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New Astronomy Reviews 50 (2006) 938–944

Cosmological science enabled by Planck

Martin White *

Department of Physics and Astronomy, University of California, 601 Campbell Hall, Berkeley, CA 94720, United States

Available online 27 October 2006

Abstract

Planck will be the first mission to map the entire cosmic microwave background (CMB) sky with mJy sensitivity and resolution betterthan 10 0. The science enabled by such a mission spans many areas of astrophysics and cosmology. In particular it will lead to a revolutionin our understanding of primary and secondary CMB anisotropies, the constraints on many key cosmological parameters will beimproved by almost an order of magnitude (to sub-percent levels) and the shape and amplitude of the mass power spectrum at high red-shift will be tightly constrained.� 2006 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9382. The universe at z = 103 and cosmological parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 939

1387-6

doi:10.

* TelE-m

2.1. Constraining cosmological parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9392.2. The CMB and dark energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 940

2.2.1. Acoustic oscillations and the sound horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9412.2.2. What could go wrong? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 942

2.3. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 942

3. The CMB prior and structure formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9434. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943

1. Introduction

Planck will be the first mission to map the entire cosmicmicrowave background (CMB) sky with mJy sensitivityand resolution better than 10 0 (The Planck collaboration,2005). The science enabled by such a mission spans manyareas of astrophysics and cosmology, but in this short pro-

473/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

1016/j.newar.2006.09.008

.: +1 510 642 1969; fax: +1 510 642 3411.ail address: mwhite@berkeley.edu.

ceedings I can focus on only a few. (Further discussion ofthe cosmological science enabled by Planck was coveredby Lloyd Knox in his talk at this meeting.) In particularI want to focus on the dramatic revolution Planck will rep-resent in the study of primary CMB anisotropies and theuniverse at z = 103, with its implications for low-z studiessuch as those of dark energy. I also want to make a pushfor a CMB-centric view of structure formation whichemphasizes the exquisite constraints on large-scale struc-ture that we already have from the CMB at high-z.

Fig. 1. Forecast measurements of the temperature anisotropy powerspectrum from 4 years of WMAP or 1 year of Planck data assumingnominal sensitivities. We have chosen the same binning scheme to showthe advantage that higher resolution and sensitivity confers on Planck forhigh-‘ science. Figures from (The Planck collaboration, 2005).

M. White / New Astronomy Reviews 50 (2006) 938–944 939

Before I begin with these science topics, it is important toremind ourselves how revolutionary Planck will be (see Figs.1 and 2). In addition to wider frequency coverage (crucialfor control of foregrounds) and better sensitivity thanWMAP, Planck has the resolution needed to see into thedamping tail of the anisotropy spectrum. In fact, Planck willbe the first experiment to make an almost cosmic variancelimited measurement of the temperature anisotropy spec-trum around the 3rd and 4th acoustic peaks.

What does this dramatic increase in our knowledge ofthe temperature and polarization anisotropy spectra tellus about cosmology, fundamental physics and the forma-tion of structure? Here I will highlight just a few areaswhere we expect a large impact.

2. The universe at z = 103 and cosmological parameters

2.1. Constraining cosmological parameters

It is well known that detailed observations of CMBanisotropy, coupled with accurate theoretical predictions,constrain the high redshift universe. The most stronglyconstrained is the physics which gives rise to the acousticpeaks in the CMB power spectrum, since that is both wherethe measurements are most accurate and the structure themost rich. To a first approximation the acoustic peaks con-strain the physical matter density, xm ” Xmh2, the physicalbaryon density, xb ” Xbh2, and an acoustic scale, hA or ‘A

(Peebles and Yu, 1970; Sunyaev and Zel’dovich, 1970; Dor-oshkevich et al., 1978). From this we can derive other con-straints, for example the distance to last-scatteringD(z = 103). Currently we know D(z = 103) to about 2%(Spergel et al., submitted), with the main source of uncer-tainty coming not from our knowledge of the peak posi-tions but from the 8% uncertainty in xm. This translatesinto an uncertainty in the expansion rate of the universenear last scattering and hence the distance.

The key to improving our knowledge of xm is the higherpeaks. Planck should determine xm to 0.9% (The Planckcollaboration, 2005), almost an order of magnitudeimprovement over current knowledge. In principle thisallows us to determine D(z = 103) to 0.2%! This providesan important constraint for cosmological models, e.g. onthe dark energy and allows us to calibrate the baryonacoustic oscillation method for measuring dA(z) and H(z)in the range z = 0.3–3 (Eisenstein, 2005).

Why are the higher peaks crucial to constraining thematter density? To understand this let us consider howthe temperature anisotropies are formed. We know thaton small scales the CMB anisotropy spectrum is dampedby photon diffusion (Silk, 1968; Hu and White, 1997). Thisprocess is well understood and essentially independent ofthe source of the anisotropies. If we remove it we can seethe combined effects of the baryon loading and the epochof equality (Fig. 3).

The baryons give weight to the photon-baryon fluid.This makes it easier to fall into a potential well to become

a compression and harder to ‘‘bounce’’ out to become ararefaction. For adiabatic models the baryon loading thusenhances the compressions (odd peaks) and weakens therarefactions (even peaks) leading to an alternatingsequence of peak heights. Superposed upon this alternationis a general rise in power to small scales – usually obscuredby the effects of the exponential Silk damping. The powerincrease arises because at early times – when the perturba-tions giving rise to the higher peaks are entering the hori-zon – the baryon-photon fluid contributes more to thetotal energy density of the universe than the dark matter.The effects of baryon-photon self-gravity enhance the fluc-tuations on small scales as follows (Hu and White, 1996).Since the fluid has pressure it is hard to compress. Thismakes the infall into the potential wells slower than free-fall, retarding the growth in the overdensity. Because theoverdensity cannot grow rapidly enough the potential isforced to decay by the expansion of the universe (see lower

Fig. 2. Forecast measurements of the polarization anisotropy power spectrum from 4 years of WMAP or 1 year of Planck data assuming nominalsensitivities. One can see clearly the advantage that higher sensitivity confers on Planck for polarization science. Figures from (The Planck collaboration,2005).

940 M. White / New Astronomy Reviews 50 (2006) 938–944

panel of Fig. 3). The photons are then left in a compressedstate with no need to fight against the potential as theyleave – enhancing the small scale power. As the universeexpands and larger scales enter the horizon the dark matterpotentials become increasingly important and the boost isreduced.1

Thus measuring the higher peaks constrains the behav-ior of the potentials, which respond to the expansion rate

1 If we were to ignore the effects of neutrinos near equality and the darkenergy at late times the asymptotic value of the excess power would be afactor of 25 compared to the low ‘ plateau. The plateau has an amplitudeset by �U/3 (Sachs and Wolfe, 1967; White and Hu, 1997). The infall intothe potential well and subsequent decay boosts the power by 2U makingthe small-scale effective temperature perturbation (2 � 1/3)U = (5/3)U. Inreality because of the effects of dark energy and neutrinos the effect is morelike a factor of 15.

of the universe near last scattering. If dark energy is sub-dominant at high z this becomes a constraint on the epochof equality, zeq, or the matter density. Since it is able tomake an almost cosmic variance limited measurement ofthe higher acoustic peaks, Planck provides us with anunparalleled constraint on the (physical) matter density.

2.2. The CMB and dark energy

The nature of the dark energy believed to be causing theaccelerated expansion of the universe is one of the mostimportant questions facing cosmology, with implicationsfor our understanding of physics at the deepest levels.For this reason the community has been pursuing darkenergy science with a number of different probes. It issometimes stated that the CMB does not directly constrain

a

bFig. 4. (a) The linear theory matter and radiation power spectra vs.wavenumber. The upper panel shows the contribution to the RMStemperature fluctuation per logarithmic interval in wavenumber, and isclosely related to the more familiar angular power spectrum plotted vs.angular wave mode ‘. The lower panel shows the (dimensionless) masspower spectrum (divided by wavenumber k). Note the similar scale of theacoustic oscillations in each spectrum, and the damping to higherwavenumber. (b) The correlation function, or Fourier transform of thepower spectrum plotted in the lower left panel. Note that the almostharmonic series of peaks in Fourier space translates into a single welldefined peak in real space with a width of Oð10%Þ. From (White, 2005).

Fig. 3. The temperature anisotropy spectrum with the effects of Silkdamping removed. Concentrating on the triangles in the upper panel wesee the effects of baryon loading in the modulation of the peaks. If weremove the modulation the boost at high ‘ due to potential decay becomesapparent (squares, see text). The lower panel shows by what fraction thepotential has decayed by the present as a function of wavenumber. Figuretaken from (Hu and White, 1997).

M. White / New Astronomy Reviews 50 (2006) 938–944 941

dark energy, and this is true. However it is important topoint out that almost all of the methods which seek to con-strain the dark energy do much better if they include infor-mation from the CMB. In fact most analyses includeWMAP (or projected Planck) priors as a matter of course.As a field we have not been particularly effective in promot-ing the importance of improved CMB anisotropy/polariza-tion measurements for future dark energy experiments, solet me take some time to show one example here: baryonacoustic oscillations.

2.2.1. Acoustic oscillations and the sound horizon

The idea behind the baryonic acoustic oscillation (BAO)method is to make measurements of dA(z) and H(z) using acalibrated standard ruler which can be measured at a num-ber of redshifts (Eisenstein, 2005). The CMB provides thecalibrated ruler through its measurement of the soundhorizon:

s �Z trec

0

csð1þ zÞdt ¼Z 1

zrec

cs dzHðzÞ : ð1Þ

The sound horizon is extremely well constrained bythe structure of the acoustic peaks. For example from(Spergel et al., submitted) we find s = 147.8 ± 2.6 Mpc =(4.56 ± 0.08) · 1024 m. As can be seen from Eq. (1) thesound horizon depends on the expansion history (matter-radiation equality) and the sound speed (baryon-photonratio). Once s is known and the angular scale of the peaks,hA, is measured the distance to last-scattering follows from

s = DhA. The same physical scale is imprinted upon thematter power spectrum (see Fig. 4), and can serve as a cal-ibrated standard ruler at lower z.

If we Fourier transform the almost harmonic series ofpeaks seen in Fig. 4 we predict that the correlation functionshould have a single well-defined peak at �100 h�1 Mpc(see (Eisenstein et al., in press) for a discussion of the phys-ics of the BAO in Fourier and configuration space). Thisfeature has now been seen by several groups (Eisensteinet al., 2005; Hutsi, 2006a,b; Padmanabhan et al., preprint;Blake et al., preprint) in both configuration, n(r), and Fou-rier, D2(k), space at intermediate redshift, z � 0.35. Thismeasurement, along with the CMB, is enough to show

a

bFig. 5. A plot of the power spectra for decaying neutrino scenarios (seetext). (a) The upper panel shows the (dimensionless) mass power spectrum(divided by wavenumber k) for models which have 10% more matter andradiation than the standard model. The lower left panel shows the ratio ofthe curves to the Nm = 3.784 result. (b) The radiation spectra for the samemodels, along with cosmic variance error bars averaged in bins of widthD‘/‘ = 0.1.

942 M. White / New Astronomy Reviews 50 (2006) 938–944

the existence of dark energy but larger surveys are neededto constrain its properties.

2.2.2. What could go wrong?

With so much riding on the CMB calibration it is impor-tant to ask what could go wrong? Recall the method hingeson the ability to predict s, for which we need zrec, cs andH(z). It turns out that recombination is very robust, andour current uncertainties in recombination (Peebles, 1968;Zel’dovich et al., 1969; Seager et al., 1999) lead to shiftsin the sound horizon well below a percent. If we assumethe standard radiation content (3 nearly massless neutrinospecies plus photons) knowing qc from Tc gives xr. Thenknowing zeq is the same as knowing xm and H(z). But whatif xr was different? Could we mistake m for DE?

It turns out that as long as zeq is still known well fromthe CMB is does not matter! We would misestimate xm

however in comparing our standard ruler at z � 1 andz � 103 the same xm prefactor enters H�1, dA and s: eachscales as x�1=2

m . Thus all distance ratios and DE inferencesgo through unchanged (Eisenstein and White, 2004). Whatwe do is misestimate the overall scale, and hence H0! It isironic that we may end up understanding quantum gravityand the mysterious dark energy but still be uncertain aboutthe Hubble constant.2

What about more bizarre histories? As an exampleimagine a non-relativistic particle of mass m which decayswith lifetime s into massless neutrinos (Bardeen et al.,1987; Bond and Efstathiou, 1991; Chun et al., 1994; Whiteet al., 1995; Bowen et al., 2002; Pierpaoli, 2003; Crottyet al., 2004). We arrange m and s so that there is 10%more radiation today than in the standard model, butincrease xm by 10% so that equality is held fixed. Sinceit is equality that primarily controls the decay of thepotentials at early times the CMB fluctuations look verysimilar. However, because the universe would be slightlymore matter dominated at early times (when the massiveparticle was a non-negligible contribution to the totalenergy density) we would expect excess power on smallscales, and we can shift the acoustic peaks. Can this leadto a false signature of dark energy?

We show in Fig. 5 the mass and CMB temperaturepower spectra for a sequence of models with log10syr = 2,3and 4. While one can see subtle shifts in the sound horizon,any model which appreciably shifts s changes the tempera-ture anisotropies at high ‘ enough to be easily seen byPlanck. Thus while one may not be able to fit the spectrumwith a standard model, one would not mistake strangephysics at z � 103 for dark energy at z � 0.

2.3. Conclusions

To recap the main points of this section, Planck will dra-matically improve our knowledge of the physical condi-

2 I term this the Hubble uncertainty principle.

tions in the universe at z � 103. The physical matter andbaryon densities and the distance to last-scattering will beknown to sub-percent accuracy. The epoch of equality willbe tightly constrained, as will extra species, anisotropicstresses and decaying components at high redshift (Eisen-stein and White, 2004).

Fig. 6. The range of D2mðkÞ allowed by the WMAP 3 yr data assuming a

standard CDM model. The data already constrain D2(k . 0.01 MPc�1) to7%. This drops to 3% if the degeneracy with s is controlled for.

M. White / New Astronomy Reviews 50 (2006) 938–944 943

3. The CMB prior and structure formation

Already with WMAP, and certainly after Planck, we willhave very precise knowledge of the universe at z = 103. Wewill have tightly constrained the densities of matter andbaryons, the amplitude of the fluctuations in the linearphase over three decades in length scale and the shape ofthe primordial power spectrum. Our knowledge of thephysical conditions and large-scale structure at z = 103 willbe better than our knowledge of such quantities at z = 0.One should not ignore this dramatic advance in our knowl-edge – when forecasting the future we should hold thez = 103 universe ‘‘fixed’’, not the z = 0 one. This is equiva-lent to imposing strong CMB priors on futuremeasurements.

As an example, knowing xm and xb allows us to predictthe shape of the linear theory (matter) power spectrumextremely accurately over many orders of magnitude inlength scale, providing that the lengths are measured inMPc (or meters) rather than h�1 MPc as would be morefamiliar from low-z measurements. Note that knowingxm and zeq fixes H(z) at high-z

Hðz� 1Þ ’ H 0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXmð1þ zÞ3 þ Xrð1þ zÞ4

q

/ x1=2m

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 1þ z

1þ zeq

s: ð2Þ

The amplitude of the fluctuations is well constrained byanisotropy measurements, up to a degeneracy with s –the constrained quantity is roughly dme�s. Further, unlessdark energy is important at z� 1, we can evolve the fluc-tuations reliably from z � 103 to lower z, since dm � a formost of the time. In combination this enables us to con-strain the high-z matter power spectrum (with lengths mea-sured in physical units). For example, Fig. 6 shows therange of matter power spectra at z = 3 allowed by theWMAP 3 yr data assuming a standard3 KCDM modeland that dark energy is negligible for z P 3. The error barsexpand slightly at high-k if we additionally allow massiveneutrinos, but near the scales contributing to the firstacoustic peak (k . 10�2 Mpc�1) the constraint is already7% in power. Half of the uncertainty comes from the uncer-tainty in the optical depth, s. If we remove that degeneracythe constraint becomes 3% in power or 1.5% in amplitude!We expect this to improve with future WMAP data, butwith Planck the uncertainty will drop to sub-percent levelseven with improved modeling of the reionization epoch.Thus in a post-Planck world the uncertainty in large-scalestructure comes from the extrapolation from z � 3 toz = 0 (which depends on the nature of the dark energy)and the conversion between physical distances and redshift

3 We neglect here a possible running of the spectral index, massiveneutrinos or a warm dark matter candidate. These will increase theuncertainty on small scales and may be relevant for the formation of thefirst structures.

space measures (which depend on h). The former lead tovertical shifts in the spectrum, while the latter give horizon-tal shifts.

4. Conclusions

Planck will provide a dramatic advance in our knowl-edge of primary and secondary CMB anisotropies. Theconstraints on many key cosmological parameters will bedropped to percent, or sub-percent, levels and the shapeand amplitude of the mass power spectrum at high redshiftwill be tightly constrained. Beyond our desire to know thebasic parameters of the universe accurately, and to performtruly precision tests of our cosmological model, theincrease in precision will be important for a host of lowredshift experiments, including those that aim to constrainthe nature of the dark energy.

Acknowledgements

I thank the organizers of this conference for a pleasantand productive meeting, and Daniel Eisenstein and WayneHu for conversations and collaborations upon which someof this work rests. I am grateful to the many members ofthe Planck collaboration who have labored tirelessly tomake Planck a reality, and especially to Charles Lawrencefor his leadership and tireless enthusiasm – and the choco-late donuts. MJW was supported in part by NASA.

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