Academic Training LecturesRocky Kolb

Fermilab, University of Chicago, & CERN

Cosmology and theCosmology and theorigin of structureorigin of structure

Rocky I: The universe observed

Rocky II: The growth of cosmological structure

Rocky III: Inflation and the origin of perturbations

Rocky IV: Dark matter and dark energy

Rocky Rocky II: The universe observed: The universe observedRocky Rocky II: The universe observed: The universe observed• Cosmological parameters:

• Power spectrum of large-scale structure:

• Anisotropy of CMB:

0

0

0

0

0

Hubble's constant

deceleration parameter

the cosmic food chain

, , , , , , .....

age of the universe

temperature of the u

i

M B

H

q

t

T

niverse

( )P k

lC

Theoretical developments (1917-1927)Theoretical developments (1917-1927)• Cosmological principle

• Robertson-Walker metric

• Expansion natural

22 2 2 2 2 2 2 2

2( ) sin

1

0, 1 (flat, positive, negative spatial curvature)

drds dt a t r d r d

kr

k

Observational developments (1912-1929)Observational developments (1912-1929)

“… physically, he is a splendid specimen…”“… magnificent physique ….”“… manly …”“… loveable character …”

University of Chicago 1909 National Champions

Observational developments (1912-1929)Observational developments (1912-1929)

• Cosmological principle (extragalactic astronomy)

• Universe expands

0

-1 -10

recessional velocity

Hubble's constant = 100 km s Mpc

Luminosity distance

R L

R

L

v H d

v c c

H h

d

z

Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929s -1 -1

0 500 km s MpcH

constant sHubble'

v

0

0

H

dH

0.72 .03 .07 Freedman et al. (Hubble Key Project)

0.57 .02 Sandage, Tammann, et al.

h

h

Riess et al astro-ph/9410054

Hubble’sdata

Distance-luminosity relationDistance-luminosity relationDistance-luminosity relationDistance-luminosity relation

2

2

2

2(

defines luminosity distance - "know" , measure

Conservation of energy: flux redshifted:

redshift of energy redshift of time interval:

area of

1 )

(1 )

2L

0 1

LF = L F

4 d

=z

z

a t a t

LF = A

A

0

22 2 2 2 2 2 2

0

0

2

2 2 20

centered on sour

(

ce at time of detection,

( ) 4 ( )1

) (1 4 (

)) (1 ) L

S t

drds dt a t r d A a t r

kr

LF =

ad a t r z

t r z

light from comoving coordinate reaches

us now redshifted by an amo ( )unt 1

r

z

Field equationsField equationsField equationsField equations

2

2

2

8 expansion rate

3

4 13 deceleration parameter

3

a k G aH

a a a

a G ap q

a a H

......M R w

3(1 )whatever: 1

w

w w wp w w p z

0vacuum: 1 1p w z

4radiation: 3 1 3 1R R Rp w z

3matter: 0 0 1 M Mp w z

Distance-luminosity relationDistance-luminosity relationDistance-luminosity relationDistance-luminosity relation

0( ) (1 )Ld a t r z 2

2 2 2 2 22

( )1

drds dt a t r d

kr

22 ( ) ( )1

dr dt da

a t H a akr

2 2 2 3 3(1 )0 0(1 )(1 ) (1 ) (1 ) ...w

M wH H z z z

light travels on geodesics2 0ds

20

0 0

3 8

... (1 )

i i

M R w

H G

k

1 1

0 0

2 2 3 3(1 )0 00

( )

1 (1 )(1 ) (1 ) (1 ) ...

r z

wM w

a t H dzdr

kr z z z

Distance-luminosity relationDistance-luminosity relationDistance-luminosity relationDistance-luminosity relation

0( ) (1 )Ld a t r z 1 1

0 0

2 2 3 3(1 )0 00

( )

1 (1 )(1 ) (1 ) (1 ) ...

r z

wM w

a t H dzdr

kr z z z

Program:• measure via

• input and calculate

( )Ld z 2 / 4Ld L F

i 0( )a t r

20 ( )

L

i

H d z O z

Example: matter + lambda 0 M

Lu

min

osi

ty /

So

lar

Lu

min

osi

ty

10

9

9

8

10

4 10

1.6 10

6.4 10

Type Ia Supernovae

-20 0 20 40 60days

Type Ia supernova are standard candlesType Ia supernova are standard candlesType Ia supernova are standard candlesType Ia supernova are standard candles

app

aren

t m

agn

itu

de

[lo

g(d

ista

nce

)]

redshift z

Perlmutter et al. (1998)

Type Ia supernova Hubble diagramType Ia supernova Hubble diagramType Ia supernova Hubble diagramType Ia supernova Hubble diagram

cosmological constant, …some changing non-zero vacuum energy, … or some unknown systematic effect(s)

MATTER

V

AC

UU

M

maximumtheoretical

bliss

scal

e fa

cto

r a

time

normal0a

Newton Ga pGa 3Einstein

3 0p

scal

e fa

cto

r a

time

accelerated

030

p

a

vacuumenergy?

The accelerating universe?The accelerating universe?The accelerating universe?The accelerating universe?• Normal matter slows the expansion of the

universe (deceleration). Gravity is attractive.

• Negative pressure would push apart space.

• “Vacuum energy” (the mass-energy density of

space) is positive, but its pressure is negative.

cosmological constant, …some changing non-zero vacuum energy, … or some unknown systematic effect(s)

MATTER

V

AC

UU

M

The case for :1) acceleration

maximumtheoretical

bliss

2) large-scale structure

0.25 0.05 0.25 1 0.25

0.25 0.35 0.70

M M

M

h h

h

2dF data

cosmological constant, …some changing non-zero vacuum energy, … or some unknown systematic effect(s)

MATTER

V

AC

UU

M

The case for :1) acceleration2) large-scale structure

maximumtheoretical

bliss

3) age of the universe

13.5 2 Gyr

Chaboyer (2001) H0 =70 M t0 (Gyr)

Flat 1.0 0 9.3

Open 0.3 0

12

Open 0.2 0 14

Flat 0.3 0.7 13.5

Flat 0.2 0.8 15

tt00 : age of the universe : age of the universe• white dwarf cooling

• nucleocosmochronology

• globular cluster evolution

Cayrel (2001)

12.6 3 Gyr

First measurement

of stellar uranium

12.6 3 Gyr

13.5 2 Gyr

cosmological constant, …some changing non-zero vacuum energy, … or some unknown systematic effect(s)

MATTER

V

AC

UU

M

The case for :1) acceleration2) large-scale structure3) age of the universemaximum

theoreticalbliss

4) flatness= 1= 0.31 0.3 = 0.7

Flat universeFlat universeFlat universeFlat universe

0 1.03 0.06

Hu

B B hh QSO 1937-1009

Ly

Tytler Tytler

galaxy kinematics

x-ray gas lensing

M M

= 1

= 0.3

1 0.3 = 0.7

Cosmo-illogical constantCosmo-illogical constantCosmo-illogical constantCosmo-illogical constant

Mass density of space:

Who ordered that?

The unbearable lightness of nothing!

30 -310 g cm

Temperature of the universeTemperature of the universeTemperature of the universeTemperature of the universe

The cosmic food chain (The cosmic food chain (ii))The cosmic food chain (The cosmic food chain (ii))

Radiation: 0.02%

Visible matter: 0.1%

Neutrinos: 0.1%

Dark neutrons & protons: 9.78%

Dark matter: 30%

Dark energy: 60%

Observer’s view of the universeObserver’s view of the universe

lumpy (inhomogeneous and anisotropic) full of stars, galaxies, clusters, ….

NGC 6070NGC 6070

Theorist’s view of the universeTheorist’s view of the universe

smooth (homogeneous and isotropic) full of dark matter (and dark energy)

Actual image of dark matterActual image of dark matter

• Assume there is an average density

• Expand density contrast in Fourier modes

• Autocorrelation function defines power spectrum

Power spectrumPower spectrumPower spectrumPower spectrum

3exp k

xx ik x d k

2 3 2

20

( )( ) ( )

2k

kx dkx x

k

x

3 2

2 22

( ) ( )2

k

k

kk P k

• Power spectrum related to rms fluctuations

Power spectrumPower spectrumPower spectrumPower spectrum

1( )( )

R

xk R

sphere of radius R

2 2 N

3 3 N

N

. . . . . . . . . .

trial N

1 1 N

. . . . .

1N N2N N

3N N

2iN N

variance

Power spectrumPower spectrumPower spectrumPower spectrum

3 2

2 1

2k

k

118 Mpch

Observer’s Observer’s

view of the view of the

universeuniverse

(fluctuations)(fluctuations)

Theorist’s Theorist’s

view of the view of the

universeuniverse

(isotropic)(isotropic)

1 2

1/ 22

( , )lm lm

lm l

T T a Y

a C

Angular correlation function, lC

1 1 1 2 2 2( , ) ( , )T T

Angular power spectrumAngular power spectrumAngular power spectrumAngular power spectrum

LAST CENTURY

Angular power spectrumAngular power spectrumAngular power spectrumAngular power spectrum

Angular power spectrumAngular power spectrumAngular power spectrumAngular power spectrum

expected precision

-1 -101 0 50 km s Mpc

0.9 0.1CDM B

n r H

MAP

Rocky Rocky II: The universe observed: The universe observedRocky Rocky II: The universe observed: The universe observed• Cosmological parameters:

• Power spectrum of large-scale structure:

• Anisotropy of CMB:

0

0

0

0

0

Hubble's constant

deceleration parameter

the cosmic food chain

, , , , , , .....

age of the universe

temperature of the u

i

M B

H

q

t

T

niverse

( )P k

lC

Academic Training LecturesRocky Kolb

Fermilab, University of Chicago, & CERN

Cosmology and theCosmology and theorigin of structureorigin of structure

Rocky I: The observed universe

Rocky II: The growth of cosmological structure

Rocky III: Inflation and the origin of perturbations

Rocky IV: Dark matter and dark energy