Frontiers of the Universe : What do we know, what do we understand?
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
Disclaimer: layout of this document may differ from the published version.
What do we know, what do we understand?
Universite de Geneve
Departmentde Physique Theorique
24,Quai Ernest Anserment, 1211 Geneve4, Suisse
In this talk I summarize the topis addressed during the onferene. We have disussed
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
The fatthat thisamplitude of the gravitationalpotentialis saleindependent isequiv-
alentto the fat that the observed utuations obey a HarrisonZel'dovih spetrum.
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-
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
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
The deuterium and Lithium abundanes determine the density of baryons in the
=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
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
=0,thisan be astas
= 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
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
Atually,wean alsofaethisresultinapositiveway: nobody(exeptperhapsProf.
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
whih is due to our motion with respet to the CMB
rest frame) are of the order of
' : (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.
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
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
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-
; h; r =T=S; n
; ; (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
= 0:042 with osmologial onstant,
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
forward waystomeasure thegravitationalpotentialand henethe metriperturbations.
Unfortunately, they are notoriouslydiÆultto measure, sine
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
; this implies 10 5
where is again the (dimensionless)gravitational potential.
But also on smaller sales, 0:1Mp
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
Clearly, to determine bulk veloity ows, a preise measurement of the Hubble pa-
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
not suer frommany of the problems of bulk veloities [13℄.
5 Large sale struture
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
(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
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
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
P(k) 10 3
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,
The expetation value of is relatedto the onvergene powerspetrum P
) ; (10)
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
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
from the weaklensing analysis ofthe
VIRMOS deep imaging survey. Figure from Werbaeke et al. [17℄, where one an nd
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
L. Baudis and others), we have not observed the partile giving rise to
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
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
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.
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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