Cosmology and the Dark Universe

Geheimnis der dunklen Materie

Geheimnis der dunklen Materie

Cosmology and the

Dark Universe

Cosmology and the

Dark Universe

Georg Raffelt, Max-Planck-Institut für Physik, München

Thomas

Title

Title

Dark Energy 73%

Dark Energy 73%

(Cosmological Constant)

(Cosmological Constant)

Neutrinos

Neutrinos

0.1

0.1−

−

2%

2%

Dark Matter

Dark Matter

23%

23%

Ordinary Matter 4%

Ordinary Matter 4%

(of this only about

(of this only about

10% luminous)

Inner Space, Outer Space

Inner Space, Outer Space

Microcosm at

Microcosm at

smallest distances

smallest distances

Universe

Universe

at large

at large

Understanding of nature spans

Understanding of nature spans

about 42 orders of magnitude

about 42 orders of magnitude

Title

Title

Inner space and

Inner space and

outer space

outer space

are closely related

Title

Title

Dark Energy 73%

Dark Energy 73%

(Cosmological Constant)

(Cosmological Constant)

Neutrinos

Neutrinos

0.1

0.1−

−

2%

2%

Dark Matter

Dark Matter

23%

23%

Ordinary Matter 4%

Ordinary Matter 4%

(of this only about

(of this only about

10% luminous)

Geheimnis der dunklen Materie

Geheimnis der dunklen Materie

1. Evidence for Dark Matter

and Dark Energy

1. Evidence for Dark Matter

and Dark Energy

Georg Raffelt, Max-Planck-Institut für Physik, München

Structure of Spiral Galaxies

Structure of Spiral Galaxies

“Rotation Curve” of the Solar System

“Rotation Curve” of the Solar System

Kepler’s Law

Kepler’s Law

radius

M

G

v

_rotation

=

Newton

central

radius

M

G

Rotation curve of the galaxy

Rotation curve of the galaxy

NGC 6503

NGC 6503

from radio observations of hydrogen motion

from radio observations of hydrogen motion

[MNRAS 249 (1991) 523]

[MNRAS 249 (1991) 523]

Galactic Rotation Curve from Radio Observations

Galactic Rotation Curve from Radio Observations

Expected from luminous

Expected from luminous

matter

matter

in the disk

in the disk

Observed flat

Observed flat

rotation curve

rotation curve

Spiral galaxy

Spiral galaxy

NGC 3198

NGC 3198

overlaid

overlaid

with hydrogen column density

with hydrogen column density

[

Rotation Curve of the Milky Way

Rotation Curve of the Milky Way

Xue et al.,

Xue et al.,

arXiv:0801.1232v5 (2008)

arXiv:0801.1232v5 (2008)

Finch & Tremaine

Finch & Tremaine

ARAA 29 (1991) 409

ARAA 29 (1991) 409

Expect dark matter density

Expect dark matter density

near solar system of about

near solar system of about

300 MeV cm

Dark Matter in Spiral Galaxies

Dark Matter in Spiral Galaxies

-

-

Summary

Summary

Flat rotation

Flat rotation

curve

curve

instead of

instead of

Keplerian

Keplerian

No obvious

No obvious

limit to

limit to

total mass

total mass

Expected

Expected

from

from

luminosity

luminosity

distribution

distribution

Infered

Infered

from

from

rotation

rotation

curve

curve

Vera

Structure of a Spiral Galaxy

Structure of a Spiral Galaxy

Dark Halo

Structure of a Spiral Galaxy

Structure of a Spiral Galaxy

Dark Halo

Coma Cluster

Coma Cluster

Dark Matter in Galaxy Clusters

Dark Matter in Galaxy Clusters

A gravitationally bound

A gravitationally bound

system of many particles

system of many particles

obeys the virial theorem

obeys the virial theorem

grav

kin

E

E

2

E

_kin

=

−

E

_grav

2

=

−

r

m

M

G

2

mv

2

2

=

N

r

r

m

M

G

2

mv

2

2

=

N

r

1

r

N

2

_G

_M

_r

v

2

≈

G

_N

M

_r

r

−

1

v

≈

−

Velocity dispersion

Velocity dispersion

from Doppler shifts

from Doppler shifts

and geometric size

and geometric size

Total Mass

Dark Matter in Galaxy Clusters

Dark Matter in Galaxy Clusters

Fritz

Fritz

Zwicky:

Zwicky:

Die

Die

Rotverschiebung

Rotverschiebung

von

von

Extragalaktischen Nebeln

Extragalaktischen Nebeln

(The redshift of extragalactic

(The redshift of extragalactic

nebulae)

nebulae)

Helv

Helv

. Phys.

. Phys.

Acta

Acta

6 (1933) 110

6 (1933) 110

In order to obtain the observed average Doppler effect of

In order to obtain the observed average Doppler effect of

1000 km/s or more, the average density of the Coma cluster

1000 km/s or more, the average density of the Coma cluster

would have to be at least 400 times larger than what is found

would have to be at least 400 times larger than what is found

from observations of the luminous matter.

from observations of the luminous matter.

Should this be confirmed one would find the surprising result

Should this be confirmed one would find the surprising result

that

Giant Arc in Cluster Cl 2244

Giant Arc in Cluster Cl 2244

-

-

02

02

z = 2.237

z = 2.237

z = 0.336

Giant Arcs

Giant Arcs

−

−

Gravitationally Lensed Background Galaxies

_{Gravitationally Lensed Background Galaxies}

Observer

Observer

Foreground

Foreground

cluster of

cluster of

galaxies

galaxies

Background galaxy

Background galaxy

Distorted image

Distorted image

(Partial Einstein ring)

Gravitational Lensing in Clusters of Galaxies

Gravitational Lensing in Clusters of Galaxies

Galaxy cluster Cl

Galaxy cluster Cl

0024+1654

0024+1654

[Hubble Space Telescope]

Hot X

Hot X

-

-

Ray Gas in Clusters of Galaxies

Ray Gas in Clusters of Galaxies

Most of the baryonic mass in a typical galaxy cluster

Most of the baryonic mass in a typical galaxy cluster

resides in hot, x

resides in hot, x

-

-

ray emitting intergalactic gas

ray emitting intergalactic gas

Abell 2029

Galaxy Cluster Abell 2029 (composite optical & x

Cluster Gas Fraction

Cluster Gas Fraction

Gas fraction in clusters

Gas fraction in clusters

f

f

_gas

_gas

h

h

3/2

3/2

_{= 0.075}

_{= 0.075}

±

_±

_0.002

_0.002

•

•

Assume the cluster matter

Assume the cluster matter

inventory represents a fair

inventory represents a fair

sample of the universe

sample of the universe

•

•

Use the measured baryon

Use the measured baryon

content

content

Ω

Ω

_B

_B

(BBN, CMBR)

(BBN, CMBR)

•

•

h = 0.72

h = 0.72

±

±

0.08

0.08

Cosmic matter content

Cosmic matter content

Ω

Ω

_M

_M

=

=

Ω

Ω

_B

_B

/f

/f

_gas

_gas

= 0.325

= 0.325

±

±

0.034

0.034

(Fabian, astro

(Fabian, astro

-

-

ph/0304020)

ph/0304020)

Mohr et al., astro

Bullet Cluster (1E 0657

Expanding Universe and the Big Bang

Expanding Universe and the Big Bang

Hubble’s law

Hubble’s law

v

v

_expansion

_expansion

= H

= H

₀

₀

×

×

distance

distance

Hubble’s

Hubble’s

constant

constant

H

H

₀

₀

= h 100 km s

= h 100 km s

-

-

1

1

Mpc

Mpc

-

-

1

1

Measured value

Measured value

h = 0.72

h = 0.72

±

±

0.04

0.04

Expansion age of the

Expansion age of the

universe

universe

t

t

₀

₀

≈

≈

H

H

₀

₀

−

−

1

1

≈

≈

14

14

×

×

10

10

9

9

years

years

1

1

Mpc

Mpc

= 3.26

= 3.26

×

×

10

10

6

6

lyr

lyr

=

=

3.08

3.08

×

×

10

10

24

24

cm

cm

Expanding Universe and the Big Bang

Expanding Universe and the Big Bang

Hubble’s law

Hubble’s law

v

v

_expansion

_expansion

= H

= H

₀

₀

×

×

distance

distance

Hubble’s

Hubble’s

constant

constant

H

H

₀

₀

= h 100 km s

= h 100 km s

-

-

1

1

Mpc

Mpc

-

-

1

1

Measured value

Measured value

h = 0.72

h = 0.72

±

±

0.04

0.04

Expansion age of the

Expansion age of the

universe

universe

t

t

₀

₀

≈

≈

H

H

₀

₀

−

−

1

1

≈

≈

14

14

×

×

10

10

9

9

years

years

1

1

Mpc

Mpc

= 3.26

= 3.26

×

×

10

10

6

6

lyr

lyr

=

=

3.08

3.08

×

×

10

10

24

24

cm

cm

Expanding Universe and the Big Bang

Expanding Universe and the Big Bang

Hubble’s law

Hubble’s law

v

v

_expansion

_expansion

= H

= H

₀

₀

×

×

distance

distance

Hubble’s

Hubble’s

constant

constant

H

H

₀

₀

= h 100 km s

= h 100 km s

-

-

1

1

Mpc

Mpc

-

-

1

1

Measured value

Measured value

h = 0.72

h = 0.72

±

±

0.04

0.04

Expansion age of the

Expansion age of the

universe

universe

t

t

₀

₀

≈

≈

H

H

₀

₀

−

−

1

1

≈

≈

14

14

×

×

10

10

9

9

years

years

1

1

Mpc

Mpc

= 3.26

= 3.26

×

×

10

10

6

6

lyr

lyr

=

=

3.08

3.08

×

×

10

10

24

24

cm

cm

Big Bang

Big Bang

Friedmann

Friedmann

-

-

Lemaître

Lemaître

-

-

Robertson

Robertson

-

-

Walker Cosmology

Walker Cosmology

r,

r,

θ

θ

,

,

φ

φ

,

,

co

co

-

-

moving

moving

spherical coordinates

spherical coordinates

r is dimensionless

r is dimensionless

•

•

On scales

On scales

≳

≳

100 Mpc, space is maximally symmetric

100 Mpc, space is maximally symmetric

(homogeneous & isotropic)

(homogeneous & isotropic)

•

•

The corresponding

The corresponding

Robertson

Robertson

-

-

Walker metric

Walker metric

is

is

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

φ

θ

+

θ

+

−

+

=

r

(

d

sin

d

)

r

k

1

dr

)

t

(

a

dt

ds

2

2

2

2

₂

2

2

2

2

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

φ

θ

+

θ

+

−

+

=

r

(

d

sin

d

)

r

k

1

dr

)

t

(

a

dt

ds

2

2

2

2

₂

2

2

2

2

Cosmic

Cosmic

scale

scale

factor

factor

Clock time

Clock time

of co

of co

-

-

moving

moving

observer

observer

Curvature

Curvature

k = 0,

k = 0,

±

±

1

1

k = 0

k = 0

k =

k =

−

−

1

1

k =

k =

+

+

1

1

Cosmic Expansion

Cosmic Expansion

•

•

Space between galaxies grows

Space between galaxies grows

•

•

Galaxies

Galaxies

(stars,

(stars,

people)

people)

stay the same

stay the same

(dominated by local gravity

(dominated by local gravity

or by electromagnetic forces)

or by electromagnetic forces)

•

•

Cosmic scale factor today:

Cosmic scale factor today:

a = 1

a = 1

Cosmic Scale Factor

Cosmic Scale Factor

Cosmic Redshift

Cosmic Redshift

•

•

Wavelength of light gets “stretched”

Wavelength of light gets “stretched”

•

•

Suffers redshift

Suffers redshift

•

•

Redshift today:

Redshift today:

z = 0

z = 0

then

today

1

z

λ

λ

=

+

then

today

1

z

λ

λ

=

+

then

today

then

today

a

a

1

z

+

=

=

λ

λ

then

today

then

today

a

a

1

z

+

=

=

λ

λ

Friedmann Equation

Friedmann Equation

−

−

Newtonian Derivation

_{Newtonian Derivation}

•

•

Birkhoff’s theorem

Birkhoff’s theorem

Spherical symmetry implies that only mass

Spherical symmetry implies that only mass

interior to radius

interior to radius

R = ra

R = ra

is relevant for motion of a test mass

is relevant for motion of a test mass

m

m

at

at

R

R

•

•

Energy conservation

Energy conservation

const

m

R

R

m

R

G

₂

2

1

3

3

4

N

=

+

ρ

−

π

&

m

const

R

R

m

R

G

₂

2

1

3

3

4

N

=

+

ρ

−

π

&

2

N

3

8

2

R

const

G

R

R

_⎟

₌

₊

⎠

⎞

⎜

⎝

⎛

&

_π

_ρ

2

N

3

8

2

R

const

G

R

R

_⎟

₌

₊

⎠

⎞

⎜

⎝

⎛

&

_π

_ρ

2

N

3

8

2

2

a

k

G

a

a

H

_⎟

=

ρ

−

⎠

⎞

⎜

⎝

⎛

=

&

2

8

₃

π

_N

₂

2

a

k

G

a

a

H

_⎟

=

ρ

−

⎠

⎞

⎜

⎝

⎛

=

&

π

•

•

Rescale r = a/R with cosmic scale factor a

Rescale r = a/R with cosmic scale factor a

1

,

0

k

=

0

,

±

1

k

=

±

with

with

Friedmann equation

Friedmann equation

R

R

m

m

Density

Density

ρ

ρ

Critical Density and

Critical Density and

Ω

Ω

-

_-

Parameter

Parameter

Evolution of cosmic scale factor a(t)

Evolution of cosmic scale factor a(t)

governed by

governed by

Friedmann equation

Friedmann equation

2

N

2

2

a

k

G

3

8

a

a

H

_⎟

=

π

ρ

−

⎠

⎞

⎜

⎝

⎛

= &

2

_N

₂

2

a

k

G

3

8

a

a

H

_⎟

=

π

ρ

−

⎠

⎞

⎜

⎝

⎛

= &

In a flat universe (k = 0), there is a

In a flat universe (k = 0), there is a

unique relationship between H and

unique relationship between H and

ρ

ρ

,

,

defining the

defining the

“critical density”

“critical density”

(

)

2

Pl

N

2

crit

=

₈

3

_π

H

_G

=

₈

3

_π

H

m

ρ

(

_Pl

)

2

N

2

crit

=

₈

3

_π

H

_G

=

₈

3

_π

H

m

ρ

Cosmic density always expressed

Cosmic density always expressed

in terms of

in terms of

crit

ρ

ρ

=

Ω

=

ρ

ρ

_crit

Ω

With

With

the

the

present

present

-

-

day

day

Hubble

Hubble

parameter

parameter

H

H

₀

₀

= h 100 km s

= h 100 km s

−

−

1

1

Mpc

Mpc

−

−

1

1

the critical density is

the critical density is

3

29

2

crit

=

h

1

.

88

×

10

−

g

cm

−

ρ

_crit

=

h

2

1

.

88

×

10

−

29

g

cm

−

3

ρ

With the measured value

With the measured value

h = 0.72 ± 0.04

h = 0.72 ± 0.04

the critical density is

the critical density is

3

29

crit

=

(

0

.

97

±

0

.

12

)

×

10

−

g

cm

−

ρ

_crit

=

(

0

.

97

±

0

.

12

)

×

10

−

29

g

cm

−

3

ρ

4

10

]

meV

)

07

.

0

55

.

2

(

[

SUSY

15

4

4

4

3

4

4

4

2

1

Λ

≈

−

±

=

4

10

]

meV

)

07

.

0

55

.

2

(

[

SUSY

15

4

4

4

3

4

4

4

2

1

Λ

≈

−

±

=

Expansion of Different Cosmological Models

Expansion of Different Cosmological Models

Time (billion years)

Time (billion years)

Cosmic scale factor a

Cosmic scale factor a

today

today

−

−14

14

Ω

Ω

_M

_M

= 0

= 0

−

−

9

9

Ω

Ω

_M

_M

= 1

= 1

−

−

7

7

Ω

Ω

_M

_M

> 1

> 1

Supernovae

Supernovae

−

−

Almost as Bright as Galaxies

_{Almost as Bright as Galaxies}

SN 1994D in NGC 4526

SN 1994D in NGC 4526

SN 1998S in NGC 3877

Universal Supernova Ia Light Curve

Universal Supernova Ia Light Curve

Supernova Ia lightcurves are

Supernova Ia lightcurves are

empirically a 1

empirically a 1

-

-

parameter family

parameter family

After transformation

After transformation

a universal light curve,

a universal light curve,

i.e. a de

Hubble Diagram

Hubble Diagram

Supernova Ia

Supernova Ia

as cosmological

as cosmological

standard candles

standard candles

Redshift

Redshift

Apparent Bri

ghtness

Apparent Bri

ghtness

Hubble’s orginal data (1929)

Hubble’s orginal data (1929)

z

Hubble Diagram

Hubble Diagram

Accelerated expansion

Accelerated expansion

(

(

Ω

Ω

_M

_M

=

=

0.3,

0.3,

Ω

Ω

_Λ

_Λ

=

=

0.7)

0.7)

Decelerated expansion

Decelerated expansion

(

(

Ω

Ω

_M

_M

=

=

1)

1)

Supernova Ia

Supernova Ia

as cosmological

as cosmological

standard candles

standard candles

Latest Supernova Data

Latest Supernova Data

Kowalski et al.,

Kowalski et al.,

Improved cosmological constraints from new, old and

Improved cosmological constraints from new, old and

combined supernova datasets, arXiv:0804.4142

Expansion of Different Cosmological Models

Expansion of Different Cosmological Models

Time (billion years)

Time (billion years)

Cosmic scale factor a

Cosmic scale factor a

today

today

−

−14

14

Ω

Ω

_M

_M

= 0

= 0

−

−

9

9

Ω

Ω

_M

_M

= 1

= 1

−

−

7

7

Ω

Ω

_M

_M

> 1

> 1

Ω

Ω

_M

_M

= 0.3

= 0.3

Ω

Ω

_Λ

_Λ

= 0.7

= 0.7

Einstein’s “Greatest Blunder”

Einstein’s “Greatest Blunder”

Friedmann equation for

Friedmann equation for

Hubble’s expansion rate

Hubble’s expansion rate

_a

₃

k

3

N

G

8

a

a

H

2

_⎟

2

=

π

ρ

−

₂

+

Λ

⎠

⎞

⎜

⎝

⎛

= &

3

a

k

3

N

G

8

a

a

H

2

_⎟

2

=

π

ρ

−

₂

+

Λ

⎠

⎞

⎜

⎝

⎛

= &

Yakov

Yakov

Borisovich

Borisovich

Zeldovich

Zeldovich

1914

1914

-

-

1987

1987

•

•

Quantum field theory of elementary particles

Quantum field theory of elementary particles

inevitably implies vacuum fluctuations because

inevitably implies vacuum fluctuations because

of Heisenberg’s uncertainty relation,

of Heisenberg’s uncertainty relation,

e.g. E and B fields can not simultaneously vanish

e.g. E and B fields can not simultaneously vanish

•

•

Ground state (vacuum) provides gravitating energy

Ground state (vacuum) provides gravitating energy

•

•

Vacuum energy

Vacuum energy

ρ

ρ

_vac

_vac

is equivalent to

is equivalent to

Λ

Λ

Cosmological constant Λ

(new constant of nature)

allows for a static universe

by “global anti-gravitation”

Newton’s constant

Newton’s constant

Density of gravitating mass & energy

Density of gravitating mass & energy

Curvature term

Curvature term

is very small or zero

is very small or zero

(Euclidean spatial geometry)

Zero Point Energy of Quantum Fields

Zero Point Energy of Quantum Fields

Energy levels of the harmonic oscillator

Energy levels of the harmonic oscillator

ω

⎟

⎠

⎞

⎜

⎝

⎛ +

=

n

_h

2

1

E

_n

_⎟

ω

⎠

⎞

⎜

⎝

⎛ +

=

n

_h

2

1

E

_n

•

•

Non

Non

-

-

vanishing zero

vanishing zero

-

-

point energy because of

point energy because of

Heisenberg’s uncertainty relation

Heisenberg’s uncertainty relation

•

•

Location and momentum not simultaneously

Location and momentum not simultaneously

determined and therefore not both zero

determined and therefore not both zero

Electromagnetic field:

Electromagnetic field:

E and B not simultaneously zero

E and B not simultaneously zero

because of uncertainty relation

because of uncertainty relation

Energy density in the ground level (vacuum) is

Energy density in the ground level (vacuum) is

sum over infinitely many oscillators

sum over infinitely many oscillators

∞

=

ω

=

+

=

ρ

_∑

n

n

2

2

2

2

B

E

+

₌

_h

ω

₌

_∞

=

ρ

_∑

n

n

2

2

2

2

B

E

_h

Nominal vacuum energy of the quantum fields

Nominal vacuum energy of the quantum fields

+

+

f

f

o

o

r every bosonic degree of freedom (photons etc.)

r every bosonic degree of freedom (photons etc.)

−

−

f

f

o

o

r every fermionic degree of freedom (electrons etc.)

r every fermionic degree of freedom (electrons etc.)

How to interpret ???

How to interpret ???

∞

∞

∞

∞

Casimir Effect (1948)

Casimir Effect (1948)

Hendrik Bugt Casimir

Hendrik Bugt Casimir

(1909

(1909

-

-

2000)

2000)

A measurable manifestation of the zero

A measurable manifestation of the zero

-

-

point energy

point energy

of the electromagnetic field

of the electromagnetic field

Bordag et al., New Developments in the Casimir Effect, Phys. Rep

Bordag et al., New Developments in the Casimir Effect, Phys. Rep

t. 353 (2001)

t. 353 (2001)

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛ μ

×

≈

π

=

2

₄

−

7

4

₂

cm

1

A

d

m

1

N

10

3

.

1

A

d

c

240

F

h

_⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛ μ

×

≈

π

=

2

₄

−

7

4

₂

cm

1

A

d

m

1

N

10

3

.

1

A

d

c

240

F

h

Casimir force between parallel

Casimir force between parallel

plates (distance d, area A)

plates (distance d, area A)

Long

Long

-

-

wavelength field

wavelength field

modes between the

modes between the

plates are “displaced,”

plates are “displaced,”

causing a reduction of

causing a reduction of

the vacuum energy

the vacuum energy

compared with free space

Generic Solutions of Friedmann Equation

Generic Solutions of Friedmann Equation

Radiation

Radiation

p =

p =

ρ

ρ

/3

/3

ρ

ρ

∝

∝

a

a

−

−

4

4

Dilution of radiation

Dilution of radiation

a(t)

a(t)

∝

∝

t

t

1/2

1/2

and redshift of energy

and redshift of energy

Matter

Matter

p = 0

p = 0

ρ

_ρ

∝

∝

a

a

−

−

3

3

Dilution of matter

Dilution of matter

a(t)

a(t)

∝

∝

t

t

2/3

2/3

Vacuum

Vacuum

energy

energy

p =

p =

−

−

ρ

ρ

ρ

ρ

= const

= const

Vacuum energy not

Vacuum energy not

diluted by expansion

diluted by expansion

(

3

t

)

exp

)

t

(

a

(

t

)

∝

exp

(

Λ

3

t

)

a

∝

Λ

vac

N

G

8

π

ρ

=

Λ

=

8

π

G

_N

ρ

_vac

Λ

Equation

Equation

of state

of state

Behavior of energy

Behavior of energy

-

-

density under

density under

cosmic expansion

cosmic expansion

Evolution of

Evolution of

cosmic scale factor

cosmic scale factor

Energy

Energy

-

-

momentum tensor of perfect fluid with density

momentum tensor of perfect fluid with density

ρ

ρ

and pressure p

and pressure p

⎟⎟

⎟

⎟

⎟

⎠

⎞

⎜⎜

⎜

⎜

⎜

⎝

⎛ρ

=

μν

p

p

p

T

⎟⎟

⎟

⎟

⎟

⎠

⎞

⎜⎜

⎜

⎜

⎜

⎝

⎛ρ

=

μν

p

p

p

T

⎟⎟

⎟

⎟

⎟

⎠

⎞

⎜⎜

⎜

⎜

⎜

⎝

⎛

ρ

−

ρ

−

ρ

−

ρ

=

ρ

=

μν

μν

_g

T

_vac

⎟⎟

⎟

⎟

⎟

⎠

⎞

⎜⎜

⎜

⎜

⎜

⎝

⎛

ρ

−

ρ

−

ρ

−

ρ

=

ρ

=

μν

μν

_g

T

_vac

Best

Best

-

-

Fit Universe

Fit Universe

Perlmutter

Physics Today

(Apr. 2003)

Kowalski et al.

arXiv:0804.4142

Scalar Fields and Cosmological Constant

Scalar Fields and Cosmological Constant

Higgs field

Higgs field

Φ

Φ

V

V

₀

₀

V

V

High

High

-

-

T phase

T phase

Low

Low

-

-

T phase

T phase

Why is zero of all

Why is zero of all

scalar field potentials

scalar field potentials

(almost) exactly at

(almost) exactly at

V

Quintessence

Quintessence

Quintessence field

Quintessence field

Φ

Φ

V

V

Absolute zero

Absolute zero

determined by

determined by

unknown effect

unknown effect

Scalar field still

Scalar field still

relaxing to zero

relaxing to zero

(slowly rolling)

(slowly rolling)

Lagrangian

Lagrangian

L

L

=

=

g

g

[

[

₂

1

₂

1

∂

∂

μ

μ

Φ

Φ

∂

∂

_μ

_μ

Φ

Φ

+

+

V

V

(

(

Φ

Φ

)

)

]

]

Equations of

Equations of

motion for

motion for

homogeneous

homogeneous

mode (

mode (

∇

∇

Φ

Φ

=0)

=0)

]

[

(

)

V

(

)

G

3

8

H

2

=

π

G

_N

[

₂

1

(

∂

_t

Φ

)

2

+

V

(

Φ

)

]

3

8

H

2

=

π

_N

₂

1

∂

_t

Φ

2

+

Φ

0

)

(

V

H

3

_t

2

t

Φ

+

∂

Φ

+

′

Φ

=

∂

2

_t

Φ

+

3

H

∂

_t

Φ

+

V

′

(

Φ

)

=

0

∂

System of

System of

coupled

coupled

nonlinear

nonlinear

equations

equations

Quintessence as a Perfect Fluid

Quintessence as a Perfect Fluid

Energy

Energy

-

-

momentum tensor of homogeneous

momentum tensor of homogeneous

Φ

Φ

-

-

mode that of an isotropic perfect fluid

mode that of an isotropic perfect fluid

)

(

V

)

(

_t

2

2

1

∂

Φ

+

Φ

=

ρ

=

₂

1

(

∂

_t

Φ

)

2

+

V

(

Φ

)

ρ

)

(

V

)

(

p

=

₂

1

(

∂

_t

Φ

)

2

−

V

(

Φ

)

p

=

₂

1

∂

_t

Φ

2

−

Φ

Example: Exponential potential

Example: Exponential potential

_V

_V

₍

₍

Φ

_Φ

₎

₎

=

₌

_V

_V

₀

₀

_e

_e

−

−

λ

λ

8

8

π

π

G

G

N

N

Φ

Φ

General equation of state

General equation of state

p

p

= w

= w

ρ

ρ

Explicit solution of eqs of motion imply

Explicit solution of eqs of motion imply

1

3

p

w

=

λ

2

−

ρ

=

1

3

p

w

=

λ

2

−

ρ

=

Like vacuum energy

Like vacuum energy

λ

λ

2

2

_{= 0}

_{= 0}

_w

_w

₌

₌

₋

₋

₁

₁

Accelerated expansion

Accelerated expansion

λ

λ

2

2

_{< 2}

_{< 2}

_w

_w

_<

_<

₋

₋

_1/3

_1/3

Like matter

Like matter

λ

λ

2

2

_{= 3}

_{= 3}

_w

_w

_{= 0}

_{= 0}

Like radiation

Like radiation

λ

λ

2

2

_{= 4}

_{= 4}

_w

_w

_{= 1}

_{= 1}

Observational

Observational

evidence for

evidence for

equation of state

equation of state

with “nonstandard”

with “nonstandard”

w

w

-

-

parameter?

parameter?

Phantom Energy

Phantom Energy

What is the meaning of w <

What is the meaning of w <

−

−

1 ?

1 ?

•

•

Violates “dominant energy condition”

Violates “dominant energy condition”

ρ

ρ

+ 3p > 0

+ 3p > 0

•

•

Signals vacuum instability

Signals vacuum instability

(e.g. Cline, Jeon & Moore, hep

(e.g. Cline, Jeon & Moore, hep

-

-

ph/0311312)

ph/0311312)

Singularity of scale factor in the

Singularity of scale factor in the

finite

finite

future (“big rip”)

future (“big rip”)

(

(

Caldwell

Caldwell

,

,

Kamionkowski

Kamionkowski

&

&

Weinberg

Weinberg

, astro

, astro

-

-

ph/0302506)

ph/0302506)

2

/

1

M

0

0

)

1

(

1

w

1

1

H

1

3

2

t

~

t

Ω

−

+

+

₁

_/

₂

M

0

0

)

1

(

1

w

1

1

H

1

3

2

t

~

t

Ω

−

+

+

Constraints on Quintessence

Constraints on Quintessence

Kowalski et al.,

Kowalski et al.,

arXiv:0804.4142

arXiv:0804.4142

Λ

Early

Title

Title

Dark Energy 73%

Dark Energy 73%

(Cosmological Constant)

(Cosmological Constant)

Neutrinos

Neutrinos

0.1

0.1−

−

2%

2%

Dark Matter

Dark Matter

23%

23%

Ordinary Matter 4%

Ordinary Matter 4%

(of this only about

(of this only about

10% luminous)

Geheimnis der dunklen Materie

Geheimnis der dunklen Materie

2. Structure Formation and

Precision Cosmology

2. Structure Formation and

Precision Cosmology

Georg Raffelt, Max-Planck-Institut für Physik, München

Sky Distribution of Galaxies (XMASS XSC)

Sky Distribution of Galaxies (XMASS XSC)

Galaxy Distribution in the Sky

Galaxy Distribution in the Sky

Sky distribution (equal area Aitoff projection) of the 2MASS

Sky distribution (equal area Aitoff projection) of the 2MASS

Extended Source Catalog (> 1.5 mio galaxies).

Extended Source Catalog (> 1.5 mio galaxies).

Color coding according to redshift.

Color coding according to redshift.

T.H.Jarrett, PASA 21 (2004) 396

T.H.Jarrett, PASA 21 (2004) 396

http://web.ipac.caltech.edu/staff/jarrett/2mass/LSS/

http://web.ipac.caltech.edu/staff/jarrett/2mass/LSS/

A Slice of the Universe

A Slice of the Universe

Galaxy distribution from the

Galaxy distribution from the

CfA redshift

CfA redshift

survey

survey

[

[ApJ

ApJ

302 (1986) L1]

302 (1986) L1]

Cosmic

Cosmic

“Stick Man”

“Stick Man”

~ 18

₅

~ 18

₅

Mp

c

Mp

c

2dF Galaxy

2dF Galaxy

Redshift

Redshift

Survey (2002)

Survey (2002)

~ 1

₃₀

0

~ 1

₃₀

0

Mp

_c

Mp

_c

Sloan Digital Sky Survey

SDSS Survey

SDSS Survey

Structure Formation in the Universe

Structure Formation in the Universe

Smooth

Smooth

Structured

Structured

Structure forms by

Structure forms by

gravitational instability

gravitational instability

of primordial

of primordial

density fluctuations

density fluctuations

Generating the Primordial Density Fluctuations

Generating the Primordial Density Fluctuations

Zero

Zero

-

-

point fluctuations of quantum

point fluctuations of quantum

fields are stretched and frozen

fields are stretched and frozen

Early phase of exponential expansion

Early phase of exponential expansion

(Inflationary epoch)

(Inflationary epoch)

Cosmic density fluctuations are

Cosmic density fluctuations are

frozen quantum fluctuations

Structure Formation by Gravitational Instability

Structure Formation by Gravitational Instability

Millenium Simulation

Millenium Simulation

Redshift Surveys vs. Millenium Simulation

Redshift Surveys vs. Millenium Simulation

Power Spectrum of Density Fluctuations

Power Spectrum of Density Fluctuations

Field of density fluctuations

Field of density fluctuations

ρ

δρ

=

δ

(

x

)

(

x

)

ρ

δρ

=

δ

(

x

)

(

x

)

Fourier transform

Fourier transform

∫

d

3

x

e

ik

x

(

x

)

k

=

δ

δ

_k

=

_∫

d

3

x

e

−

ik

⋅

x

δ

(

x

)

δ

−

⋅

Power spectrum essentially square

Power spectrum essentially square

of Fourier transformation

of Fourier transformation

( )

2

3

ˆ

(

k

k

)

P

(

k

)

k

k

δ

=

π

δ

−

′

δ

_k

δ

_k

_′

=

( )

2

π

3

δ

ˆ

(

k

−

k

′

)

P

(

k

)

δ

_′

δˆ

δˆ

Power spectrum is Fourier transform of

Power spectrum is Fourier transform of

two

two

-

-

point correlation function (

point correlation function (

x=x

x=x

₂

₂

−

−

x

x

₁

₁

)

)

( )

2

e

P

(

k

)

k

d

)

x

(

)

x

(

)

x

(

₂

₁

_⎮

3

₃

ik

⋅

x

⌡

⌠

π

=

δ

δ

=

ξ

( )

2

e

P

(

k

)

k

d

)

x

(

)

x

(

)

x

(

₂

₁

_⎮

3

₃

ik

⋅

x

⌡

⌠

π

=

δ

δ

=

ξ

3

2

1

)

k

(

2

3

x

ik

2

2

)

k

(

P

k

e

k

dk

4

d

Δ

⋅

π

⎮

⌡

⌠

π

Ω

=

3

2

1

)

k

(

2

3

x

ik

2

2

)

k

(

P

k

e

k

dk

4

d

Δ

⋅

π

⎮

⌡

⌠

π

Ω

=

with the

with the

δ

δ

-

-

function

function

Gaussian random field (phases of

Gaussian random field (phases of

Fourier modes

Fourier modes

δ

δ

_k

_k

uncorrelated) is fully

uncorrelated) is fully

characterized by the power spectrum

characterized by the power spectrum

2

k

)

k

(

P

(

k

)

=

δ

_k

2

P

=

δ

or equivalently by

or equivalently by

π

δ

=

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

π

=

Δ

2

k

2

)

k

(

P

k

)

k

(

3

2

k

2

1

2

3

π

δ

=

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

π

=

Δ

2

k

2

)

k

(

P

k

)

k

(

3

2

k

2

1

2

3

Gravitational Growth of Density Perturbations

Gravitational Growth of Density Perturbations

The dynamical evolution

The dynamical evolution

of small perturbations

of small perturbations

1

)

x

(

)

x

(

<

<

ρ

δρ

=

δ

(

x

)

(

x

)

<

<

1

ρ

δρ

=

δ

is independent for each

is independent for each

Fourier mode

Fourier mode

δ

δ

_k

_k

•

•

For pressureless,

For pressureless,

nonrelativistic matter

nonrelativistic matter

(cold dark matter)

(cold dark matter)

naively expect

naively expect

exponential growth

exponential growth

•

•

Only power

Only power

-

-

law

law

growth in expanding

growth in expanding

universe

universe

Matter dominates

Matter dominates

a

a

∝

∝

t

t

2/3

2/3

Sub

Sub

-

-

horizon

horizon

λ

λ

≪

_≪

H

H

−

−

1

1

Super

Super

-

-

horizon

horizon

λ

λ

≫

_≫

H

H

−

−

1

1

δ

δ

_k

_k

≈

≈

const

const

δ

δ

_k

_k

∝

∝

a

a

2

2

∝

∝

t

t

δ

δ

_k

_k

∝

∝

a

a

∝

∝

t

t

2/3

2/3

Radiation dominates

Radiation dominates

a

a

∝

∝

t

t

1/2

1/2

Processed Power Spectrum in Cold Dark Matter Scenario

Processed Power Spectrum in Cold Dark Matter Scenario

Primordial spectrum

Primordial spectrum

usually assumed to be

usually assumed to be

of power

of power

-

-

law form

law form

n

2

k

k

)

k

(

P

(

k

)

=

δ

_k

2

∝

k

n

P

=

δ

∝

Harrison

Harrison

-

-

Zeldovich

Zeldovich

(“flat”) spectrum

(“flat”) spectrum

n

n

=

=

1

1

expected from inflation

expected from inflation

(may be slightly less

(may be slightly less

than 1, depending on

than 1, depending on

details of inflationary

details of inflationary

phase)

phase)

Primordial

Primordial

spectrum

spectrum

Suppressed by stagnation

Suppressed by stagnation

during radiation phase

Power Spectrum of Cosmic Density Fluctuations

Power Spectrum of Cosmic Density Fluctuations

Lyman

Lyman

-

-

alpha Forest

alpha Forest

•

•

Hydrogen clouds absorb from QSO

Hydrogen clouds absorb from QSO

continuum emission spectrum

continuum emission spectrum

•

•

Absorption dips at Ly

Absorption dips at Ly

-

-

α

α

wavelengh

wavelengh

corresponding to redshift

corresponding to redshift

www.astro.ucla.edu/~wright/Lyman

www.astro.ucla.edu/~wright/Lyman

-

-

alpha

alpha

-

-

forest.html

forest.html

Examples for Lyman

Examples for Lyman

-

-

α

α

forest in

forest in

low

Weak Lensing

Weak Lensing

−

−

A Powerful Probe for the Future

_{A Powerful Probe for the Future}

Unlensed

Unlensed

Lensed

Lensed

Distortion of background images by foreground matter

Discovery of the Cosmic Microwave Background Radiation

Discovery of the Cosmic Microwave Background Radiation

Discovery of 2.7 Kelvin

Discovery of 2.7 Kelvin

Cosmic microwave background radiation

Cosmic microwave background radiation

by Penzias and Wilson in 1965

by Penzias and Wilson in 1965

(Nobel Prize 1978)

(Nobel Prize 1978)

Beginning of “big

Beginning of “big

-

-

bang cosmology”

bang cosmology”

Robert W. Wilson

Robert W. Wilson

Born 1936

Last Scattering Surface

Last Scattering Surface

1

1

3

3

20

20

10

00

1000

15

00

15

00

Redshift

Redshift

z

z

Here & Now

Here & Now

Horizon

COBE Temperature Map of the Cosmic Microwave Background

COBE Temperature Map of the Cosmic Microwave Background

T = 2.725 K (uniform on the sky)

COBE Temperature Map of the Cosmic Microwave Background

COBE Temperature Map of the Cosmic Microwave Background

T = 2.725 K (uniform on the sky)

T = 2.725 K (uniform on the sky)

Dynamical range

Dynamical range

Δ

Δ

T = 3.353

T = 3.353

mK (

mK (

Δ

Δ

T/

T/

T

T

≈

≈

10

10

-

-

3

3

)

)

Dipole temperature distribution from Doppler effect

Dipole temperature distribution from Doppler effect

caused by our motion relative to the cosmic frame