Lectures

• Lecture I• Basis of cosmology• An overview: the density budget and the concordance

model

• Lecture II• The dark matter

• Lecture III• The CMB

• Lecture IV• The dark energy

Lecture IIDark matter

• Evidence for dark matter– Galaxies, clusters and lensing

• Measuring the matter density• The large structure • Cosmological perturbation theory (basis)• Structure formation • Dark matter candidates• Future measurements

4

Evidence for dark matter

Experimental probes to measure m

dynamics ( galaxies)

dynamics ( galaxies)

From x-ray

From x-ray large structure (LSS)

large structure (LSS)

(cluster of galaxies)

(cluster of galaxies)

lensing effect

lensing effect

6

Our Galaxy:The Milky Way

The mass of the galaxy:

1210

1210 solar masses

There is little evidence for the presence of considerable amounts of dark matter near the Galactic plane

Rotation of galaxies

Balance between gravitational pull and centrifugal force implies:

m v2 / R = G m M(R) / R2

v = [ G M(R) / R]1/2

From the visible matter distribution in galaxies one expects that M(R) ~ constant for large R, leading to the 1/R1/2 behavior plotted in the diagram. This is clearly not in agreement with the observational curve. Apparently there is more matter than can be seen!

The rotating disks of the spiral galaxies that we see are not stableDark matter halos provide enough gravitational force to hold the galaxies togetherThe halos also maintain the rapid velocities of the outermost stars in the galaxies

New Evidence: X-ray Observations of hot gaz in Clusters

Optical Image X-ray Image from the ROSAT satellite

Without dark matter, the hot gas would evaporate.

10

11

Gravitational lensing

12

Gravitational lensing

3 regimes:•Strong lensing with giant arcs and multiple images•Arclets where there is distorsion but not multiple images•Weak lensing where the distorsion is weak and isrecover in a statistical way

13

14

Measuring the matter density

The baryon densityThe total matter density

m 8G m

3H2b

8G b

3H2

15

Big Bang Nucleosynthesis Theory vs. Observations:

Remarkable agreement over 10 orders of magnitudein abundance variation

Deuterium: strongest constraint

4He

b

It is all baryonic components …( visible or

not…)

Concordance region:b h2 = 0.023For h=0.7, b = 0.04.

16

Measuring m

• Two approaches:• Local approach ( look at some galaxies or clusters)

– Measure mass to luminosity or mass to baryon content ratio

• Statistical approach– Map a large portion of sky and measure the statistical

properties of the objects» Correlation function in structures» Weak lensing measurement (see annexe)

17

measure Hot Gas in Galaxy Clusters

• Emits X-rays– Scattering of electrons off nuclei

produces X-rays called bremsstahlung..

• Interacts with the CMB– ~1% of CMB photons passing

through cluster scatter off hot electrons (inverse Compton)

– Called Sunyaev-Zel’dovich Effect (SZE) ..

• Combining observations of two processes allows one to measure the size of the cluster! Then can give the mass

X-ray Image of Abell 262

SZE Image of MS 1054

CMB coolest in cluster center

SZ C

olla

bora

tion

18

Ω m From Baryon Fraction

HYPOTHESIS

Fraction of baryon and DM areUniversal

Clusters are potential wellsX rays in equilibriumMX = Mb

mm

b

023.0

7.01.005.0

5.1

hhM

M

m

b

m

b

tot

b

23.01.0

023.0 m

nucleosynthesis

19

Ω m From Luminosity

• Mesure masse M by virial method

hDV

DL

L

M LM

m 1500

In cluster : M/L > 250h = > m > 0.2

Difficulty is to know where the cluster stop

20

LOCAL DYNAMICS (NO DE)

LOCAL LENSING (NO DE)

BARYON FRACTION (NO DE)

RELIABILITY AND DE ??

POWER SPECTRUM

0.15 < Ω m < 0.3

FROM PEEBLES (THE « POPE »)

Synthesis of current measurements

Large scale structures

LSSSDSS/ 1 million of galaxies in 6 color + spectra

23

Density distribution of luminous matter of late type galaxies in the Sloan Digital Sky Survey. Superclusters are seen as high-density regions (red). Faint galaxy filaments are seen in low-density regions (voids).. There is more late type galaxies In low density region. Structures are formed after galaxies. Fine structure forms only in models of Cold Dark Matter

24

Overview of LSS picture• Galaxies are not uniformly distributed

– There is structures of some ~ 10 Mpc ( wall …)– Vacuum of 50 Mpc to 70 Mpc – Density contrasts are small – Galaxies seems older than structures

• Dark matter exists, should play a role in structure formation

• Tools to quantify this picture– Correlation function of galaxies– Matter Power spectrum

• And a model to explain the formation of these structures…

25

Measuring the amplitude : definitions

Contrast of density:

in comoving coordinate where x = a(t) r

2-point correlation function:

rxxr

rnrnb

1

(r)(r)

ξ(r) quantify the excess probability from a Poisson case of finding a neighbor galaxy at a distance r.It is a statistical measurement

26

Ω m Correlation Function of Galaxies

• The probability of finding a pair of objects separated by distance r, in each occupying volume elements dV is: dP = n2 [1+ξ(r) ] dV1dV2

Studies done from redshift surveys

BUT:

Z = distance + peculiar velocity

Although redshift (velocity) corresponds to true distance according to the Hubble Law, small peculiar velocities not associated with the Hubble flow can cause distortions in redshift space.

The most evident of these is the Fingers-of-God effect, where long thin filaments in redshift space point directly back at observer.

27

Ω m From Correlation FunctionWhen computing ξ(r) in redshift space, the r coordinate is separated into the transverse component σ and the radial component π.

The transverse component σ is a true measure of distance, while π is distorted by peculiar velocities as explained above.

Ω m 0.3

If no peculiar motion: circular shape is expected

Distorsion is a measure of velocity and of (Ω m

0.6 / b) => for b ~ 1 … b is a bias parameter..

28

Cosmic shearCosmic shear

First detection Van Waerbeke et al.(2000); Wittman et al. (2000); Bacon et al. (2000); Kaiser et al. (2000)

Distortion of distant-galaxy images by the weak lensing effect

Background galaxydeformed deformed image!!image!! Large-scale structure

Powerful future cosmological tool probing Dark matter distribution

Cosmological parameters

The important cosmological information can be obtained by quantifying the non-Gaussianity of weak lensing fields.

29

To complete the m evaluation at large scale ..CMB give also a very precise value ( see lecture 3 for details on interpretation and assumption…)

m = 0.27 0.04

30

Warning on interpretation ….

As soon as we measure large scales, we are more sensitive to m but also to fluctuations (statistical measurement)quantified by 8

(typical size of fluctuation for galaxies)

We can conclude than m < 0.5 Two other proofs with CMB and supernovae (lecture 3 and 4) be explain later

8

31

COSMOLOGICAL FLUCTUATIONSAND

STRUCTURE FORMATION

32

Density Fluctuations in the Universe

•Observations of the distribution of galaxies in the nearby universe–provide direct measurements of the density fluctuations when the

universe is 13 billion years old–current accurate measurements lie between scales of 1 and

several hundred million light years

+ Observation of the CMB (next lecture) (fluctuation ~ 10-5)

•Structure formation models–can we produce structure like that we see today from a universe

that is consistent with the CMB observations when it was ~300,000 years old?

33

From Homogeneity to Structure

• Structure Evolution is a Basic Component of the Big Bang model–well constrained observationally–sensitive to cosmological parameters and the nature of dark

matter• can provide way of addressing these outstanding issues

Gravity amplifies inhomogeneities, even in an expanding universe

Structure evolutionThe picture:

• Structures are formed from gravitational instability of small primordial fluctuations

• Fluctuations are assumed to be

– Scale invariant

– Gaussian

– Adiabatic (compared to isocurvature )

– With Scalars et tensor modes ….

Fluctuations are generated by a mecanism :the inflation and with initial density conditions (see lecture 3)

35

Gravitational Instability

Small departures from uniformity are amplified in an expanding universe

Overdense regions

greater deceleration of expansion leads to greater overdensityexpand more slowly than typical part of the universeeventually collapse if sufficiently overdense

Underdense regions less deceleration of expansion leads to even larger underdensities regions expand faster than typical part of the universe underdense regions grow and form voids

36

Gravitational Instability•General relativity provides solutions for the evolution of density perturbations

Increasing TimeIn

crea

sin

g S

ize

Life and Times of 4Density Perturbations

lowest amplitude

highest amplitudeOverdensity of very small perturbations grows linearly with the expansion of the universe until perturbations become large

Power spectrum

• Define the fourier transform of the density contrast -> k

The power spectrum is the fourier transform of the correlation function

= 2 a(t)/k

Each mode can evolute in time independently of others. is constant but is increasing with the expansion

xkkk

x .iexp2 2/3

3

d

)(x

What mean power?

Power is the amplitude

Scale is the wavelength

This exemple has power at large scalesAnd small power at small scales

39

Why study P(k)?: test of all hypotheses including inflation CDM…

• Shape depends on– m total matter content

– b baryon content

– DE dark energy content

Probed by galaxy surveys: 2dFGRS, SDSSThe link with CMB which gives the same on large scales ! (in lecture 3)

Why this shape ???

Level of amplitudeOf the fluctuations

Can be define for each scale at a given time

Or can be define at a time which depend of the scale (for example when the scale enter the horizon)(often use later)

Power spectrum of SDSS

LuminosityIs decreasing

Small scalesLarge scales

The modelling

• start with primordial fluctuations adiabatic (fixe the initial condition in density (b,k = CDM,k = ¾ ,k = ¾ ,k)

• Physics affect fluctuations which are inside the horizon

• primordial fluctuations can only be observed with the CMB for size > hubble radius ( > 1°)

• Primordial fluctuations are otherwise modified by a transfer function

Transfer function

P(k,t) = P0(k) D2(t) T2(k)

Transfert function

Initial spectrum

nkkP all the fluctuations are entering horizon with the same amplituden=1(No privileged scales)

Growth factor

The growth depend of the time (expansion )

Calculated from

hydodynamic in RG

Will depend of the kind of component (DM, baryons, etc…)

The linear growth of fluctuation(basis)

• Hydrodynamic equation in an expanding universe (eq of continuity, Euler and Poisson)

Consider small fluctuations around the homogeneous solution in a pertubated metric

= > Express in term of contrast of density …linear << 1

expansion Gravitational instability

45

Solutions

Matter domination: (t) t2/3 a(t) 1/(1+z) croissance ~ a

Radiation domination: (t) t a2(t) croissance ~ a2 (true outside horizon)

Inside the horizon, need to add the radiation pressure =>

Jeans scale … fluctuation can grow or can oscillate ( will be explain in more details in lecture 3)

46

What mean scale inside horizon?

Power is the amplitude

Scale is the wavelength

This exemple has power at large scalesAnd small power at small scalesOnly small scales are inside horizon

rH

Evolution of a density perturbationBefore horizon… P(k) = k correspond to fluctuations growing as a2 after horizon, grows as a if there is matter domination …

Small scales can enter horizon before matter domination, then are frozen until zeq we see them with a default of amplitude of =a2 compare to large scales

2 = a4

=>P(k) = k / a4

= k-3

After zeq

Turn over dependof Zeq

=> Depend of m

48

Key summary of the shape

Slope at small k~/ k Slope at large k

~/ k-3

Dependence of turnoverposition on m

Baryon supression and wiggles

49

Dark matter and the model of structure formation

Dark matter is needed to start early enough gravitational clustering to form structure.

SOME DARK MATTER SHOULD BE NON BARYONIC

If DM is non-baryonic then this helps to explain the paradox of small temperature fluctuations of cosmic microwave background radiation

Non baryonic =>No pressureNot interacting Only sensitive to gravitation

50

Why we need DM?

R or t

Radiation dominated

CDM dominated

Post-recombination

Dark m

atter

Baryons

Plasma -baryon Interaction oscillation

radiation-DM equalityCold DM no pressuregravitationnels

Recombinaison baryons fall in DM Structures can start

Zeq ~ mh2Zdec 1100

51

Numerical Structure Formation Simulations

• Model matter in universe as collection of particles that interact gravitationally (and perhaps hydrodynamically)

• 100 million particles is current maximum– one chooses particle mass by choosing a simulation volume

– for cosmological simulations the typical particle mass is around the mass of a galaxy or somewhat less (~1012 solar masses)

• Simulation process– distribute particles in early universe

– account for underlying expansion and turn gravity loose!

• Compare properties of simulated universe with those of the observed universe!

Movies from structure formation simulations available at http://www.astro.princeton.edu/~gbryan/

Formation of Structure: Numerical Simulations

Dark Matter particles come together to make galaxies, clusters, and larger scale structures

Dark matter : the candidates

ModifiedGravity

Low MassStars

Black Holes

Light Particles (eg axions) 10-5 - 10-2 eV

Tau NeutrinoMass 10 - 30 eV

Weakly interactingmassive particles 10-1000GeV

Examinewith dark energy

59

There are two types of matter:• baryonic can be luminous galaxies and clusters

but also can have massive none luminous objects inside galaxies…

• non-baryonic in dark halos

60

b ~ 0.023 h-2 ~ 0.01 - 0.09

•Visible matter is only * ~ 0.003 (M/L/5) h-1

(+0.006 h-1.5 for gaz inside the cluster)

=> 90% of baryons are dark…

61

Search for baryonic dark matter

• Compact objects : search for brown dwarfs and black holes using gravitational effects

A single image is amplified

Collaborations MACHOS, EROS: (Alcock et al 2001, Lasserre et al 2000)After 6 years ~ 10 millions stars of LMC13-17 candidats (>> 2-4 expected from visible stars in 34-230 days)

<20% of DM (< 50kpc) can be MACHOS to the best….

62

Non baryonic

• Hot dark matter• Relativistic• As neutrinos

• Cold dark matter– Non interacting– No pressure– massive

They give different predictions on the structure formation

weakly interactive particles ( WIMPS )were suggested (Peebles 1982, Bond, Szalay, Turner 1982, Sciama 1982).

LSP (neutralinos, axinos)AxionsSupermassives relics….

Cold or hot???

63

Degenerate with m

Why not neutrinos ?

• Pseudo scalar (proposed to solve the strong CP problem)• Pseudo Nambu Golston boson• Very weakly interacting with matter: interactions are

1012 weaker than ordinary weak interaction• Extremely light particles, with masses in the range of

10-3 eV/c2 to 10-6 eV/c2

• Axions may be detected when they convert to low energy photons after passing through a strong magnetic field

Axions

WIMPS

• Weakly Interacting Massive Particles (WIMPs)

• Non relativistic

• WIMPS arise in some Supersymmetric (SUSY) theories of particle physics and are the lightest neutral SUSY particle (LSP)

•WIMPs would have been easily detected in accelerators if M < 15 GeV/c2

Neutralino: the elegant candidate

• The lightest WIMP would be stable, and could still exist in the Universe, contributing most if not all of the Dark Matter

• Cross-sections for various interactions can be calculated if the WIMP is assumed to be a neutralino (from mSUGRA for instance).

• Very small

68

10 WIMPlog GeVM

log 10

(/p

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arns

)

Les particules candidatesLes particules candidates

SUSYM

GUTSM

PLANCKM

PQf

IH

coldthermalrelics w

imp

zilla

gravitino

axionQCD

WEAK" "

69

Direct searchs for Wimps…

Nuclear recoil elastic scattering (germanium detectors, scintillating crystals)

70

Some results

Need to increase sensitivity with a factor 100

71

Prospectives

72

• Increase the sky coverage of cluster surveys

new tools promising•Weak lensing•Baryon oscillation

Go to space…

73

The latest: 2dF and SDSS

• 2dFGRS:– 250,000 galaxies with redshifts– galaxies selected from APM– Median redshift 0.17– Final data released in summer 2004

• SDSS GRS– aims at 1,000,000 redshifts– DR3 was 11 days ago– >5000 square degrees– 141,000,000 objects– 374,000 galaxy spectra

74

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75

Ongoing galaxy redshift surveys

• Completion of SDSS

• 6dF

• DEEP 2 (like 2dFGRS at z~1)

• VIRMOS VLT Deep Survey – (VVDS)

• UKIDSS

76

Scientific Promise of Weak Lensing

• Mapping of the distribution of Dark Matter on various scales

• Measurement of the evolution of structures

• Measurement of cosmological parameters, breaking degeneracies present in other methods (SNe, CMB)

• Explore models beyond the standard osmological model (CDM)

From the statistics of the shear field, weak lensing provides:

Jain, Seljak & White 1997, 1x1 deg, SCDM

77

PSF anisotropy

Very soon dominate by systematic effects => space is required

78

Weak Lensing Power Spectrum

CDM

CDM(linear)

OCDM

SNAP WF survey [300 deg2; 80 g arcmin-2; HST image quality]

Future surveys:CFHT, Keck, WHT, Subaru, ACS/HST

Future Instruments:Megacam, VST, VISTA, LSST, WHFRI, SNAP, GEST

Measure cosmological parameters (8, m, , , w, etc) very sensitive tonon-linear evolution ofstructures

79

Cosmological Implications

13.097.03.0

68.0

8

m

07.000.13.0

60.0

8

m

Shear Variance: (CDM)8.07.02.1

8 mm z

WHT+ Keck measurement:

Clusters: Pierpaoli et al. 2001

Clusters: Seljak 2001

06.075.03.0

44.0

8

m

Bacon et al. 2002

80

Future SurveysSurvey Diameter

(m) FOV (deg2)

Area (deg2)

start

DLS 24 20.3 28 1999

CFHTLS 3.6 1 172 2003

VST 2.6 1 x100 2004

VISTA 4 2 10000 2007

Pan-STARRS 41.8 44 31000 2008

LSST 8.4 7 30000 2012

SNAP 2 (space) 0.7 300 2014

81

The long term future

• CMB (next lecture)

• plus cosmic shear and velocities

• will tell us all about dark matter and early universe

• Galaxy surveys will tell us about galaxy formation.

• …

82

• Sunyaev-Zel’dovich Effect surveys : deg2 #amas SZA (Carlstrom et al.) Olimpo 2004 AMI, Ameba ~12 ~200 APEX, ACT (Page) ~200 ~2,000 SPT (Carlstrom et al.) ~4,000 ~20,000 Planck ~20,000 ~10,000 2007

• X-ray surveys:

REFLEX (Boehringer) ~4 ~1,000 XMM ~103 ~2,000 running DUET (Petre et al.) ~104 ~20,000

Futur large Surveys

83

Baryon Oscillations in the Matter Power Spectrum

Standard ruler:

ratio of wiggle scale to sound horizon H(z)

Just like CMB – simple, linear physics

Eisenstein astro-ph/0301623

kobs / kA ~ H(z) s H(z) / (mh2)1/2

84

annexe

85

From X measurement to mass

• X Flux : fX = L/4dL2 ( dL = (1+z)2 d )

• fx T3

• SZ viriel theorem => relation betweel M-T (m , z, )

2A

virvir2

CMB

2d

TMTkndl

cm

σ

T

ΔTΔS eBe

e

T

R

dA

dA R

(Still works for elliptical clustersas long as there is a large sample)

86

Ω m From Local dynamics:

e.g: Virgocentric infall as pedagogical example • Density fluctuations in the

Universe produce velocity perturbations of galaxies which are located near them.

• The linear approximation to this perturbation, which works in the limit of small / is the following:

• The unperturbed velocity in this case is given by v = Hr where r is the distance from the source which is causing the perturbation.

• We can apply this equation to the case of Virgo Infall as schematically shown below:

CMB DIPOLE

87

The Virgo cluster is a nearby cluster or region of mass overdensity. The diagram above shows three components:

* Our infall to Virgo * The CMB Dipole Anisotropy --> note that its direction is not pointed at Virgo and the amplitude is larger than our Infall into Virgo. Therefore, the Virgo cluster alone is not causing this motion.

* Possible motion of the entire Local Supercluster towards the next nearest supercluster, Hydra-Centaurus ( GREAT ATTRACTOR CONTROVERSY) For now ,let's just consider our infall into Virgo.

* The distance to Virgo is 15 Mpc. If we use H = 100, then the predicted expansion velocity is 1500 km/s.

* The observed velocity of Virgo, however, is 1200 km/s

* The difference represents our infall of 300 km/s to Virgo

* v/v = 300/1500 = 0.2

* We can now determine Ω (Ωm !!!!) if we can measure / that is interior to us

in the direction of Virgo.

88

But we can only measure / in light ( in fact N/N) when it is really / in mass that is causing our velocity perturbation.

Hence bias or the b parameter (or more generally a function ) becomes important.

The measured / in light is 1.9. If we assume there is no bias then we have with :

=> 0.2 = (1/3)(1.9) Ω 0.6

which yields Ω (Ωm !!!!) = 0.15 !!!!!!! Very far from Ωtot =1 !!!!

SO : Suppose there is a bias such that we really area measuring

0.2 = (1/3)(1.9) (Ω 0.6 / b)

and hence we only have (Ω 0.6 / b) = 0.15

For Ωtot = 1 this would require b = 6.6 - which is a huge bias !!!

Recent data, however, strongly suggests that b is not larger than 1.5 which is

Ωm = 0.23

89

Hot Gas and Galaxies

• Measure the mass of light

emitting matter in galaxies in the cluster (stars)

Measure mass of hot gas - it is 3-5 times greater than the mass in stars

Calculate the mass the cluster needs to hold in the hot gas - it is 5 - 10 times more than the mass of the gas plus the mass of the stars!

90

Distribution of early (top) and late (bottom) type galaxies in SDSS Northern equatorial strip.

Dark blue – galaxies in low-den environmentRed – galaxies in high-den environment

91

Biasing

• Relation of galaxies to mass ≡ “bias”

• Comparision of different galaxy types there must be some bias

• Theoretical models speculative

• Do galaxies tell us about cosmology…– or about galaxy formation??

92

AND about Bias

≡ galaxy power spectrum is a constant multiple of the matter power spectrum

– Pg(k) = b2 P(k)

– 8g = b 8

• Assumed for 2dFGRS and SDSS cosmological parameter analyses

• Could more generally have b(k)= non-linear bias eg. b=b0 + b1 k

93

Local dark matter

• Local dark matter …Local density of matter near the Sun from velocity and matter density dispersions near the plane of the Galaxy using Poisson equation

Density of matter in the disk of the Galaxy is equal to the density of stars (no dark matter in Galactic disk).

94

Black Hole at Center of Galaxy

At the center of every galaxy is a very massive black hole, as massive as a million suns.

These massive black holes form from mergers and are NOT the dark matter.

95Averaged shape: 0e γe

The underlying assumption is that the position angles are random in the absence of lensing. At some level intrinsic alignments will complicate things (can be dealt with using photometric redshifts).

no lensing lensing

Introduction: what is weak lensing?Introduction: what is weak lensing?

96

Weak Gravitational Lensing

Distortion Matrix:

Direct measure of the distribution of mass in the universe, as opposed to the distribution of light, as in other methods (eg. Galaxy surveys)

jij

iij zgdz

2

)(

Theory

97

Cosmic shearCosmic shear

First detection Van Waerbeke et al.(2000); Wittman et al. (2000); Bacon et al. (2000); Kaiser et al. (2000)

Distortion of distant-galaxy images by the weak lensing effect

Background galaxydeformed deformed image!!image!! Large-scale structure

Powerful cosmological tool probing Dark matter distribution

Cosmological parameters

The important cosmological information can be obtained by quantifying the non-Gaussianity of weak lensing fields.

98

Principles of Weak Lensing

Distortion matrix:

Convergence:

Shear:

Critical surface density:

221

crit

212221121

1 ;)(

lsol

oscrit DD

D

G

c

4

2

22

21

1

1

j

iij

Weak lensing regime: << 1 (linear approximation) Measure shear and solve for the projected mass

99

Measuring the Shear

)()(2 xIxwxxxdQ jiij

Ellipticity:2211

122

2211

22111

2,

QQ

Q

QQ

QQ

12

A measurement of the ellipticity of a galaxy provides an unbiased but noisy measurement of the shear:

observed = intrinsic

Quadrupole moments:

100

Status

Mellier et al. 2002

Mass-to-light ratio:<M/L> 400 h Mo/Lo

corresponding to:m 0.3in agreement withother methods

Use for shearmeasurements

101

Cosmic Shear Measurements

2()=<2

>Bacon, Refregier & Ellis 2000Bacon, Massey, Refregier, Ellis 2001Kaiser et al. 2000Maoli et al. 2000Rhodes, Refregier & Groth 2001Refregier, Rhodes & Groth 2002van Waerbeke et al. 2000van Waerbeke et al. 2001Wittman et al. 2000Hammerle et al. 2001*

Hoekstra et al. 2002 *

Brown et al. 2002 *

Hamana et al. 2002 * * not shown

Shear variance in circularcells:

102

Primordial fluctuations

Adiabatic Fluctations

Changes number density of photons and matter particles equally but their mass densities change differently

( predicted by inflation)

103

Size of fluctuation

nk kkP 2

all the fluctuation are entering horizon with the same amplitude

Fluctuation are growing with timeThe growth depend of the time(expansion ) and size (scale)

No privileged scales

=>Spectrum is scale invariant (Harrison-Zeldovich) n=1(mean no dependant of scale and time)

104

Some remarks on a pertubated metric

• General form– Scalar perturbation 2 scalar fcts s– Vectorial perturbations 1 vector wi

– tensorial 1 tensor hij with 3 indices

• Minimal perturbation of the metric g g = a2 2 -i B -i B 2[ij - i j E] With 4 scalars , , B et E

• For a fluid,with T diagonal, we can choose a jauge with B = E = 0 et = (Newtonian)

105

Correlation function and normalisation

8 ~ amplitude of P(k) at k ~ 2 /8 Mpc-1 corresponding at = 1

Vacuum => fluctuation

Often used to fix amplitude of primordial fluctuations, A in P(k) = A kn

106

Growth of DM and horizon

a

dtrH

1kEnter the horizon at

Horizon of a particle

For scales greater than horizon:

growth ~ a2

For scales smaller than horizon: it depends if the matter dominates ( STAGNATION/MESZAROS EFFECT) then: growth ~ a(more the scale is small, more has beenaffected by this in the past)

107

Theoritical

Zeq

108

Power spectrum

P(k)

k

Horizon à zeq

Dissipation

TURN OVER IN THE POWER SPECTRUM DEPENDING ON m VIA Zeq

kPtDkP init2

linéaire )(

Growth of the fluctuation

109

CFHT Legacy SurveyCFHT Legacy Survey

Megacam: FOV 1 square degree

110

The Canada-France-Hawaii Telescope Legacy Surveyis a five year project, with three major components:

Very wide/shallow survey: solar system• ~1500 square degrees• around ecliptic (strip)

Wide/deep survey: weak lensing• ~140 square degrees (3 fields)• 5 filters (u,g,r,i,z’)• i<24.5

Ultra deep: type Ia supernovae • 4 square degrees (4 fields)• repeated observations in 5 filters• expect ~1000 supernovae!

CFHT Legacy SurveyCFHT Legacy Survey

111

Further ahead: Pan-STARRSFurther ahead: Pan-STARRS

PANoramic Survey Telescope And Rapid Response System

4x1.8m telescopes 3 square deg FOV each Orhogonal Transfer CCDs

112

Further ahead: LSSTFurther ahead: LSST

8.4 meter diameter 7 square deg. FOV

Large Synoptic Survey Telescope