Lecture 1 - IIHEcdeclerc/astroparticles/2012-13/...• Lightyear = Ly = 0.946 x 1016 m • 1 year =...

The expanding universe

Lecture 1

The early universechapters 5 to 8chapters 5 to 8

Particle Astrophysics , D. Perkins, 2nd edition, Oxford

5. The expanding universe6 Nucleosynthesis and baryogenesis6. Nucleosynthesis and baryogenesis7. Dark matter and dark energy components8. Development of structure in early universe

Expanding universe : content• part 1 : ΛCDM model ingredients: Hubble flow,

cosmological principle, geometry of universe• part 2 : ΛCDM model ingredients: dynamics of expansion,

energy density components in universe• Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light

element abundances - ΛCDM parameter fits• Part 4: radiation density, CMB• Part 5: Particle physics in the early universe, neutrino

density• Part 6: matter-radiation decoupling• Part 7: Big Bang Nucleosynthesis• Part 8: Matter and antimatter

2011-12 Expanding Universe 3

The ΛCDM cosmological model• Concordance model of cosmology – in agreement with all

observations = Standard Model of Big Bang cosmology

• ingredients:Universe = homogeneous and isotropic on large scalesUniverse = homogeneous and isotropic on large scales

Universe is expanding with time dependent rate

Started from hot Big Bang, followed by short inflation period

Is essentially flat over large distances

Made up of baryons, cold dark matter and a constant darkade up o ba yo s, co d da atte a d a co sta t daenergy + small amount of photons and neutrinos

Is presently acceleratingIs presently accelerating


Expanding Universe 6© Rubakov

2012-13

Part 1Part 1ΛCDM ingredientsg

Hubble expansion – redshiftp

Cosmological principle

Geometry of the universe Robertson Walker metricGeometry of the universe – Robertson-Walker metric

Some distances• Earth-Sun = AU = 150 x 109 m = 150 x M km• Lightyear = Ly = 0.946 x 1016 m• 1 year = 31.5 106 s• parsec = pc = 3.3 Lyparsec pc 3.3 Ly• Mpc = 3.3 MLy• Radius Milky Way ª 15 kpc

ruler in cosmologyi O(M )• Radius Milky Way ª 15 kpc

• Sun to centre MW ª 8 kpcA d d l (M31) t th 800 k

is ~ O(Mpc)

• Andromeda galaxy (M31) to earth ª 800 kpc• Width Local Group of ª 30 galaxies ª 2 Mpc• Average inter-galactic distance ª Mpc• highest redshift observed : dwarf galaxy at z ª 11


Hubble law 1• Hubble(1929): spectral lines of distant galaxies are

redshifted fi galaxies move away from Earth• Receding velocity increases with distance : Amount of shift Dl depends on apparent brightness (~distance D) of galaxyDl depends on apparent brightness ( distance D) of galaxy

Original Hubble plot

m/s

) SuperNovaeIa and II

eloc

ity(k

mVe

Cepeids

2012-13 Expanding Universe 9Distance (Mpc)

Hubble law 2• Interpret redshift z as Doppler effect• For relativistic objectsFor relativistic objects

( )11 11

obs emobs em em

βλ λ βλ λ λ βλ β− += = ⎯⎯⎯→ +Δλz =

λ

• For close-by objects, in non-relativistic limit

( )1emλ β−λ

1 1obsem

vz zc

λ β βλ

+ = ≈ + → ≈ =

• Hubble law becomes linear relation between velocity and Distance

em

H DDistance 0z c v H D≈ =

• Confirms theories of Friedmann and Lemaître2012-13 Expanding Universe 10

Hubble law 3• H0 = Hubble constant today – present value (PDG 2012)

t today=( ) ( )0 0( ) 70.2 1.4 km/sec /MpcH H t= = ±

If H(t) i t ll ti t t d if

0t today=( ) ( )0 0( ) p0 100 / sec/ 0.702 0.014H km Mpc h h= → = ±i

• If H(t) is same at all times → constant and uniformexpansion

• Observations show that expansion was not constant and that Hubble ‘constant’ depends on time

• Expansion rate evolves as function of changing energy-matter density of universe (see Friedman equations)

( ) ( )( )( )

2

28

3NG c

R ttπ= −2H t ktotρ


( )( )3 R t

Sources of redshift• Motion of object with respect to observer – Doppler effect

(red and blue shifts): e.g. rotation of stars in galaxies – seegalaxy rotation curves (dark matter)

• Gravitational redshift : stretching of wavelength close toGravitational redshift : stretching of wavelength close to heavy object - local effect – negligible over long distances

• Cosmological redshift : stretching of wavelength due to• Cosmological redshift : stretching of wavelength due to expansion of universe – dominant at high redshifts

( )( )

( )( )

0 01 obst R t

zt R t

λλ

+ = = R(t)=Scale of universe at time t( ) ( )em t R tλ


Cosmological redshift - time • Redshift is the measured quantity – it is related to a given

time during the expansion

• Large z means small t , or early during the expansion

0t t t=0tz== ∞

0

0t tz==

todayBigBang

• Actual (proper) distance D from Earth to distant galaxy attime t

• D can only be measured for nearby objects( ) ( )D t r= ⋅R t

ca o y be easu ed o ea by objects

• r = co-moving coordinate distance – in reference frame co-moving with expansion - in which 2 objects are at restmoving with expansion - in which 2 objects are at rest


Cosmological principle - large scales• universe is isotropic and homogeneous at large scales• There is no preferred position or direction• Expansion is identical for all observers• Is true at scale of inter-galactic distances : O(Mpc)

•2dF quasar surveyq y•Two slices in declination and right Rig

ascention•Plot redshift vs right ascension

ght ascenascension•Each dot = galaxy

nsion


Cosmic Microwave Background photons

WMAP 5 years dataUniform temperature up to ΔT/T ~ 10-5Uniform temperature up to ΔT/T 10


Structures - small scales• Over short distances universe is clumpy• Galaxy clusters O(10 Mpc) diameter• galaxies, eg Milky Way : 15 kpc COMA cluster: 1000 galaxies

20Mpc diameterM74 IR

p100 Mpc(330 Mly) from EarthOptical + IR

M74- IR


Milky WayCOBE - radio

Olbers’ paradox• Olber (~1800): Why is the sky not bright at night?• Suppose that universe is unlimited & filled uniformly withSuppose that universe is unlimited & filled uniformly with

light sources (stars) - total flux expected is μ rmaxThe sky does not look dark because:The sky does not look dark because:

• Observable universe has finite age – for constant i li ht h f i O( t )expansion: light can reach us from maximum rmax = O(ct0 )

• Stars emit light during finite time Dt – flux reduced by factor Dt/t0

• Light is redshifted due to expansion - eg red light Æ IR –finally undetectable flows

• CMB fills universe – dark matter does not light upg p


Robertson-Walker metric 1assume universe = homogeneous and isotrope fluid

• Distance between 2 ‘events’ in 4-dimensional space-timeDistance between 2 events in 4 dimensional space time2 2 2 2 2 2ds c dt dx dy dz⎡ ⎤= − + +⎣ ⎦

Co-movingdistance dr

Universe is expanding

⎣ ⎦ distance dr

• scale factor R(t), identical at all locations, only dependenton time ( )22 2 2 2 2 2ds c dt dx dy dz⎡ ⎤= − + +⎣ ⎦R (t )

• proper distance D from Earth to distant galaxy at time t

( )ds c dt dx dy dz⎡ ⎤= − + +⎣ ⎦R (t )• proper distance D from Earth to distant galaxy at time t

( ) ( )D t r= ⋅R t• r = co-moving coordinate distance2012-13 Expanding Universe 18

Stretching of the universe scaleExample: closed universe

R(t1) R(t2)

© L B t ö


© L. Bergström

Robertson-Walker metric 2space is not necessarily flat

• Introduce k = spatial curvature of universeIntroduce k spatial curvature of universe• Distance between 2 events in 4-dim space-time

⎡ ⎤( ) ( )2

2 2 2 2 2 2 22 sin1

drds c dt r d dr

θ θ φ⎡ ⎤= − + +⎢ ⎥−⎣ ⎦k2R t

• k : curvature of space → geometry – obtained from

⎣ ⎦

k : curvature of space geometry obtained fromobservations – can be -1,0,1

• R(t) : dynamics of expansion → Friedman-Lemaître• R(t) : dynamics of expansion → Friedman-Lemaître equations – model dependent


Curvature k in FLRW model • k = +1, 0, -1 depends on space geometry• Curvature is independent of timeCurvature is independent of time• Curvature is related to global mass-energy density of

universe 2kcuniverse ( ) ( ) ( )2 2 1energy matterkct

H t R t−Ω − =

• It affects the evolution of density fluctuations in CMB radiation – path of photon is different

• Therefore it affects pattern of the CMB radiation today• For universe as a whole, over large distances, space-timeFor universe as a whole, over large distances, space time

seems to be flat: k=0 from CMB observations

( ) ( )t tρ ρ=2012-13 Expanding Universe 21

( ) ( )tot critt tρ ρ=

C i d tiGlobal energy tCosmic destinyGlobal energydensity

geometry

k0 big crunch

2012-13 22Expanding Universe

Excercise• D. Perkins, chapter 5• Oplossing meebrengen op het examenOplossing meebrengen op het examen


k from CMB observations

Curvature of universe

CMB photons

movie

z = 1100model

CMB photonst=380.000 y

k 0k>0

k

Hubble time – Hubble distance• Expansion parameter H(t) has dimension of (time)-1

• Hubble time = expansion time today for constant expansionHubble time expansion time today for constant expansion9

01 1 13.9 10( )

t t yearH t H

= ⇒ = = ×

• Horizon distance today in flat static universe (Hubble 0( )H t H

distance) ( )0 0 4.2HD t c t Gpc= =

• But! Look back time and distance in expanding universedepend on dynamics in H(t) (see part 2) depe d o dy a cs (t) (see pa t )

( ) ( )( )( )

22

28

3NG c

R ttπ= −H t ktotρ


( )( )R t

Matter dominated flat universe• Integration of Friedman equation with k=0 and only non-

relativistic matter

( )13 2

392

GMR t t⎛ ⎞= ⎜ ⎟⎝ ⎠

( )2⎜ ⎟⎝ ⎠

( )0 031 R t t 92 1 9 1 10t yr= = ×( )( )

0

0 0 2H R t= = 0

0

9.1 103

t yrH

= = ×

• Dating of earth crust and old stars shows that age of universe is of order 14 x 109 yru e se s o o de 0 y

• → Need other energy components (see part 2)


Part 2Part 2ΛCDM ingredientsg

Dynamics of the expansion – Friedman Lemaître y pequations

Energy density of universeEnergy density of universe

Dynamics of the expansion• Einstein field equations of general relativity

1 8R G Tℜ Λ82 N

R g G T g

g

μν μν μν μνπ− ℜ = −Λ

Λ⎛ ⎞ Cosmological8

8N N

gG T

Gμν

μνπ πΛ⎛ ⎞

= −⎜ ⎟⎝ ⎠

Cosmologicalconstant

Geometry of space-timeRobertson-Walker metric

Energy-momentumFunction of energy content of universegyIs model dependent11 3 -1 -26.67 10 m kg sNG

−= ×

• Friedmann & Lemaître (1922) : Solutions for uniform and homogeneous universe behaving as perfect frictionlessfluidfluid


Friedmann-Lemaître equation• Time dependent evolution of universe = Friedman-Lemaître

equation( ) ( ) ( )

22

2 8 NR t G cπ⎛ ⎞⎜ ⎟k( ) ( )( ) ( ) ( )( )

22

83

NR t G cR t R t

tπ⎛ ⎞

= −⎜ ⎟⎜ ⎟⎝ ⎠

H t ktotρ≡

curvature term=2

2kcR

( ) energy density of universe globally, 'at large'=ttoρ t

( ) expansion rate = Hubble 'constant' at time t=H t( )( ) ( )( )expansion rate = Hubble constant at time t

km= 70.2 1.4 /Mpc = Hubble constant todays

=

= ±0 0HH

H t

t

• energy density ρ is model dependent - ΛCDM model :

( ) ( ) ( ) ( )

( )s


( ) ( ) ( ) ( )baryon coldDM rad DarkEntot t t t tρ ρ ρ ρ ρ= + + +

Second Friedman equation• Consider universe = perfect fluid with energy density ρc2

• Conservation of energy in volume element dV ; P = pressure of fluid

dE PdV= − ( )2 23 RP c Rcρ ρ⎛ ⎞

= − + ⎜ ⎟⎝ ⎠

( ) ( )2 3 3d c R Pd Rρ ⋅ = −

• Differentiate 1st Friedman equation & substitute

Rc⎝ ⎠

43

NG RdRRdt

π⎛ ⎞⎛ ⎞= = − ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ 2

3Pρ +c

Equation of state

• ΛCDM model : Energy density consists of 3 components: matter, radiation (incl. relativistic particles), constant vacuum energy

3dt ⎝ ⎠⎝ ⎠ c

with 8matter vacuum vacradiation G

ρ ρ ρ ρ ρ ρπ ΛΛ= + + = =


8 NGπ

Equations of state 11. Matter component: ‘dust’ of non-relativistic particles

(v

Equation of state 2• Relation between pressure and energy - introduce w

P w=2 wcρ=

( ) R⎛ ⎞ R⎛ ⎞( )2 23 RP c Rcρ ρ⎛ ⎞

= − + ⎜ ⎟⎝ ⎠

( )2 23 1Rc w

Rcρ ρ ⎛ ⎞= − + ⎜ ⎟

⎝ ⎠

( ) ( ) ( )3 1 3 11w wconst R zρ − + += ∝ +

• For small t assume that ~R tβ ( ) ( )2

3 1 wR t t

+∼

1di ti1

2R130

radiation w

matter w

=

=

2

23

R t

R t

∼

∼


1&vacuum w constρ= − = HtR e∼

( ) ( )3 11 wρ ++( ) ( )1 zρ ∝ +

1 0 2±2012-13 Expanding Universe 33

© J. Frieman1 0.2DarkEnergyw = − ±

Critical density• flat universe (k=0) = equilibrium between open and close universe• Friedmann equation becomes

( ) ( )( )2 2

22

8 33 8

N

N

cR t G HH tR t G

πρπ

⎛ ⎞≡ = ⇒ =⎜ ⎟⎜ ⎟⎝ ⎠

cρ

• density ρc is called critical density

( ) 3 8 NR t Gπ⎝ ⎠

ρc• Value today is

( )2

27 300

3 9.6 108c

Ht kg mG

ρπ

− −= = ×

2 3 3

8

5.4 5 protons at rest per mN

c

G

c GeV m

πρ = ≈

• Observations →universe is geometrically flat, so present averagedensity of universe, away from galaxies, is a few protons per m3


closure parameter• Define closure parameter W

( ) ( )( )ctt

ρρ

=Ω t

• For general geometry with k≠0, Friedmann equation becomes

( )cρ

2 2 22

2

83

N

c c

G H H kcHR

π ρρ ρ

⎛ ⎞= ⇒ = −⎜ ⎟

⎝ ⎠

( )( ) ( ) ( ) ( )

2

2 21t kcρ= − ⇒

2

2 2kc1 = Ω t -

H t R t

3 c c Rρ ρ⎝ ⎠

• Define curvature term

( ) ( ) ( ) ( )2 2c t H Rρ 2 2H t R tObservations:

2

2 2K

c

kcH R

ρρ

= = −kΩ ( ) ( ) 1kt tΩ +Ω =flat universeand Ω=1 at

ll ti


cρ all times

pauze


Observed energy densities 1• Energy density is composed of: dust/matter (non-rel),

radiation (incl. rel particles), vacuum energy (L)

• Relative contributions unfluence dynamics of expansion( ) 1k kΩ+Ω = +Ω =m r ΛΩ + Ω + Ω

• Relative contributions unfluence dynamics of expansionPresent-day observations:

1. Radiation (from CMB energy density)

( )( )0 55 10radtρ

−Ω

2 Luminous baryonic matter : p n nuclei in stars gas dust

( )( )( )

50

0

5 10radradc

ttρ

−Ω = ≈ ×

2. Luminous baryonic matter : p,n,nuclei in stars, gas, dust

29 39 10 0.01lumlum lumkg mρ

ρρ

− −≈ × ⇒ Ω = ≈


cρ

Observed energy densities 23. total baryon density – from fit of the model of primordial

nucleosynthesis to measurements of light elementabundances (chapter 6)

30.26 baryons bn m−≈

4 T t l tt d it f l ti t ti

28 3

y

4.0 10 0.042 0.004b

b bkg mρ− −= × ⇒ Ω = ±

4. Total matter density - from galactic rotation curves, gravitational lensing, etc (chapter 7) - is clumpy

in ΛCDM model this is composed of baryons and (mostlycold) dark matter

5. Neutrino density – relics of early universe

27 32.2 10 0.24 0.03m m B DMkg mρ− −= × ⇒ Ω = Ω +Ω = ±

0 004 0 02Ω

Observed energy densities 35. total density: fit of ΛCDM cosmological model to large set

of observation data (CMB, SN, …) – PDG 2010

6 By subtraction we obtain the vacuum energy density

1 1.006 0.006ktotalΩ = −Ω = ± 0k ≈6. By subtraction we obtain the vacuum energy density

non clumpy – homogeneous effect – PDG 2010

Conclusions:0.726 0.015ΛΩ = ±

– 95% of energy content of universe is of unknown type– Today most of it is dark vacuum energyy gy– See further in chapter 7


Evolution of energy components 1• Cosmological redshift is related to the expansion rate

( ) ( )01 0R t ( ) ( )3 1 w+

1 R di ti h t d l ti i ti ti l

( )( ) ( )

001 0z z tR t

+ = = ( ) ( )3 11 wzρ +∝ +

1. Radiation = photons and relativistic particles

( )2 23 3 41 1 1E hc cνρ ρλ= ⇒∼ ∼ ∼( )( ) ( ) ( ) ( ) ( )

3 3 4

2 44 40 21 1

radV R R Rc t R t

z c z

ρ ρλ

ρρ= = + ⇒ +∼

2 Non relati isti matter

( ) ( ) ( ) ( ) ( )2 40 1 1radz c zc t R t ρρ = = + ⇒ +∼

2. Non-relativistic matter

( ) ( )32 23 3 31 1 1E mc c zρ ρ= ⇒ +∼ ∼ ∼ ∼2012-13 Expanding Universe 40

( ) ( )3 3 3 1mc c zV R R Rρ ρ⇒ +

Evolution of energy components 23. Vacuum energy is constant in our model

4. Curvature term( )2c cstρ Λ =

4. Curvature term

( ) ( )2

22 2 1 1kcc c zρ ρ−= ⇒ +∼ ∼( ) ( )2 2 2 1kc c zH R Rρ ρ⇒ +

• Dynamics of expansion can be rewritten

( ) ( ) ( ) ( ) ( )2 8 Gπ ⎡ ⎤( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

2

20

83 m r k

k

GH t t t t t

H t t t t

π ρ ρ ρ ρΛ

Λ

⎡ ⎤= + + +⎣ ⎦

⎡ ⎤= Ω +Ω +Ω +Ω⎣ ⎦( ) ( ) ( ) ( )( )( ) ( )( ) ( ) ( )( )0 0

0

30

4 220 01 1 1

m r k

m r kt

H t t t t

H z t z zt t

Λ

Λ

⎡ ⎤Ω +Ω +Ω +Ω⎣ ⎦⎡ ⎤= + + + + Ω+ +Ω Ω⎣Ω ⎦


⎣ ⎦

Summary

( )42 1radiation c zρ +∼ ( )( )32

2

1matter c z

t

ρ

ρ

+∼

( )

2

22 1

vacuum c cst

curvature c z

ρ

ρ +

∼

∼


Lookback time

dz( )( )0

11 1 zdR dRHR dt R t

tH H

d dRR+

= ⇒ = =

( )1dzdtz H

= −⎡ ⎤+⎣ ⎦

( )0R dt R tH HR

( ) ( ) ( )0 0 21d

R tR t R tR zd−= ⇒ =( ) ( )

( )0 21 1z z+ +

• Time elapsed between emission of a photon at expansion time tE by object at redshift zE and todayE E

0

0

0t

Edzt t dt− = = −

⎡ ⎤∫ ∫ ( ) ( )0 1EE

Et z

t t dtz H z⎡ ⎤+⎣ ⎦

∫ ∫


age of the universe• Age of universe from integration

From Big Bang time ( t=0 and z=∞) to present time ( t=t0) 0and z=0)

00

0t

dzt dt− = = −∫ ∫• Example: flat universe (Wk=0) with Wm=0.24, WΛ=0.76

( ) ( )0 00

1t dt

z H t∞= =

⎡ ⎤+⎣ ⎦∫ ∫

Example: flat universe (Wk 0) with Wm 0.24, WΛ 0.76

( )13 95 0 4 G±( )0 13.95 0.4t Gyr= ±

• Uitwerking meebrengen op examen2012-13 Expanding Universe 44

Age of the universe

( ) 1m r kΛΩ +Ω +Ω +Ω =

0=rΩ00.24

==

k

m

ΩΩ

H t 1 0.76Λ = − =mΩ Ω0 0H t

( )0 0

0

1.02613.95 0.4

H tt Gyr

== ±( )0 y

Only matter


Only matter

mΩ

Horizon 1 • Extent of region accessible via light signals to comoving

observer at given time t

• In static flat universe• In an expanding FLRW universe for a photon following a

( )0 0 4.2static flatHD t ct Gpc− = =• In an expanding FLRW universe, for a photon following a

line with fixed θ and φ( )

22 2 2 ⎡ ⎤dr2 0ds = ( )2 2 2 21c R t kr

⎡ ⎤⎢ ⎥−⎣ ⎦

drdt =

• Proper distance travelled by photon emitted at time tE and comoving position rE ( ) ( )0 0ED t r R t= ⋅E

• Observed at time t0 and position r=0

( ) ( )0 0ED t r R t


Horizon 2• Particle horizon for observer at time t0 : tE →0

td dt⎡ ⎤( ) ( ) ( ) ( )0 0 020 00

1H

Er t cD dr dt R t R tR tkr

t⎡ ⎤= =⎢ ⎥−⎣ ⎦

∫ ∫i

• Expanding, flat, radiation dominated universe1

( )( )0 0

12R t t

R t t⎛ ⎞

= ⎜ ⎟⎝ ⎠

( )0 02HD t ct=

• Expanding, flat, matter dominated universe( )0 0R t t⎝ ⎠

( )( )0 0

23R t t

R t t⎛ ⎞

= ⎜ ⎟⎝ ⎠

( )0 03HD t ct=


( )0 0R t t⎝ ⎠

Horizon 3• For a more complex cosmological model

( )( ) ( )0 200 1

r cI zdr cdzR tH Hkr

= − =−∫ ∫

( )( )( ) ( )( ) ( ) ( )( )3 4 20

121 1 1

z dzI zt t t t

=⎡ ⎤Ω + +Ω + +Ω +Ω +∫

• For Wk=0, Wm=0.24, WΛ=0.76 and integration to z=∞

( )( ) ( )( ) ( ) ( )( )0 0 0 0 01 1 1m r Kt z t z t t zΛ⎡ ⎤Ω + +Ω + +Ω +Ω +⎣ ⎦For Wk 0, Wm 0.24, WΛ 0.76 and integration to z

03.3 3.3 14BBexpansionH

cD ct GpcH

=∼ ∼0H


Deceleration parameter 1• Taylor expansion of expansion parameter around t0

(present time)

( ) ( ) ( )( ) ( )( )20 0 0 0 012

R t R t R t t t R t t t⎛ ⎞= + − + − +⎜ ⎟⎝ ⎠

( )( ) ( )( )

( ) ( )( ) ( )( )

220 0 0 0

2

11R t

H t t t H t t t

⎝ ⎠⎡ ⎤⎛ ⎞= + − − +⎢ ⎥⎜ ⎟

⎝ ⎠−− 0 02

R t R t( ) ( )( ) ( ) ( )( )

( ) ( ) ( )

0 0 0 00

22

2

11

R t

R tH t t H t t

⎢ ⎥⎜ ⎟⎝ ⎠ ⎢ ⎥⎣ ⎦

⎛ ⎞+ +⎜ ⎟

20R t

q( )( ) ( ) ( )2

0 0 0 00

12

H t t H t tR t

= + − − +⎜ ⎟⎝ ⎠

− 0q

• Deceleration parameter q(t): acceleration or decelerationof expansion at time tof expansion at time t


Deceleration parameter 2• Deceleration parameter q(t) is related to energy density at

time t – for flat universe (k=0)

( )2

2

RR R Rq tR R R

⎛ ⎞⎛ ⎞= − = −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ ( ) 0 0q t R deceleration> ⇒ < ⇒

( ) ( )22 24 133

R R R

Gq t c Pc Hπ ρ

⎝ ⎠⎝ ⎠⎡ ⎤ ⎛ ⎞= − − + ⎜ ⎟⎢ ⎥⎣ ⎦ ⎝ ⎠

( ) 0 0q t R acceleration< ⇒ > ⇒

• Energy-pressure relation: equations of state for

( )3c H⎢ ⎥⎣ ⎦ ⎝ ⎠

– Dust/matter

– Radiation/relativistic particlesp

– Vacuum energy( ) ( ) ( ) ( )

2m

rt

q t t tΛΩ

= +Ω −Ω


2

Acceleration or deceleration?

( ) ( ) ( ) ( )2

mr

tq t t tΛ

Ω= +Ω −Ω

• A universe dominated by matter decelerates due to gravitational collapse :gravitational collapse : ( ) ( ) 0 0mq t t RΩ > ⇒

• Observations show that today( ) ( )

( ) ( )0 00 0r m q t R tΛ

Ω Ω ⎫⇒ < ⇒ >⎬Ω > Ω ⎭


mΛΩ > Ω ⎭

Deceleration in past & acceleration nowPhysics Nobel prize 2011


Part 3Observation dataObservation data

Redshift measurementsRedshift measurementsLuminosity distance

S N ISuperNovae IaCosmic Microwave Background

Large galaxy surveysLight element abundances

Measuring redshift• Atoms emit light at certain

wavelengths – is measuredin laboratory (atom at rest)

• Atoms in quasars emitRestframe wavelength (Å)2000 4000 6000

Atoms in quasars emitsame spectrum but light isredshifted when reaching

Restframe wavelength (Å)

CIV redshifted when reachingEarth

• Comparison of observed• Comparison of observedspectrum with labspectrum gives redshift zspectrum gives redshift z


examples

( )( )

01 obst

zt

λλ

+ = ( )em tλ


Magnitude and distance• Luminosity distance DL to star with intrinsic luminosity L • F = power measured at Earth LF =

• Absolute magnitude M = magnitude at 10pc distance

24 LF

Dπ

• Effective magnitude m of star with absolute magnitude M2.5logM L cst= − +

( ) 10

g

5log 251Mpc

z M⎛ ⎞

− = +⎜ ⎟⎝ ⎠

LDm

• Large negative magnitude = bright star: e.g. m(Sun)=-26 ; m(Sirius,

1Mpc⎝ ⎠

g g g g g ( ) ; ( ,brightest star) = -1.7

• Far away object is dimmer and has larger (=smaller negative) m


SN Ia as standard candlesS I b i ht li ht f di t t SN b• Supernovae Ia are very bright – light from very distant SN can beobserved – up to z=1.7

• Are hydrogen poor• Are hydrogen poor• All have roughly the same luminosity curve

M101 at 20 MlySN2011feSN2011fe Flashed on 18 december 2011


SN Ia as standard candles1995 (H Phili ) l ti b t k l i it d d li• 1995 (Hamuy, Philips): relation between peak luminosity and declinerate

em

agni

tude

solu

tem

Abs

Δm15


SN Ia – Nobel Prize 2011• S. Perlmutter - Supernova Cosmology Project (SCP)

http://supernova.lbl.gov/

• A. Riess & B. Schmidt – High-z Supernova Search Team (HZSNS) http://www.cfa.harvard.edu/supernova//HighZ.html

• High statistics SN monitoring– Distance: observed magnitude

18 December 1998

g

+ absolute magnitude from lightcurve

– Redshift from spectrak h hk h h f hf h

Redshift from spectra

• 1998: discover acceleratedosmi e pansion

BreakthroughBreakthrough of the of the yearyear

cosmic expansion


Deceleration in past & acceleration nowPerlmutter, 2003

0% matter

00%100% matter

t di hth id

Lage dichtheidVersnelde expansie

e D

(z)

grote dichtheidVertraagde expansie

ista

ncd

Redshift z pastnow

2012-13 Expanding Universe 60( ) ( )01 0.5R z R t= = ×

CMB in Big Bang modell h i di i ( l i i i i l ) d i• early hot universe : radiation (relativistic particles) dominates over

matter (dust, non-relativistic particles) & vacuum energy is negligible

• When cooled down below kT few MeV :• When cooled down below kT ª few MeV : – Free p, n, e, g (+neutrino’s)

Pl f H+ d H ++ l i– Plasma of H+ and He++ nuclei– Matter-radiation thermal equilibrium

Wh E V (i i ti t ti l ) bi ti t t

e p H γ− + ↔ +

• When E < eV (ionisation potentials) : recombination to atoms

e p H γ− + → +

( ) dec1 1100 and 380.000 and T 3000decdecz t y K+ ≈ ≈ ≈

• Matter-radiation decoupling• Expect to see γ’s today as uniform Cosmic Microwave Background• Observed 3K background photon radiation with black body spectrum2012-13 Expanding Universe 61

A i t i iStructure Anisotropies in atom distribution

are ‘frozen’ in CMB

Structure formation in

early universe? are frozen in CMBy

hCMB photonsare released

© Univ Oregon


What can we learn from CMB• Density (pressure) anisotropies in photon-baryon fluid at time of

decoupling should leave imprint in distribution of g’s today• observe temperature anisotropies O(10-5)

• Growth of anisotropies depends on dark matter & dark energy duringexpansion

• Angular distance between 2 photondirections depends on curvature

of space

• CMB observations probe universeat z ~1100


Large Scale Structures• Redshift measurements of large samples of galaxies • Sloan Digital Sky Survey (SDSS 2000-2014): million ofSloan Digital Sky Survey (SDSS 2000 2014): million of

galaxies being recorded

• On average uniform population• On average uniform population• Galaxies = baryonic matter• Density (pressure) anisotropies in photon-baryon fluid at

time of decoupling are expected to leave imprint in distribution of baryons today

• Baryon Acoustic Oscillations (BAO) observations probe universe at small z – are sensitive to dark matter


2dF quasar redshift survey 2003

SDSS survey of local skyLow z – recent universe


Baryon Acoustic Oscillations

Abundances of light elements• Model of Big Bang Nucleosynthesis predicts abundances of

light nuclei: H, D, He, Li , ..

• They were formed at t ~3min when kT ~ 3MeV• Abundances are measured today – probe expansion model• Abundances are measured today – probe expansion model

before decoupling

All t b d it 0 042 0 004Ω ±• Allow to measure baryon density 0.042 0.004bΩ = ±


Fit ΛCDM model to observationsPdg.lbl.gov

ΛΩSN Ia distance-redshift surveys

ΛΩ

CMB anisitropiespsurvey by WMAP

Anisotropies in l

2012-13 Expanding Universe 67mΩ

galaxy surveys

Fit ΛCDM model to observationsPdg.lbl.govg g


Expanding universe : content• part 1 : ΛCDM model ingredients: Hubble flow,

cosmological principle, geometry of universe• part 2 : ΛCDM model ingredients: dynamics of expansion,

energy density components in universe• Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light

element abundances - ΛCDM parameter fits• Part 4: radiation density, CMB• Part 5: Particle physics in the early universe, neutrino

density• Part 6: matter-radiation decoupling• Part 7: Big Bang Nucleosynthesis• Part 8: Matter and antimatter


Lecture 1 - IIHEcdeclerc/astroparticles/2012-13/...• Lightyear = Ly = 0.946 x 1016 m • 1 year =...

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Transcript of Lecture 1 - IIHEcdeclerc/astroparticles/2012-13/...• Lightyear = Ly = 0.946 x 1016 m • 1 year =...