J.A. Peacock- Future questions for cosmology

8/3/2019 J.A. Peacock- Future questions for cosmology

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Cosmology, Galaxy Formation and Astroparticle Physics

on the pathway to the SKA

Klockner, H.-R., Rawlings, S., Jarvis, M. & Taylor, A. (eds.)April 10th-12th 2006, Oxford, United Kingdom

Future questions for cosmologyJ.A. Peacock

Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, United Kingdom

Abstract. This review attempts to summarize recent progress in cosmology, and outline some of the main openquestions for the forthcoming decade. Following the year-3 WMAP results, the basic CDM model seems betterestablished than ever, with the exciting addition of a rejection of the n = 1 scale-invariant spectrum. It is arguedthat this alone is insufficient to constitute proof that inflation occurred, and B-mode CMB polarization mustcontinue to be a prime target. Structure formation within the standard model is well understood in principle, butsignificant open issues remain where the modelling of galaxy formation is concerned. A major item for the futurewill be attempting to detect dynamical vacuum energy beyond a simple cosmological constant. However, the overalllevel of the vacuum density remains poorly understood; anthropic reasoning is probably required to make sense of

what we see.

1. Introduction

This is intended to be a linking review, as the meetingmoves from consideration of particle astrophysics to cos-mological issues. In practice, I will focus more on the lat-ter, since the bulk of the meeting lies ahead. This is ahappy time to be speaking about cosmology, given theriches recently revealed by WMAP3 (Spergel et al. 2006),although one might be forgiven for taking the comprehen-sive nature of this work as a cue to ask: what is left to do?Fortunately, as I will argue, several important questions

remain, which one might summarize as:

1. Does rejection of scale-invariance confirm inflation?2. What is the dark matter?3. What is the vacuum energy?4. What was the character of the initial fluctuations?5. At what point is galaxy formation understood?

Owing to time limits, I will have little to say aboutitems (2) & (4). It is unclear how much more cosmology

can tell us about the nature of dark matter. Making it col-lisional is not a success (e.g. Natarajan et al. 2002), andwe know from the Lyman-alpha forest that the mass fora thermal relic must exceed about 1 keV (e.g. Seljak etal. 2006). Beyond that, we are very much in the hands ofthe particle experimentalists. The main remaining scopefor observation lies in the search for gamma rays fromWIMP annihilations in high-density regions. As for theinitial fluctuations, they are consistent with being adia-batic and Gaussian. In the former case, it is always hardto rule out a small admixture of isocurvature modes, butcertainly this must be subdominant, and we can clearlyrule out the simplest version of the curvaton model, in

which correlated adiabatic and isocurvature fluctuationsare generated by the decay to radiation of a scalar field(e.g. Gordon & Lewis 2003).

Fig. 1. The CMB power spectrum, showing the two main sig-natures of inflation: tilt and gravity waves.

2. The impact of the CMB

The main thing to say about the CMB is how exception-

ally fortunate we are to be working in cosmological re-search at the unique era in history when this picture ofthe early universe comes into focus. The great significanceof the CMB is as a testbed for inflationary (or other) theo-ries for the origin of the expanding universe and the seedsof structure formation.

The two main signatures of inflation are a tilted scalarspectrum, plus a tensor contribution, as illustrated in Fig.1. As is well known, with tilt we are talking about a pri-mordial matter power spectrum P(k) kn, and simpleinflation models predict |n 1| of order a few per cent.Detection of these features is complicated not least be-cause the CMB spectrum is sensitive to perhaps 5-9 other

parameters. These manifest themselves mainly in the char-acteristic length scales imprinted on the universe as itpasses through key stages. These are related to the horizon


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length these times i.e. to the distance over which causalinfluences can propagate. There are two main lengths ofinterest: the horizon at matter-radiation equality (DEQ)and the acoustic horizon at last scattering (DLS). The for-mer governs the general break scale in the matter power

spectrum, and the latter determines the Baryon AcousticOscillations by which the power is modulated:

DEQ 123 (mh2/0.13)1 MpcDLS 147 (mh2/0.13)0.25(bh2/0.023)0.08 Mpc,

These scales can be seen projected on the sky via the CMBpower spectrum, and also in the matter power spectrum.

The angular size corresponding to these lengths comeswhen dividing by the size of the current horizon, and theapproximate scaling of the location of the peaks in theCMB power spectrum is then

H (mh3.4)0.141.4tot.

The location of the 1-degree peak therefore does not tellus that the universe is flat unless we have at least someconstraints on the density and the Hubble parameter. Thisis an example of a more general geometrical degeneracy(Efstathiou & Bond 1999): if m ( mh2) and b arefixed, then can be traded against curvature so thatthe CMB stays identical in appearance (excepting ISWeffects at low from evolving potentials). Thus it wasonly with the addition of external constraints such as thegalaxy power spectrum that the evidence for flatness be-

came compelling (e.g. Efstathiou et al. 2002).Following the superb recent 3-year WMAP results

(Spergel et al. 2006), the detailed shape of the CMBpower spectrum breaks the degeneracies implicit in theabove scaling formulae, so that the individual parame-ters and thus the key horizon lengths can be determinedquite accurately from the CMB alone. Adding other in-dependent constraints (particularly galaxy clustering andSupernovae) yields a very well specified standard model,as shown in Fig. 2 and Table 1.

The main change in the past three years is that thepreferred value of the optical depth due to reionization

has gone down, which increases the weight of evidence infavour ofn < 1. This small but critical alteration has comefrom an in-depth investigation of the polarization data. InWMAP1, the only evidence bearing on came from thepolarizationtemperature cross-correlation. After 3 yearsof data, we also have the polarization autocorrelationdata, plus an improved attempt to subtract backgrounds.Since the residual polarization signal has gone down, oneshould be tempted to believe this: errors in foreground cor-rection lead to a spuriously high signal. The low opticaldepth also implies a low normalization, since 8 exp()is measured very well. This is something of a puzzle, sinceweak lensing data prefer a higher value, 8

0.9 (see the

discussion in Spergel et al. 2006). The lens results mayhave a systematic (e.g. from the fact that weak lens sig-nals originate from pretty nonlinear structures) but it

Fig. 2. The basic WMAP3 confidence contours on the key cos-mological parameters (revised version of plot from Spergel etal. 2006).

would be good to see the CMB polarization results on made more robust.

The detection of tilt (a roughly 3.5 rejection of then = 1 model) has to be considered an impressive suc-cess for inflation, given that such deviations from scaleinvariance were a clear prediction. So should we considerinflation to be proved? Perhaps not yet, since in retro-spect it should perhaps have been clear that exact scaleinvariance was implausible. Recall the main argument: forP(k) kn, the spectrum of potential fluctuations in thepower per ln k from, is

2(k)

2H

kn1.

Thus n = 1 give a fractal spacetime: constant deviationsfrom the smooth RW form on all scales. Any other spec-trum would contain a preferred lengthscale, which seemsundesirable without a specific theory. And yet there is onelength that is almost bound to enter: the Planck scale.

H(L) = ln(L/LP) 105 1 n = 2/ ln(L/LP) 0.03

(remembering that the physical size of the current horizonwas 104 m at the Planck era). In other words, what wehave learned from WMAP3 is that the data are consistent

with a logarithmic running of H. A proper test of infla-tion requires more than this: we need to detect primordialgravity waves.

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Table 1. Constraints on the basic 6-parameter model (flat;no tensors) from WMAP1 and WMAP3, in combination with2dFGRS in each case.

Parameter WMAP1 WMAP3

8 0.830 0.033 0.737+0.033

0.045

0.146 0.066 0.083+0.0270.031

n 0.954 0.023 0.948+0.0140.018

b 0.023 0.001 0.022+0.000070.00008

c 0.105 0.005 0.104+0.0050.010

h 0.735 0.023 0.737+0.0330.045

m 0.237 0.020 0.236+0.0160.029

So far, the tensor contribution to the large-angleanisotropy power spectrum is limited to a fraction r

0.1, although the

ultimate limit from cosmic variance is more like r 105.This sounds like there is a lot of future scope, but it shouldbe recalled that the energy scale of inflation scales as thetensor C

1/4 . Therefore, we will need a degree of luck with

the energy scale if there is to be a detection.

3. The vacuum: a search for two numbers

3.1. Signatures of dark energy

The most radical conclusion of cosmological research overthe past decade has been that the universe contains a non-zero vacuum density, with antigravity properties akin to

a cosmological constant. This discovery has profound im-plications for fundamental physics, and a top priority formuch cosmological research is now unravelling the nature

Fig. 3. The marginalized WMAP3 confidence contours on theinflationary r n plane (revised version of plot from Spergelet al. 2006).

of this phenomenon. The general term dark Energy tendsto be used to encapsulate our ignorance of the detailedphysics that is being probed.

Dark Energy can differ from a classical cosmologicalconstant, in being a dynamical phenomenon. Empirically,this means that it is endowed with two thermodynamicproperties that astronomers can try to measure: the bulkequation of state and the sound speed. If the soundspeed is anywhere close to the speed of light, the ef-fect of this property is confined to very large scales, andmainly manifests itself in the large-angle multipoles ofthe CMB anisotropies. The equation of state, however,is more readily probed. This is quantified via the param-eter w P/c2, which can in principle be an evolvingfunction of scale factor, w(a). Some complete dynamicalmodel is needed to calculate w(a). Given the lack of aunique model, the simplest non-trivial parameterizationis

w(a) = w0 + wa(1 a).As discussed further below, this formulation obscures thefact that most probes of dark energy derive the majority oftheir power from intermediate redshifts. Thus, it is morereasonable to think of a given experiment as measuring wat some pivot redshift, together with a constraint on how

rapidly w changes around that redshift. In most cases, thepivot redshifts are close to z = 0.6.For adiabatic expansion of the vacuum, we should in

general regard 3(w + 1) as giving the rate of changed ln /d ln a, so the Friedmann equation gives the epoch-dependent Hubble parameter as

H2(a) = H20

ve3(w(a)+1) d ln a

+ ma3 + ra

4 ( 1)a2,where a = 1/(1 + z) is the dimensionless scale factor.This change in expansion rate is observable in two ways:the geometry of the universe and the growth of density

perturbations.The comoving distance-redshift relation is one of the

chief diagnostics ofw. The general definition of the differ-

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ential increment of comoving radius is

dD/dz = c/H(z).

As shown in Fig. 4, perturbing this about a fiducialm = 0.25 w =

1 model shows a multiplier of about

5 e.g. a measurement of w to 1% requires D to 0.2%.Furthermore, there is a near-perfect degeneracy with m.The D(z) relation is thus a double integral over w(z),making it rather hard to detect any sudden evolution inw via this geometrical means. By attempting to measurelengths in the radial direction only, one can in principleremove one integration and access H(z) directly, but eventhis responds rather slowly to changes in w.

The other main signature of dark energy lies in its ef-fect on the growth of density inhomogeneities. The equa-tion that governs the gravitational amplification of densityperturbations is

+ 2a

a =

4G0 c2sk2/a2

,

where is the fractional density perturbation, k is comov-ing wavenumber and cs is the sound speed. The propertiesof the vacuum manifest themselves in the damping termproportional to . For w = 1, the differential equationfor has to be integrated directly. In doing this, we seethat the situation is the opposite of D(z): the effects ofchanges in w and m now have opposite signs (see Fig.4).

The geometrical effect of dark energy can be observedbecause the pattern of density inhomogeneities in theuniverse contains preferred scales related to the horizonlengths at certain key times, depending on key cosmo-logical parameters such as the density. Datasets at lowerredshifts probe the same parameters in a different way,which also depends on the assumed value of w: either di-rectly from D(z) as in SNe, or via the horizon scales asin LSS. Consistency is only obtained for a range of valuesof w, and the full CMB+LSS+SNe combination alreadyyields impressive accuracy:

w = 0.926+0.0510.075

(for a spatially flat model). The confidence contours areplotted in detail in Fig 5. Any future experiment must aimfor a substantial improvement on this baseline figure.

3.2. Models for dark energy

The simplest physical model for dynamical vacuum en-ergy is a scalar field, sometimes termed quintessence. TheLagrangian density for a scalar field is as usual of the formof a kinetic minus a potential term:

L = 12 V().In familiar examples of quantum fields, the potentialwould be a mass term:

V() = 12

m2 2,

Fig. 4. Perturbation around m = 0.25 of distance-redshiftand growth-redshift relations. Solid line shows the effect of in-crease in w; dashed line the effect of increase in m.

where m is the mass of the field. However, it will be betterto keep the potential function general at this stage. Notethat we use natural units with c = h = 1 for the remainder

of this section. Gravity will be treated separately, definingthe Planck mass mP = (hc/G)1/2, so that G = m2P innatural units.

The Lagrangian lacks an explicit dependence on space-time, and Noethers theorem says that in such cases theremust be a conserved energymomentum tensor. In the spe-cific case of a scalar field, the energy density and pressureare

= 12 2 + V() + 12()2

p = 12

2 V() 16

()2.If the field is constant both spatially and temporally, the

equation of state is then p = , as required if the scalarfield is to act as a cosmological constant; note that deriva-tives of the field spoil this identification.

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Fig. 5. The WMAP3 constraints on w, in the case where al-lowance is made for dark-energy perturbations with c as thespeed of sound (revised version of plot from Spergel et al. 2006).

Treating the field classically (i.e. considering the ex-pectation value ), we get from energymomentum con-servation (T; = 0) the equation of motion

+ 3H

2 + dV/d = 0.

Solving this equation can yield any equation of state,depending on the balance between kinetic and potentialterms in the solution. The extreme equations of state are:(i) vacuum-dominated, with |V| 2/2, so that p = ;(ii) kinetic-dominated, with |V| 2/2, so that p = . Inthe first case, we know that does not alter as the uni-verse expands, so the vacuum rapidly tends to dominateover normal matter. In the second case, the equation ofstate is the unusual p = , so we get the rapid behaviour a6. If a quintessence-dominated universe starts offwith a large kinetic term relative to the potential, it may

seem that things should always evolve in the direction ofbeing potential-dominated. However, this ignores the de-tailed dynamics of the situation: for a suitable choice ofpotential, it is possible to have a tracker field, in whichthe kinetic and potential terms remain in a constant pro-portion, so that we can have a, where can beanything we choose.

Putting this condition in the equation of motion showsthat the potential is required to be exponential in form.More importantly, we can generalize to the case wherethe universe contains scalar field and ordinary matter.Suppose the latter dominates, and obeys m a. Itis then possible to have the scalar-field density obeyingthe same a law, provided

V() exp[/M],

where M = mP/

8. The scalar-field density is =(/2)total (see e.g. Liddle & Scherrer 1999). The im-pressive thing about this solution is that the quintessencedensity stays a fixed fraction of the total, whatever theoverall equation of state: it automatically scales as a4 at

early times, switching to a

3 after matter-radiation equal-ity.

This is not quite what we need, but it shows how theeffect of the overall equation of state can affect the rollingfield. Because of the 3H term in the equation of motion, knows whether or not the universe is matter dominated.This suggests that a more complicated potential than theexponential may allow the arrival of matter dominationto trigger the desired -like behaviour. Zlatev, Wang &Steinhardt (1999) tried to design a potential to achievethis, but a slight fine-tuning is still required, in that anenergy scale M 1 meV has to be introduced by hand,

so there is still an unexplained coincidence with the energyscale of matter-radiation equality.

3.3. Measuring the evolution of dark energy

Most existing studies of dark energy have tended to treatw as a constant. When the evolving w(a) = w0+wa(1a)model is introduced, typically a strong correlation is seenbetween the inferred values of w0 and wa. This correla-tion is readily understandable: the bulk of the sensitivitycomes from data at non-zero redshifts, so the z = 0 valueis an unobserved extrapolation. It is better to assume thatwe are observing the value at some intermediate pivot red-

shift:

w(a) = wpivot + wa(apivot a).The pivot redshift is defined so that wpivot and wa are un-correlated in effect rotating the contours on the w0waplane. If we do not want to assume the linear model forw(a), a more general approach is given by Simpson &Bridle (2006), who express the effective value ofw (treatedas constant) as an average over its redshift dependence,with some redshift-dependent weight. Both these weightsand the simple pivot redshifts depend on the choice ofsome fiducial model. With reasonable justification (both

from existing data, and also because it is the fiducial modelthat we seek to disprove), this is generally taken to be thecosmological constant case. The pivot redshift for most ex-periments tends to be close to z = 0.6, reflecting the factthat (a) w manifests itself in an integrated signal thatbuilds up from z = 0; (b) for dark energy anything closeto , the dark energy contribution becomes subdominantand hard to measure for z >

1. Thus, a rough view of

the situation is that different experiments will measurew(z = 0.6) and an uncorrelated estimate of how rapidly itevolves at that time, wa. The Kolb et al. (2006) US DarkEnergy Task Force advocated a figure of merit which isthe product of these two uncertainties i.e. the area of the

error ellipse in the w0wa plane. It is not clear that this isthe best choice: as long as matches the data, the initialchallenge is to rule out this w = 1 model, so there could

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be a case for trying to optimise the accuracy of measuringwpivot, independent of evolution. But one could also envis-age models that have wpivot = 1 and yet show wa = 0; itreally depends on ones prejudice on how realistic modelsmight occupy the w0 wa plane. In practice, the axialratio of the confidence ellipse is large, so that errors inwa are around 10 times those in wpivot. Thus, if plausi-ble models occupy a small region near (w0, wa) = (1, 0),they are much more likely to be detected via their effecton wpivot than via wa. But on the optimistic assumptionthat will be rejected, measuring evolution would thenbe the next main aim.

4. The vacuum: anthropic approach

Finally, a few words about the greatest problem regard-ing the vacuum, one that we have almost learned to ig-

nore. The existence of a non-zero vacuum density raisestwo problems: (1) the scale problem and (2) the why-nowproblem. The first of these concerns the energy scale cor-responding to the vacuum density. If we adopt the valuesv = 0.75 and h = 0.73 for the key cosmological parame-ters, then

v = 7.51 1027 kg m3 = hc

Evhc

4,

where Ev = 2.39 meV is known to a tolerance of about 1%. The vacuum density should receive contributions ofthis form from the zero-point fluctuations of all quan-

tum fields, and one would expect a net value of order thescale at which new physics truncates the contributions ofhigh-energy virtual particles: anything from 100 GeV to1019 GeV. The why-now problem further states that weare observing the universe at almost exactly the uniquespecial time when this strangely small vacuum density firstcomes to dominate the cosmic density.

Taking the second problem first, a question that in-volves the existence of observers must necessarily havean answer in which observers play a role. Therefore, asolution to the why-now problem requires anthropic rea-soning. Here, one envisages making many copies of the

universe, allowing the value of the vacuum density to varybetween different versions. Although most members of theensemble will have large vacuum densities comparable inmagnitude to typical particle-physics scales, rare exam-ples will have much smaller densities. Since large values ofthe vacuum density will inhibit structure formation, ob-servers will tend to occur in models where the vacuumdensity falls in a small range about zero thus poten-tially solving both the scale and why-now problems. Thissolution was outlined by Weinberg (1989) and taken upin more detail by Efstathiou (1995). Efstathiou calculatedthe expected distribution for v for a typical observer (aterm whose meaning is discussed below); he found a re-

sult that peaked around v 0.9, in which the observedv = 0.75 would not be surprising. This is an impres-sive result, but it has two points at which further study

Fig. 6.Time dependence of star formation predicted in a sim-ple collapse model. The total stellar density produced by a

given epoch is assumed to scale with the total collapse fractionassociated with a single mass scale. The density-fluctuationparameter (T = 1000) is varied by up to 20 per cent eitherside of its canonical value = 250. This yields a good matchto the data on the empirical redshift dependence of the totalstellar mass density, taken from Merloni, Rudnick & Di Matteo(1994).

is merited. Efstathiou fixed the CMB temperature at itsobserved value; in principle, it is possible that this is nota typical value when all observers are considered. A larger

issue is the behaviour for negative , where the universeeventually recollapses into a big crunch. In the anthropicapproach, either sign of is intrinsically equally likely,and we need to understand if the normal assumption of > 0 is justified.

These issues are discussed at length in Peacock (2007),and some results are summarized here. We stick withEfstathious approach in which only varies. If the sim-plest forms of anthropic variation can be ruled out, thismight be taken as evidence in favour of the landscape pic-ture (Susskind 2003; Tegmark et al. 2005). The differentuniverses in the ensemble are assumed to receive a weightaccording to the number of observers that exist in them.We can side-step the difficult issue of defining the con-ditions for observers by exploiting the assumed similar-ity of the members of the ensemble in their non-vacuumphysics. We do not need to predict the absolute number ofobservers, nor how they are divided into different types:it is sufficient to assume that a model with twice as manystars is twice as likely to be experienced. Thus, we takethe weighting of each member of the ensemble to be givenby the fraction of the baryons that are incorporated intononlinear structures:

dP(v) fc dv,where fc is the collapse fraction: the proportion of massin the universe that has become incorporated into suffi-ciently large nonlinear objects. The uniform prior in

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Fig. 7.The collapse fraction as a function of the vacuum den-sity, which is assumed to give the relative weighting of different

models. The dashed line for negative density corresponds to theexpanding phase only, whereas the solid lines for negative den-sity include the recollapse phase, up to maximum temperaturesof 10 K, 20 K, 30 K.

around zero is defensible given the tiny range of values ofinterest. But this gives the time distribution for the for-mation of sites at which life might subsequently form. Themore serious challenge lies in predicting the history of ob-servers following a formation event, but we can avoid theworst uncertainties by turning the problem backwards. Wecan calculate the distribution of times at which stars formin the universe, and we know when the star with whichwe are associated was formed: 4.6 Gyr ago. That timecorresponds to a redshift 0.457, at which point the cosmo-logical parameters were T = 3.97 K and v = 0.49. Wecan therefore concentrate on the more concrete question ofwhether the sun formed at a typical point in comparisonto all stars in the multiverse.

The collapse fraction is conventionally calculated ac-cording to the approach of Press & Schechter (1974). Themass scale is defined by the mass in a homogeneous uni-verse contained within a sphere of radius R. The fractional

density fluctuations smoothed with such a spherical filterhave an rms value (R), and the rareness of objects of agiven mass is quantified by defining

c/(R),

where c is a density threshold of order unity. Since changes with time, we need to specify an era in order toassociate with a given mass. It is convenient to makethe arbitrary choice of T = 1000 K as a reference era(matter dominates over radiation and over any vacuumdensity of interest). Recent numerical experiments haveestablished that the collapse function has a near universal

form in terms of with c = 1.686 treated as constantfor all models (e.g. Warren et al. 2006). However, exist-ing accurate fitting formulae for the collapse fraction do

not satisfy the common-sense requirement that fc 1 asM 0. The following alternative cures this, and matchesthe numerical data as well as any alternative:

fc = (1 + a b)1 exp(c 2),

where (a,b,c) = (1.529, 0.704, 0.412). Using this, we cancalculate the probability of any given value of , usingthe asymptotic value of fc as a weight. As shown in Fig.6, a choice of (T = 1000) = 250 matches extant dataon the time dependence of the star-formation history in asatisfactory way.

This formalism presents a problem for < 0, since inall cases fc 1 in the late stages of recollapse: freeze-outonly happens for > 0, when models reach a phases of ex-ponential expansion. However, structures that form veryclose to the final singularity are not of interest for the an-thropic calculation: there is little time remaining for life to

develop, and in any case the CMB will have heated up tothe point where it interferes with life or indeed perhapseven with the formation of stars and planets themselves. Itis simplest to express this cutoff in the recollapsing phasein terms of a maximum temperature that we are willingto consider, although this can be directly translated to alimit on the time remaining before the big crunch. Sincethe recollapsing phase is the time-reversed version of theexpansion, the time remaining from temperature T untilthe big crunch is just what would have elapsed from thebig bang until this temperature. Normally, the matter-dominated approximation will apply, so

t(T) 23H0

1/2m (1 + z)3/2 =

T

18.6 K

3/2

Gyr.

We know from observations that star formation in galaxiescan proceed actively at redshift z 7, so Tmax > 10 Kon these grounds. This would leave only a few Gyr afterformation for life to evolve, so presumably Tmax shouldnot be much larger than this, and could well be smaller.This is not so much a biological argument as one based onstellar lifetimes.

With this preparation, Fig. 7 shows the posterior dis-tribution of for various values of Tmax. Provided Tmax


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Fig. 8.Contours of probability density on the log(

T

)

v

plane. The three contours shown enclose 68%, 95% and 99%of the probability. The solid point shows the conditions at theepoch of formation of the sun.

5. Concluding remarks

The three-year WMAP data leave cosmology in a stillmore exciting state, with no hint of diminishing returns.Barring some unaccounted-for systematic, we need to ac-cept that the scale-invariant n = 1 model must now jointthe museum of cosmological cast-offs, along with otherdominant figures of the past, such as the Einsteinde Sitter

universe. We have argued that tilt is plausibly somethingthat might be expected on general grounds, simply be-cause the current universe (or its size at the Planck era) isnot infinitely larger than the Planck scale. But it is hardnot to be impressed by the fact that the strong line of ar-gument for tilt has come from inflation. It is particularlyextraordinary that the very simplest model, of a mass-likepotential V 2, is consistent with the data. This newstandard model predicts that the tensor fraction shouldbe r 0.15, and this will be an encouraging target forexperimentalists.

A detection of tensor anisotropies at this level will

probably be feasible with another 5-10 years effort. Thisis an easy statement for a non-experimentalist to make,since the WMAP measurements of the polarized fore-grounds are certainly intimidating. The way ahead willnot be easy, but given what has been achieved to date, oneshould not lightly bet against it. A more significant worryis whether the theoretical prediction should be taken atall seriously, since it requires super-Planckian field val-ues. Thus, quantum-gravity corrections should destroy theV 2 potential on which everything rests. Fortunately,no amount of theoretical skepticism will stop the flood ofCMB experiments now headed in our direction.

Whatever the fate of inflation, the problem of dark

energy may be more intractable. On an optimistic readingof the data, we know that w = 1 to 5% (if constant).We also know that it will take a heroic effort to reduce this

to 1% involving photometric redshifts for a good fractionof all the galaxies out to z = 1. As Trotta (page 77) hasdiscussed at this meeting, failure to reject a cosmologicalconstant at that level of precision might formally allowus to argue that the model is proved. In any case, the

motivation (and scope) for further experimental effort maywell be exhausted at that point. Obviously, detection ofw = 1 would be a richer possibility, which would openthe door to a new era of dark-energy studies. The stakesare high.

Acknowledgements. I thank PPARC for the support of a SeniorResearch Fellowship.

References

Crittenden, R. G., Natarajan, P., Pen, U.-L., & Theuns, T.,2002 ApJ, 568, 20

Efstathiou, G. & Bond, J. R., 1999, MNRAS, 304, 75Efstathiou, G., 1995, MNRAS, 274, L73Efstathiou, G., et al., 2002, MNRAS, 330, L29Gordon, C. & Lewis, A., 2003, PRD, 67, 123513Kolb, R., et al., 2006, astro-ph/0609591Liddle, A. R. & Scherrer, R. J., 1999, Phys. Rev. D 59, 023509Malquarti, M., Copeland, E. J., & Liddle, A. R., 2003, Phys.

Rev. D, 68, 023512Merloni, A., Rudnick, G., & De Matteo, T., 2004, MNRAS,

354, L37Natarajan, P., Loeb, A., Kneib, J.-P., & Smail, I., 2002, ApJ,

580, L17Peacock, J. A., 2007, MNRAS, 379, 1067Press, W. H. & Schechter, P., 1974, ApJ, 187, 425Seljak, U., Slosar, A., & McDonald, P., 2006, JCAP, 0610, 014

(astro-ph/0604335)Simpson, F. & Bridle, S., 2006, Phys. Rev. D73, 083001Stebbins, A., 1996, (astro-ph/9609149)Susskind, L., 2003, (hep-th/0302219)Tegmark, M., Aguirre, A., Rees, M. J., & Wilczek, F., 2006,

Phys. Rev. D, 73, 023505 (astro-ph/0511774)Warren, M. S., Abazajian, K., Holz, D. E., & Teodoro, L., 2005,

ApJ, 646, 881, (astro-ph/0506395)Weinberg S., 1989, Rev. Mod. Phys. 61, 1Zlatev I., Wang L., & Steinhardt P.J., 1999, Physical Review

Letters, 82, 896

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J.A. Peacock- Future questions for cosmology