## Conference Presentation

## Reference

### Frontiers of the Universe : What do we know, what do we understand?

### DURRER, Ruth

**Abstract**

### In this talk I summarize the topics addressed during the conference. We have discussed the most relevant cosmological observations of the last say 10 years and their implications for our understanding of the Universe. My finding throughout this meeting has been that it is amazing how our knowledge of cosmological parameters has improved during the last years. It comes as a surprise to many, that the simplest inflationary model of adiabatic perturbations agrees well with present data. But it is frustrating that we have not made any progress in identifying the dark matter, in contrary, we have supplemented it by what we call the 'dark energy', a gravitationally and esthetically repulsive component which is even more mysterious than the dark matter. We have no understanding about the origin of these two most abundant energy components of the present Universe.

### DURRER, Ruth. Frontiers of the Universe : What do we know, what do we understand? In:

*Rencontres de Blois* , Blois (France), 2001, p. 11

### Available at:

### http://archive-ouverte.unige.ch/unige:2250

### Disclaimer: layout of this document may differ from the published version.

What do we know, what do we understand?

Ruth Durrer

Universite de Geneve

Departmentde Physique Theorique

24,Quai Ernest Anserment, 1211 Geneve4, Suisse

Abstrat

In this talk I summarize the topis addressed during the onferene. We have disussed

themostrelevantosmologialobservationsofthelastsay10yearsandtheirimpliations

forourunderstandingoftheUniverse. Myndingthroughoutthismeetinghasbeenthat

itisamazinghowourknowledgeofosmologialparametershasimprovedduringthelast

years. It omes as a surprise tomany,that the simplest inationarymodelof adiabati

perturbationsagreeswellwithpresentdata. Butitisfrustratingthat wehavenot made

any progress in identifying the dark matter, in ontrary, we have supplemented it by

what we all the 'dark energy', a gravitationally and esthetially repulsive omponent

whihis even more mysteriousthan the dark matter. We have no understanding about

the origin of these two most abundant energy omponents ofthe present Universe.

Mostof us are onvined that belowa ertain(very high) temperature and density and

abovea ertain(very small)lengthsale, generalrelativityisthe relevanttheory forthe

desriptionoftheinterationof matterandspaetime. TheFriedmannuniverse isoneof

the simplest solutionsof Einstein's equation and this is probably the main reason these

solutionshavebeen foundand disussed originallyby Friedmann. Inontrast toNewto-

nian gravity, Einstein'sequationsdoallowfor homogeneousand isotropisolutions,but

they are generiallynon-stati.

Nevertheless, I onsider it as a big surprise that the Friedmann universe is suh a

good approximation to the observable universe. As I will argue below, we have several

independent pieesof evidene, that the metri deviationsfrom the Friedmann solution

are of the orderof

'10 5

1; (1)

onallosmologialsalesfromabout0:1MpuptotheHubblesale,H 1

0

= 3000h

1

Mp.

The fatthat thisamplitude of the gravitationalpotentialis saleindependent isequiv-

alentto the fat that the observed utuations obey a HarrisonZel'dovih spetrum.

InthefollowingsetionsIreolletsomeobservationalevidenesanddisussthemost

importantlessons we learn from them. At several oasions I shall alsoformulatesome

doubts,espeially onerningthe data analysis.

I shall nish with a briefinventory about what we know and then turn to the more

interesting even if less well dened question of what we understand. Clearly, 'under-

standing' has many levelsand probably means something dierent for allof us. In this

sense I just present a personal pointof view.

I shall onlude with afew words about the diretionthe eld might develop into.

2 Big bang nuleosynthesis and Type Ia Supernovae

Big bang nuleosynthesis has been disussed by T. X. Thuan, S. Sarkar, and also A.

Lubowih during this onferene. The agreement of the observed light element abun-

daneswithalulationsrepresentsoneofthefundamentalpillarsofbigbangosmology.

Therearetwoosmologialparameterswhihanbedeterminedbyomparingnuleosyn-

thesis alulations with observations. The Helium abundane restrits any additional,

non-standard, relativisti ontribution to the energy density of the Universe. This an

be ast in

N

0:2 or

X

rel

1:1610 6

: (2)

Here, X

rel

denotes any 'partile' speies whih is still relativisti at the time of nule-

osynthesis (T 0:1MeV) inaddition tothe three speies of neutrinos and the photons.

Examplesare aomponentof stohastigravitywavesorsomeother unknown partiles,

e.g. sterile neutrinos, with mass m

X

<0:1MeV.

The deuterium and Lithium abundanes determine the density of baryons in the

universe [1℄,

b h

2

=0:020:002 : (3)

by J. Niemeyer and C.R. Ghezzi),we have realized observationally, that they represent

exellent 'modied standard andles'. The Supernovae type Ia measurements of the

past years [2, 3℄ have led to the most surprising result that the present universe is

aelerating, inother words the gravitationallyative ombination+3pis negative in

the present universe. Casting this in terms of an equation of state, p = w, the data

yield w

e

0:60:15. Or, if we assume the dark energy of the universe to be in the

form of a osmologial onstant with w

= 1, whih is ombined with dark matter

whihhasw

m

=0,thisan be astas

m

0:75

= 0:250:125. These resultshave

been disussed by K. Shahmanehe inthis meeting.

Clearly, it is still somewhat premature to exlude possibilities like 'grey dust' or

'osillations of the photons' (see e.g. [4℄). But alsothe large sale struture (LSS) data

ombined with osmi mirowave bakground anisotropies give strong evidene for a

osmologial onstant (or quintessene).

The only form of energy whih leads to a 'osmologial onstant' is a onstant po-

tentialenergy (inlassialphysis) orvauumenergy(inquantum physis). Butexatly

this form of energy has no dynamial onsequenes in all known physial interations

exept gravity. Only dierenes in the vauum energy are dynamially meaningful in

non-gravitational interations. One gravity is taken into aount, this otherwise arbi-

traryintegration onstantsuddenly beomesdynamially important.

Sine in supersymmetri theories the vauum energy from fermions and bosons ex-

atly anels, the typial value of the vauum energy expeted from modern partile

physis is

=

8G 'E

4

SUSY

>

10 12

GeV 4

'10 59

: (4)

Here E

SUSY

denotes the supersymmetry breaking sale whih we know to be at least

1TeV or larger. The above mentioned observations nd a non-vanishing value whih is

at least 59 orders of magnitude smaller than what one naively expets. This nding

represents probablythe most amazingpuzzle inphysis. Clearly, we are laking abasi

piee in our understanding and interpretation of the osmologial onstant and/or of

vauum energy.

Atually,wean alsofaethisresultinapositiveway: nobody(exeptperhapsProf.

Burbidge)hasexpetedit! Thisisthelearestevidenethatosmology,whihforalong

time lived from'theoretial speulations' has beomedata dominated.

I belive that the aelerating universe and the osmologial onstant represents the

biggest puzzle in present physis. There are divers attempts to address it, but none

of them so far ould onvine a majority (see ontributions from M. Turner and F.

Piazza). More observational onstraintson this mysterious dark energy are desperately

needed. Various attempts in this diretionhave been addressed inthe ontributions by

J. Newman,R. Bean and J.Weller.

The Universe is permeated by an isotropi thermal radiation at T = (2:7280:01)K,

the osmi mirowave bakground(CMB). Anisotropies inthis bakground radiation(a

part from a dipole of C

1 10

3

whih is due to our motion with respet to the CMB

rest frame) are of the order of

T

T

'10 5

' : (5)

The last' indiates that CMB anisotropies are of the same order of magnitude as the

gravitational potential (Bardeen potential). This isotropy, together with the osmo-

logial priniple (we are not sitting in a speial plae in the Universe), proves that the

Universe islose toFriedmann onlarge sales.

TheauratemappingofCMBanisotropies,espeiallybythethreelatestexperiments

Boomerang[5℄, MAXIMA[6℄and DASI[7℄teahes usmuhmorethatthis: thesimplest

model of a Harrison Zel'dovih (sale invariant) spetrum of purely adiabati salar

utuationswith reasonableosmologialparametersts the dataverywell(see Fig.1).

Figure 1: The CMB anisotropy power spetrum measurements from Boomerang

(solid,red), MAXIMA (dashed, green) and DASI (dotted,blue) are shown. A typial

inationarymodelwith saleinvariantsalarperturbationsis indiatedtoguidethe eye

(solid line). The CMB anisotropy spetrum for ausal global defets (texture) is also

shown (dashed line).

This result is by no means trivial: the simplest worked out models with 'ausal'

initialperturbations, i.e. initialonditionswhere allorrelations onsuperhorizonsales

vanish, do not t the data (dashed line in Fig. 1). The reason for this is relatively

subtle: these models, where utuations are indued by topologial defets, atually

not `in phase', i.e. at the moment of reombination not all utuations of a given

wavelength are at a maximum/minimum /zero respetively. The peak struture whih

is so harateristi of utuations reated ata very early initialtime and whih have a

xed amplitude at horizon rossing, is therefore not expeted from topologial defets.

For topologial defets the physial mehanism whih reates the utuations shortly

afterhorizonrossingisnon-linear. Thenon-linearitiesimplyaouplingof modeswhih

smearsouttheaoustipeaksatleasttosomeextend. Furthermore,tensorandespeially

vetor perturbations ontributesigniantly (more than 50%) to the CMB anisotropies

at large sales, leading to a suppression of the purely salar aoustipeaks in a COBE

normalized spetrum.

Thisisthemainlessonwhihwehavelearnedsofarfromthesebeautifulexperiments:

the osmologial initial utuations stem most probably from an inationary phase or

some equivalent,whih produed utuationson sales larger than the Hubble horizon.

I onsider this data as 'evidene for ination' of a ompletely dierent quality than

the homogeneity and isotropy of the Universe and the atness problem. For the latter

ination justies highly improbable initial onditions. In ontrary, the aousti peaks

havebeenpreditedfromination. Thisatuallyeven beforethedevelopmentofination

by Doroshkevih, Zeldovih and Sunyaev (1978)[9℄. These authors have used an initial

spetrum of utuations with orrelations on super Hubble sales whih an only be

generated during an ination-like proess. Here we use the term 'ination' in its most

generi sense asa periodwhere the o-movingsize of the Hubble sale isinreasing.

Sine the details of the aousti osillations depend sensitively on osmologial pa-

rameters like

m

;

;

b h

2

; h; r =T=S; n

s

; n

T

;

; ; (6)

many of us have used them to determine them. Progress in the determination of os-

mologialparameters has been reported here by S. Sarkar,J. Silk, M. Tegmark and C.

Pryke. A. Melhiorri has disussed to whih extend present results will improve with

new data from the MAP and PLANCK satelliteexperiments.

Even thoughthis parameterestimation is potentiallya very powerfulmethod,espe-

iallywhen ombinedwith otherdatasets, whih are desperately needed sinethe CMB

alone has important degeneraies, I think we must be areful not to over-interpret the

data. Simplyonsider the numberofpapers writtenby ustheoretiians(I, myself wrote

one of them...) about the missingseond peak after the rst Boomerang-98results [10℄

whih have now turned out to be due to a systemati error in the data analysis (a

miss-estimated beam size). The person who warned me most not to over-interpret this

marginalfeature inthe Boomerangpowerspetrum wasPaolode Bernardis himself. As

Zwiky [11℄ put it: "If only theorists would know what goes into an experimentaldata

point and if only experimenters would know what goes into a theoretial alulation,

they both would take eah other muhless serious".

Therefore, I guess we may be ondent that the osmologial parameters as deter-

mined so far seem tolie inthe rightbulk part, but I doby nomeans take seriously the

formalerrors quoted inthe published papers.

that the orret modelis in the family of models being parameterized. If one allows for

more generi models (e.g. relaxing the requirement of adiabatiity) one an nd very

dierentosmologial parameters whih alsot the present CMB data (see Fig. 2).

Figure 2: The CMB anisotropy power spetrum measurements from Boomerang are

ompared with at models with

b h

2

= 0:042 with osmologial onstant,

= 0:7.

The model with mixed isourvatureand adiabatiomponents isa goodt (solid line),

while the adiabatimodeldoes not tthe data withthis parameter hoie. Figurefrom

Trotta et al.[12℄, where one an nd more details.

Muh more remarkable than the preisionof osmologialparameters obtained from

CMB measurements so far is their onordane with independent determinations from

other data like LSS, peuliar veloities, lensing et., under the simplest possible model

assumptions. Letus thereforesummarize results fromother datasets.

4 Peuliar veloities

ApartfromtheCMB(andlensing),peuliarveloitiesrepresentoneofthemoststraight-

forward waystomeasure thegravitationalpotentialand henethe metriperturbations.

Unfortunately, they are notoriouslydiÆultto measure, sine

v pe

r

=z rH

0

(7)

isthe smalldierene oftwolarge numbers, of whihthe seond one (r)is very diÆult

to measure. Therefore, one has to onsider arefully how to use this noisy data at its

best. A rst order of magnitude result is that peuliar bulk veloities are of the order

of v (r)300km/s on sales of r 50h Mp. Usingthe saling relationfrom linear

perturbation theory,

v(r)

2

rH

0

; this implies 10 5

; (8)

where is again the (dimensionless)gravitational potential.

But also on smaller sales, 0:1Mp

<

r

<

1Mp, where strutures are virialized and

we expet '(v=) 2

, weobtain from the veloity dispersion inlusters, v 1000km/s

again 10 5

.

Together with the CMB anisotropies on large sales, this gives 10 5

on all

osmologiallyrelevantsales,fromthesizeofgalaxiesuptotheHubblesale,0:1Mp

<

r

<

6000Mp.

Clearly, to determine bulk veloity ows, a preise measurement of the Hubble pa-

rameterisdesperatelyneeded(seeontributionbyJ.Bekman). Alltheresultsdisussed

here are not very preisebut they are nevertheless very interesting and mightbe telling

us something whih we have overlooked so far...

Finally I want to mention that during the last ouple of years, a new tehnique,

namely the statistis of pairwise veloities of galaxies has been developed and it has

been shown that itan lead toarelatively preisemeasurement of

8

and

m

as itdoes

not suer frommany of the problems of bulk veloities [13℄.

5 Large sale struture

Newgalaxyredshiftsurveysarebeingompletedorunderway. Thenumberofpublished

galaxy redshifts is growing very fast. The galaxy redshift atalogs are mainly used to

determine thegalaxy power spetrumwhihwehopetobelosely relatedtothe matter

powerspetrum (see ontributionof S. Zaroubi).

Most reently, the 2dF power spetrum has been interpreted to show evidene for

osillations or at least struture, whih indiate a relatively high ratio

b

=

m

0:15

(see Ref. [14℄ and the ontribution by C. Frenk). It is really amazing to whih extent

bigbangnuleosynthesis, CMB,LSS, SNIaand alsolusterdata[15℄ ome togetherand

favor h 2

b

0:02,

m

0:3 and

0:7.

I admit,however, that I dohave reservations tointerpret the osillationsinthe 2dF

powerspetrumas aoustiosillationsof baryons (this onern is partiallysharedwith

C. Frenk, see his ontribution). First of all, aording to my naive estimate they are

not quiteat the rightposition. Seondly, they ould verywell mimisome eet froma

nite size lter, the Fourier transformof a top-hatlter simply gives aBessel funtion.

I amalsoabitrelutanttotakeseriouslytheinterpretationofthe'bend inthepower

spetrum'. Sine the mean density of the universe is set equal to the mean density of

galaxiesintheatalogathand,thepowerspetrumatthesaleofthesurvey,L,vanishes

by onstrutionP(k=2=L)0. Itistherefore notsurprising thatallobserved galaxy

powerspetra show abend inthe lastfew points,i.e. for the smallest values of k.

Furthermore, a volume limited sample out to the largest sale k 0:02h=Mp an

be estimated to ontain roughly 1% of all the galaxies in the 2dF atalog leading to

square of the utuation amplitude, 2

(k=0:02h=Mp)=k 3

P(k) 10 3

1=N.

Therefore, and also due to a 'tradition of sloppiness' in the statistial treatment

of galaxy redshift data, I am not ompletely onvined that these data is orretly

interpreted in the present literature.

6 Weak lensing

The deetion of light is fully determined by the gravitational potential, i.e. by the

lustering properties ofmatter. Thestatistialdistributionof theshear, the diretionof

elongationof galaxies, measuresthe gravitationaleld along thelineof sight. Wedene

the ampliation matrix A,

x

y

image

=A

x

y

objet

with A=

+

1

2

2

1

: (9)

The expetation value of is relatedto the onvergene powerspetrum P

via

h 2

i= 2

2

Z

1

0 dk

k P

(k)J

2

1 (k

) ; (10)

whereJ

1

isthe Besselfuntionof order1. More detailsan befound inthe ontribution

by F. Bernardeau and in Ref. [17℄. Observations of the shear of galaxies nally lead

to onstraints in the

m ,

8

plane. For present surveys, the best results are those of

Ref. [17℄ shown in Fig. 3, but this method is just oming up and willhopefully lead to

improved results,one the errorsare better under ontrol.

Figure3: The 1,2and 3 ontours for

m and

8

from the weaklensing analysis ofthe

VIRMOS deep imaging survey. Figure from Werbaeke et al. [17℄, where one an nd

more details.

We have seen in this onferene that osmology is harvesting an enormous amount of

data leading to ever better measurements of the osmologial parameters. At present

it seems that the Universe is at and -dominated with purely adiabatisalar pertur-

bations whih are responsible at the same time for the CMB anisotropies and for large

sale struture. Astrophysial observations presently undergo amazing breakthroughs

in almost all wavebands of the eletromagneti spetrum. This has been impressively

demonstrated in the talks by A. Quirrenbah, A. Omont, A. Watson, H. Meyer, C.

Cesarsky and A. Melhiorri. Also the hope that we may nallybe able to detet gravi-

tationalradiationdiretlyhas beome realisti(see ontributions by T. Damour and M.

Huber). Observational osmology is learly in its most exiting phase, new disoveries

and hallenges fortheorists are to beexpeted every day.

The main parameters of the osmologial model may very well be determined with

suÆient auray within a ouple of years. Then we will know the parameters of the

Universe we are livingin.

But do we understand osmology? I think there we are still very far from our goal:

ofthe two mainonstituentsofthe presentUniverse, wehavenoinformationother than

theirosmologialativity. Despiteintensivesearhes(seeontributionsfromT.Sumner,

L. Baudis and others), we have not observed the partile giving rise to

m

yet. There

are many dark matter andidates (see ontribution from S. Sopel), but learly not all

of theman be realizedinnature. Conerningthe dominant terminthe osmi density,

,the situationiseven worse. Therewehavenoonvining theorygivingaresulteven

in the right bulk park. Interesting ideas are being developed (see e.g. the ontribution

by T. Padmanabhan), but sofar the problemremains unsolved.

Also ination,the'explanation' of theatness and homogeneity ofthe universe, and

oftheadiabatiinitialutuations,ismoreonthelevelofaparadigmthanofatheoryof

the early universe, motivatedby high energy physis(see ontributionby S. Dodelson).

These are, as I see it, the main problems whih onern the early universe. Most

probably, they annot be solved without simultaneous progress in the theory of high

energy physis. They may atually provide our only lues to the physis at very high

energies, like stringtheory, whih are probably not aessible alsoin future aelerators

(see the ontributions fromG.Veneziano andJ. Magueijo). Cosmologymay turnout as

the ultimatetoolto study the fundamental laws of physis.

At the redshifts 10 10

>

z

>

10, i.e. from about T 1MeV until osmi strutures

beomenon-linear andthe rstobjetsform,weunderstandtheosmievolutionrather

well. We an provide good, suessful alulations of primordial nuleosynthesis and

reombination,aswell asintegratethe linearperturbation equationstodetermineCMB

anisotropies. These alulations are in good agreement with observations and, together

with other measurements,they allowus todetermine the osmologialparameters.

At low redshift, z < 10, when struture develops, radiation proesses and hemial

evolution take plae together with gravitational lustering. The physis beomes om-

plex. Many dierent eets have to be taken into aount simultaneously, if we want

to obtain a onsistent piture. Complex numerial simulations ombining gravity with

newobservationsfousingonsmallsales indierentbands ofthe eletromagnetispe-

trum are underway (see ontributions from S. Bridle, I. Lehmann, A. Bunker, E. de

GouveiaDal Pino N.Gruel and others).

I believethat, withinaoupleyears whenthe importantwork ofdeterminingosmo-

logial parameters togood auraywill have been solved, there willremain two major

diretions for osmologialresearh:

z 10 10

Earlyuniverse, towards the fundamental laws of physis.

z

<

10 The formationof galaxies and stars, omplexity.

Aknowledgment: I thank the partiipants of this 'Renontre de Blois' and Filippo

Vernizzi for interesting and stimulatingdisussions. My partiipation at the onferene

was supported by the Swiss National Siene Foundation.

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