significantlysmaller than the errors in the BAO measurements. We can obtainan approximate idea of the complementary information providedby BAO measurements by minimizing Eq. (50) with respect toeither Ωm or H0, fixing ωm and ωb to the CMB best-fit parame-ters. (We use the Planck+WP+highL parameters from Table 5.)The results are listed in Table 819.

As can be seen, the results are very stable from survey tosurvey and are in excellent agreement with the base ΛCDMparameters listed in Tables 2 and 5. The values of χ2

BAO arealso reasonable. For example, for the six data points of the6dF+SDSS(R)+BOSS+WiggleZ combination, we find χ2

BAO =4.3, evaluated for the Planck+WP+highL best-fit ΛCDM param-eters.

The high value of Ωm is consistent with the parameter anal-ysis described by Blake et al. (2011) and with the “tension” dis-cussed by Anderson et al. (2013) between BAO distance mea-surements and direct determinations of H0 (Riess et al. 2011;Freedman et al. 2012). Furthermore, if the errors on the BAOmeasurements are accurate, the constraints on Ωm and H0 (forfixed ωm and ωb) are of comparable accuracy to those fromPlanck.

19As an indication of the accuracy of Table 8, the full likelihoodresults for the Planck+WP+6dF+SDSS(R)+BOSS BAO data sets giveΩm = 0.308 ± 0.010 and H0 = 67.8 ± 0.8 km s−1 Mpc−1, for the baseΛCDM model.

Fig. 16. Comparison of H0 measurements, with estimates of±1σ errors, from a number of techniques (see text for details).These are compared with the spatially-flat ΛCDM model con-straints from Planck and WMAP-9.

The results of this section show that BAO measurements arean extremely valuable complementary data set to Planck. Themeasurements are basically geometrical and free from complexsystematic effects that plague many other types of astrophysicalmeasurements. The results are consistent from survey to surveyand are of comparable precision to Planck. In addition, BAOmeasurements can be used to break parameter degeneracies thatlimit analyses based purely on CMB data. For example, fromthe excellent agreement with the base ΛCDM model evident inFig. 15, we can infer that the combination of Planck and BAOmeasurements will lead to tight constraints favouring ΩK = 0(Sect. 6.2) and a dark energy equation-of-state parameter, w =−1 (Sect. 6.5).

Finally, we note that we choose to use the6dF+SDSS(R)+BOSS data combination in the likelihoodanalysis of Sect. 6. This choice includes the two most accu-rate BAO measurements and, since the effective redshifts ofthese samples are widely separated, it should be a very goodapproximation to neglect correlations between the surveys.

5.3. The Hubble constant

A striking result from the fits of the base ΛCDM model to Planckpower spectra is the low value of the Hubble constant, which istightly constrained by CMB data alone in this model. From thePlanck+WP+highL analysis we find

H0 = (67.3±1.2) km s−1 Mpc−1 (68%; Planck+WP+highL).(51)

A low value of H0 has been found in other CMB experi-ments, most notably from the recent WMAP-9 analysis. Fittingthe base ΛCDM model, Hinshaw et al. (2012) find

H0 = (70.0 ± 2.2) km s−1 Mpc−1 (68%; WMAP-9), (52)

consistent with Eq. (51) to within 1σ. We emphasize here thatthe CMB estimates are highly model dependent. It is important

30


Planck has produced awonderful power spectrum ofthe fluctuations in the CMBskyVery big increase in accuracy— can now definitely say DarkEnergy and Dark Matter exist,just from primordial CMBaloneProportions of DE and DMnow slightly different: insteadof what’s shown in Pie chart(based on previous spaceexperiment (WMAP) values),Planck now has 69% for DE,26% for DM and 5% forordinary matter

Planck collaboration: CMB power spectra & likelihood

2 10 500

1000

2000

3000

4000

5000

6000

D `[µ

K2 ]

90 18

500 1000 1500 2000 2500

Multipole moment, `

1 0.2 0.1 0.07Angular scale

Figure 37. The 2013 Planck CMB temperature angular power spectrum. The error bars include cosmic variance, whose magnitudeis indicated by the green shaded area around the best fit model. The low-` values are plotted at 2, 3, 4, 5, 6, 7, 8, 9.5, 11.5, 13.5, 16,19, 22.5, 27, 34.5, and 44.5.

Table 8. Constraints on the basic six-parameter ΛCDM model using Planck data. The top section contains constraints on the sixprimary parameters included directly in the estimation process, and the bottom section contains constraints on derived parameters.

Planck Planck+WP

Parameter Best fit 68% limits Best fit 68% limits

Ωbh2 . . . . . . . . . 0.022068 0.02207 ± 0.00033 0.022032 0.02205 ± 0.00028

Ωch2 . . . . . . . . . 0.12029 0.1196 ± 0.0031 0.12038 0.1199 ± 0.0027100θMC . . . . . . . 1.04122 1.04132 ± 0.00068 1.04119 1.04131 ± 0.00063

τ . . . . . . . . . . . . 0.0925 0.097 ± 0.038 0.0925 0.089+0.012−0.014

ns . . . . . . . . . . . 0.9624 0.9616 ± 0.0094 0.9619 0.9603 ± 0.0073

ln(1010As) . . . . . 3.098 3.103 ± 0.072 3.0980 3.089+0.024−0.027

ΩΛ . . . . . . . . . . 0.6825 0.686 ± 0.020 0.6817 0.685+0.018−0.016

Ωm . . . . . . . . . . 0.3175 0.314 ± 0.020 0.3183 0.315+0.016−0.018

σ8 . . . . . . . . . . . 0.8344 0.834 ± 0.027 0.8347 0.829 ± 0.012

zre . . . . . . . . . . . 11.35 11.4+4.0−2.8 11.37 11.1 ± 1.1

H0 . . . . . . . . . . 67.11 67.4 ± 1.4 67.04 67.3 ± 1.2

109As . . . . . . . . 2.215 2.23 ± 0.16 2.215 2.196+0.051−0.060

Ωmh2 . . . . . . . . . 0.14300 0.1423 ± 0.0029 0.14305 0.1426 ± 0.0025Age/Gyr . . . . . . 13.819 13.813 ± 0.058 13.8242 13.817 ± 0.048

z∗ . . . . . . . . . . . 1090.43 1090.37 ± 0.65 1090.48 1090.43 ± 0.54100θ∗ . . . . . . . . 1.04139 1.04148 ± 0.00066 1.04136 1.04147 ± 0.00062zeq . . . . . . . . . . . 3402 3386 ± 69 3403 3391 ± 60

33

WMAPvalues

Planck Cosmology Results (contd.)

Many other interesting resultsA key result for inflation is the slope of the primordial powerspectrum of perturbationsGeneric inflation models predict a primordial power spectrumslope of about 0.96 whereas pre-inflation theory expected valuewas 1Planck gets 0.9603± 0.0073Incredible that something first predicted about 30 years ago,concerning the first 10−35 seconds of the universe, we are nowstarting to get confirmation of

Planck Cosmology Results — still to come

Polarisation results will be keyover next year – potentially cantell us directly energy scale ofinflation (which is currentlyconstrained to 1012 times largerthan LHC can probe)Detecting this mode ofpolarisation (the B-mode) isequivalent to detectinggravitational waves in earlyuniverse!This may give first point ofcontact with String Theory, sincethis component predicted to begenerically small in string-basedcosmologies

LIGO

String Theory

Further space missions

PRISM (Polarized Radiation Imagingand Spectroscopy Mission) is aproposal for an L-class mission to bethe ‘ultimate’ mapper of bothtemperature and polarisation for theCMBUnfortunately has now lost out toAthena (X-ray) and eLISA(gravitatonal waves)

Euclid

For Dark Matter and Dark Energy,the future is brighter(!)Euclid is an M-Class mission alreadyselected, due for launch 2020Important for both DE and DM — DMvia lensing, and DE via mapping thedistribution and redshift of galaxies,and seeing how characteristic scalesevolve with time

Planck Results — still to come

Returning to Planck, quality ofpolarisation data on smallangular scales alreadyextremely impressiveLine shown is not a fit, butpredicted from TemperaturedataAlso Planck, with its highresolution and largefrequency coverage, is a veryimpressive instrument forGalactic studiesFirst release, with about 1000pages total, has justscratched the surface —definitely many mysteriesremaining!

Planck image of dust in the Galaxy

the planck satellite and the cosmic microwave background

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