1. Cosmic Microwave Background radiation (CMB)

Vorlesung 6:

R t F d

Roter Faden:

1. Cosmic Microwave Background radiation (CMB)

Zum Mitnehmen

Pfeiler der Urknalltheorie:

Pfeiler der Urknalltheorie:

1) Hubble Expansion 2) CMB

3) Kernsynthese

1) beweist dass es Urknall gab und 2,3) beweisen,dass Univ. am Anfang heiss war

Bisher:

Bisher:

Ausdehnung und Alter des Uni ers ms Universums berechnet.

Wie ist die Tempe- raturentwicklung?

Am Anfang ist die Am Anfang ist die Energiedichte

dominiert durch Strahlung

Strahlung.

Nach Rekombination ‘FREE STREAMING’ der Photonen

Last Scattering Surface (LSS)

Temperaturentwicklung des Universums

Entstehung der 3K Kosmischen Hintergrundstrahlung

Cosmic Microwave Background (CMB))

Schwarzkörperstrahlung:

ein Thermometer des Universums

Erwarte Plancksche Verteilung der CMB mit einer Temperatur T= 2.7 K, denn T∝ 1/S ∝ 1/1+z.

Entkoppelung bei T=3000 K , z=1100.

T j t t l 3000/1100 2 7 K

T jetzt also 3000/1100 =2.7 K

Das elektromagnetische Spektrum

Geschichte der CMB

Entdeckung der CMB von Penzias und Wilson in 1965

The COBE satellite: first precision CMB experiment

COBE orbit

Schematic view of COBE in orbit around the earth. The altitude at

i ti 900 k Th i f

insertion was 900 km. The axis of rotation is at approximately 90°

with respect to the direction to the

sun. From Boggess et al. 1992.

Kosmische Hintergrundstrahlung

gemessen mit dem COBE Satelliten (1991)

Mather (NASA) Smoot (Berke T = 2.728 ± 0.004 K ⇒ Dichte der Photonen 412 pro cm

Wellenlänge der Photonen ca 1 5 mm so dichteste Packung

Mather (NASA), Smoot (Berke Nobelpreis 2006

Wellenlänge der Photonen ca. 1,5 mm, so dichteste Packung

Bell Labs (1963)

Observing the

Microwave Background

( )

(highlights, there are many others)

COBE satellite (1992)

WMAP satellite

(2003)

ΔΤ/Τ measured by W(ilkinson)MAP Satellite

60 K

90 K

300 K

WMAP Elektronik

UHMT=

Ultrahigh Mobility Transistors (100 GHz)

Auflösungsvermögen

Nonlinear Device Mixer

Heterodyne (=mixing, Überlagerung) microwave receiver for downshifting the frequency

Nonlinear Device Mixer

Nach dem Filter:

WMAP vs COBE

7

0.2

45 times sensitivity WMAP

Lagrange Punkt 2

Himmelsabdeckung

Cosmology and the Cosmic Microwave Background

The Universe is approximately about 13.7 billion years old, according to the standard cosmological Big Bang model. At this time, it was a state of high uniformity, was extremely hot and dense was filled with elementary particles and was expanding very rapidly. About 380,000 years after the Big Bang, the energy of the photons had decreased and was not sufficient to ionise hydrogen atoms. Thereafter the photons “decoupled” from the other particles and could move through the Universe essentially unimpeded. The Universe has expanded move through the Universe essentially unimpeded. The Universe has expanded and cooled ever since, leaving behind a remnant of its hot past, the Cosmic Microwave Background radiation (CMB). We observe this today as a 2.7 K thermal blackbody radiation filling the entire Universe. Observations of the

CMB i i d d t il d i f ti b t th l U i th b

CMB give a unique and detailed information about the early Universe, thereby promoting cosmology to a precision science. Indeed, as will be discussed in

more detail below, the CMB is probably the best recorded blackbody spectrum that exists. Removing a dipole anisotropy, most probably due our motion g p py, p y

through the Universe, the CMB is isotropic to about one part in 100,000. The 2006 Nobel Prize in physics highlights detailed observations of the CMB

performed with the COBE (COsmic Background Explorer) satellite.

From Nobel prize 2006 announcement

Early work

The discovery of the cosmic microwave background radiation has an

unusual and interesting history The basic theories as well as the necessary unusual and interesting history. The basic theories as well as the necessary experimental techniques were available long before the experimental

discovery in 1964. The theory of an expanding Universe was first given by Friedmann (1922) and Lemaître (1927). An excellent account is given by ( ) ( ) g y Nobel laureate Steven Weinberg (1993).

Around 1960, a few years before the discovery, two scenarios for the Universe were discussed. Was it expanding according to the Big Bang model, or was it in a steady state? Both models had their supporters and among the scientists advocating the latter were Hannes Alfvén (Nobel prize in physics 1970), Fred Hoyle and Dennis Sciama. If the Big Bang model

h i i f h di i d i d l U i

was the correct one, an imprint of the radiation dominated early Universe

must still exist, and several groups were looking for it. This radiation must

be thermal, i.e. of blackbody form, and isotropic.

Th di f th i i b k d b P i d Wil i 1964

First observations of CMB

The discovery of the cosmic microwave background by Penzias and Wilson in 1964 (Penzias and Wilson 1965, Penzias 1979, Wilson 1979, Dicke et al. 1965) came as a complete surprise to them while they were trying to understand the source of

unexpected noise in their radio-receiver (they shared the 1978 Nobel prize in p ( y p

physics for the discovery). The radiation produced unexpected noise in their radio receivers. Some 16 years earlier Alpher, Gamow and Herman (Alpher and Herman 1949, Gamow 1946), had predicted that there should be a relic radiation field

penetrating the Universe It had been shown already in 1934 by Tolman (Tolman penetrating the Universe. It had been shown already in 1934 by Tolman (Tolman 1934) that the cooling blackbody radiation in an expanding Universe retains its blackbody form. It seems that neither Alpher, Gamow nor Herman succeeded in convincing experimentalists to use the characteristic blackbody form of the

radiation to find it. In 1964, however, Doroshkevich and Novikov (Doroshkevich and Novikov 1964) published an article where they explicitly suggested a search for the radiation focusing on its blackbody characteristics. One can note that some measurements as early as 1940 had found that a radiation field was necessary to measurements as early as 1940 had found that a radiation field was necessary to explain energy level transitions in interstellar molecules (McKellar 1941).

Following the 1964 discovery of the CMB, many, but not all, of the steady state proponents gave up, accepting the hot Big Bang model. The early theoretical work

CN=Cyan

is discussed by Alpher, Herman and Gamow 1967, Penzias 1979, Wilkinson and Peebles 1983, Weinberg 1993, and Herman 1997.

Further observations of CMB

Following the 1964 discovery, several independent measurements of the radiation were made by Wilkinson and others, using mostly balloon-borne, rocket-borne or ground based instruments. The intensity of the radiation has

it i f l th f b t 2 h th b ti i th

its maximum for a wavelength of about 2 mm where the absorption in the atmosphere is strong. Although most results gave support to the blackbody form, few measurements were available on the high frequency (low

wavelength) side of the peak Some measurements gave results that showed wavelength) side of the peak. Some measurements gave results that showed significant deviations from the blackbody form (Matsumoto et al. 1988).

The CMB was expected to be largely isotropic. However, in order to explain the large scale structures in the form of galaxies and clusters of galaxies g g g

observed today, small anisotropies should exist. Gravitation can make small density fluctuations that are present in the early Universe grow and make galaxy formation possible. A very important and detailed general relativistic calculation by Sachs and Wolfe showed how three-dimensional density

fluctuations can give rise to two-dimensional large angle (> 1°) temperature anisotropies in the cosmic microwave background radiation (Sachs and

W lf 1967)

Wolfe 1967).

Dipol Anisotropy

Because the earth moves relative to the CMB, a dipole temperature

anisotropy of the level of ΔT/T = 10

is expected. This was observed in the

1970’ (C kli 1969 H 1971 C d Wilki 1976 d S t

1970’s (Conklin 1969, Henry 1971, Corey and Wilkinson 1976 and Smoot, Gorenstein and Muller 1977). During the 1970-ties the anisotropies were expected to be of the order of 10

– 10

, but were not observed

experimentally When dark matter was taken into account in the 1980 ties

experimentally. When dark matter was taken into account in the 1980-ties,

the predicted level of the fluctuations was lowered to about 10

, thereby

posing a great experimental challenge.

Because of e.g. atmospheric absorption, it was long realized that

The COBE mission

g p p g

measurements of the high frequency part of the CMB spectrum (wavelengths shorter than about 1 mm) should be performed from space. A satellite instrument also gives full sky coverage and a long observation time The latter point is important for reducing systematic observation time. The latter point is important for reducing systematic errors in the radiation measurements. A detailed account of

measurements of the CMB is given in a review by Weiss (1980).

The COBE story begins in 1974 when NASA made an announcement of opportunity for small experiments in astronomy. Following lengthy discussions with NASA

Headquarters the COBE project was born and finally, on 18 November 1989, the COBE satellite was successfully launched into orbit. More than 1,000 scientists, engineers and administrators were involved in the mission. COBE carried three engineers and administrators were involved in the mission. COBE carried three instruments covering the wavelength range 1 μm to 1 cm to measure the anisotropy and spectrum of the CMB as well as the diffuse infrared background radiation:

DIRBE (Diffuse InfraRed Background Experiment), DMR (Differential Microwave

R di ) d FIRAS (F I f R d Ab l S h ) COBE’

Radiometer) and FIRAS (Far InfraRed Absolute Spectrophotometer). COBE’s mission was to measure the CMB over the entire sky, which was possible with the

chosen satellite orbit. All previous measurements from ground were done with limited sky coverage. John Mather was the COBE Principal Investigator and the project y g p g p j

The COBE mission

For DMR the objective was to search for anisotropies at three wavelengths, 3 mm, 6 mm, and 10 mm in the CMB with an g angular resolution of about 7°. The anisotropies postulated to explain the large scale structures in the Universe should be present between regions covering large angles For FIRAS present between regions covering large angles. For FIRAS the objective was to measure the spectral distribution of the CMB in the range 0.1 – 10 mm and compare it with the

bl kb d f t d i th Bi B d l hi h i

blackbody form expected in the Big Bang model, which is different from, e.g., the forms expected from starlight or bremsstrahlung. For DIRBE, the objective was to measure the infrared background radiation. The mission, spacecraft and instruments are described in detail by Boggess et al.

1992 Figures 1 and 2 show the COBE orbit and the satellite

1992. Figures 1 and 2 show the COBE orbit and the satellite,

respectively.

The COBE success

COBE was a success. All instruments worked very well and the results, in particular those from DMR and FIRAS contributed significantly to make

and FIRAS, contributed significantly to make

cosmology a precision science. Predictions of the Big Bang model were confirmed: temperature

fl i f h d f 10

f d d h

fluctuations of the order of 10

were found and the background radiation with a temperature of 2.725 K followed very precisely a blackbody spectrum. y p y y p

DIRBE made important observations of the infrared background. The announcement of the discovery of the anisotropies was met with great enthusiasm

the anisotropies was met with great enthusiasm

worldwide.

CMB Anisotropies

The DMR instrument (Smoot et al. 1990) measured temperature

fluctuations of the order of 10^-5 for three CMB frequencies, 90, 53 and 31.5 GHz (wavelengths 3.3, 5.7 and 9.5 mm), chosen near the CMB intensity maximum and where the galactic background was low The intensity maximum and where the galactic background was low. The angular resolution was about 7°. After a careful elimination of

instrumental background, the data showed a background contribution from the Milky Way, the known dipole amplitude ΔT/T = 10^-3 probably caused by the Earth’s motion in the CMB, and a significant long sought after quadrupole amplitude, predicted in 1965 by Sachs and Wolfe. The first results were published in 1992.The data showed scale invariance for large angles, in agreement with predictions from inflation models.

large angles, in agreement with predictions from inflation models.

Figure 5 shows the measured temperature fluctuations in galactic coordinates, a figure that has appeared in slightly different forms in many journals. The RMS cosmic

quadrupole amplitude was estimated at 13 ± 4 μK (ΔT/T = 5×10-6) with a systematic

f t t 3 K (S t t l 1992) Th DMR i t i d d

error of at most 3 μK (Smoot et al. 1992). The DMR anisotropies were compared and found to agree with models of structure formation by Wright et al. 1992. The full 4 year DMR observations were published in 1996 (see Bennett et al. 1996). COBE’s results were soon confirmed by a number of balloon-borne experiments, and, more recently, by y p , , y, y the 1° resolution WMAP (Wilkinson Microwave Anisotropy Probe) satellite, launched in 2001 (Bennett et al. 2003).

The 1964 discovery of the cosmic microwave background had a large impact

Outlook

The 1964 discovery of the cosmic microwave background had a large impact on cosmology. The COBE results of 1992, giving strong support to the Big Bang model, gave a much more detailed view, and cosmology turned into a precision science. New ambitious experiments were started and the rate of publishing papers increased by an order of magnitude.

Our understanding of the evolution of the Universe rests on a number of observations, including (before COBE) the darkness of the night sky, the dominance of hydrogen and helium over heavier elements the Hubble expansion and the existence of the CMB

helium over heavier elements, the Hubble expansion and the existence of the CMB.

COBE’s observation of the blackbody form of the CMB and the associated small temperature fluctuations gave very strong support to the Big Bang model in proving the cosmological origin of the CMB and finding the primordial seeds of the large structures observed today.

However, while the basic notion of an expanding Universe is well established, fundamental questions remain, especially about very early times, where a nearly exponential expansion, inflation, is proposed. This elegantly explains many

exponential expansion, inflation, is proposed. This elegantly explains many

cosmological questions. However, there are other competing theories. Inflation may have generated gravitational waves that in some cases could be detected indirectly by measuring the CMB polarization. Figure 8 shows the different stages in the evolution

f th U i di t th t d d l i l d l Th fi t t ft th

of the Universe according to the standard cosmological model. The first stages after the

The colour of the universe

The young Universe was fantastically bright. Why? Because everywhere it was hot, and hot things glow brightly. Before we learned why this was:

collisions between charged particles create photons of light. As long as the particles and photons can thoroughly interact then a thermal spectrum is

p p g y p

produced: a broad range with a peak.

The thermal spectrum’s shape depends only on temperature: Hotter objects appear bluer: the peak shifts to shorterpp p wavelengths, with: λpk = 0.0029/TK g , p m = 2.9×10⁶/T nm. At 10,000K we have λpeak = 290 nm (blue), while at 3000K we have λpeak = 1000 nm (deep orange/red).

Let’s now follow through the color of the Universe during its first million g g years. As the Universe cools, the thermal spectrum shifts from blue to red, spending ~80,000 years in each rainbow color.

At 50 kyr, the sky is blue! At 120 kyr it’s green; at 400 kyr it’s orange; and by 1 Myr it’s crimson. This is a wonderful quality of the young Universe: it y y q y y g paints its sky with a human palette.

Quantitatively: since λpeak ~ 3×10⁶/T nm, and T ~ 3/S K, then λpeak ~ 10⁶ / S nm. Notice that today, S = 1 and so λpeak = 10⁶ nm = 1 mm, which is, of course, the peak of the CMB microwave spectrum.

Hotter objects appear brighter. There are two reasons for this:

M i l i l lli i k i h C i λ k

Light Intensity

More violent particle collisions make more energetic photons. Converting λpk ~ 0.003/T m to the equivalent energy units, it turns out that in a thermal spectrum, the average photon energy is ~ kT. So, for systems in thermal equilibrium, the mean energy per particle or per photon is ~kT. Faster particles collide more

f l k h I f h b d i f h h

frequently, so make more photons. In fact the number density of photons, nph ∝ T³. Combining these, we find that the intensity of thermal radiation increases dramatically with temperature Itot = 2.2×10^-7 T⁴Watt /m² inside a gas at

temperature T.

At hi h t t th l di ti h th ltit d f ti l

At high temperatures, thermal radiation has awesome power– the multitude of particle collisions is incredibly efficient at creating photons. To help feel this, consider the light falling on you from a noontime sun – 1400 Watt/m² – enough to feel sunburned quite quickly. Let’s write this as Isun.

Fl t i t d l t th CMB d i di ti

Float in outer space, exposed only to the CMB, and you experience a radiation field of I_3K = 2.2×10^-7×2.7⁴ = 10 μW/m² = 10^-8 Isun – not much! Here on Earth at 300K we have I_300K ~ 1.8 kW/m² (fortunately, our body temperature is 309K so you radiate 2.0 kW/m², and don’t quickly boil!). A blast furnace at 1500 °C

( 1800K) h I 2 3 MW/ ² 1600 I ( b il i 1 i t )

(~1800K) has I_1800K = 2.3 MW/m² = 1600 Isun (you boil away in ~1 minute).

At the time of the CMB (380 kyr), the radiation intensity was I_3000K = 17 MW/m²

= 12,000 Isun – you evaporate in 10 seconds.

In the Sun’s atmosphere, we have I_5800K = 250 MW/m² = 210,000 Isun. That’s a

j it ’ f lli h t

major city’s power usage, falling on each square meter.

Warum ist die CMB so wichtig in der Kosmologie?

a) Die CMB beweist, dass das Universum früher heiß war ) , und das die Temperaturentwicklung verstanden ist

b) Alle Wellenlängen ab einer bestimmten Länge (=oberhalb den ) g g ( akustischen Wellenlängen) kommen alle

gleich stark vor, wie von der Inflation vorhergesagt.

c) Kleine Wellenlängen (akustische Wellen) zeigen

ein sehr spezifisches Leistungsspektrum der akustischen Wellen im frühen Universum, woraus man

schließen kann, dass das Universum FLACH ist und

die baryonische Dichte nur 4-5% der Gesamtdichte ausmacht. y

Akustische Wellen im frühen Universum

• Photonen, Elektronen, Baryonen wegen der starken Kopplung

Mathematisches Modell

, , y g pp g

wie eine Flüssigkeit behandelt → ρ, v, p

• Dunkle Materie dominiert das durch die Dichtefluktuationen hervorgerufene Gravitationspotential Φ

hervorgerufene Gravitationspotential Φ

• δρ/δt+∇(ρv)=0

(Kontinuitätsgleichung = Masse-Erhaltung))

• v+(v·∇)v = -∇(Φ+p/ρ)

(Euler Gleichung = Impulserhaltung)

Tiefe des Potentialtopfs be-

• ∇² Φ = 4πGρ

(Poissongleichung = klassische Gravitation)

• erst nach Überholen durch den akustischen Horizont H = c H^-1 ,

Tiefe des Potentialtopfs be- stimmt durch dunkle Materie

erst nach Überholen durch den akustischen Horizont H_s c_sH , (c_s = Schallgeschwindigkeit) können die ersten beiden Gleichungen verwendet werden

• Lösung kann numerisch oder mit Vereinfachungen analytisch Lösung kann numerisch oder mit Vereinfachungen analytisch bestimmt werden und entspricht grob einem gedämpftem

harmonischen Oszillator mit einer antreibenden Kraft

Entwicklung der Dichtefluktuationen im Universum

Man kann die Dichtefluktuationen

im frühen Univ als Temp Fluktuationen

im frühen Univ. als Temp.-Fluktuationen

M k di Di ht fl kt ti i

Entwicklung der Dichtefluktuationen im Universum

Man kann die Dichtefluktuationen im frühen Univ. als Temp.-Fluktuationen der CMB beobachten!

Early Universe

The Cosmic screen

Present Universe

Simulation der Galaxienformation

The first sound waves The first sound waves

f ti compression

dim dim

a) gas falls into valleys, gets compressed, & glows brighter

rarefaction rarefaction

bright

b) it overshoots, then rebounds out, is rarefied, & gets dimmer rarefaction

compression compression

dim

bright bright

c) it then falls back in again to make a second compression dim

Æ

Æ

the oscillation continues the oscillation continues

sound waves are created sound waves are created

Æ

Æ

the oscillation continues the oscillation continues

sound waves are created sound waves are created

• Gravity drives the growth of sound in the early Universe.

• The gas must also feel pressure, so it rebounds out of the valleys. The gas must also feel pressure, so it rebounds out of the valleys.

• We see the bright/dim regions as patchiness on the

.

Akustische Wellen im frühen Universum

Druck der akust. Welle und Gravitation verstärken die

Temperaturschwankungen in der Grundwelle (im ersten Peak)

http://astron.berkeley.edu/~mwhite/sciam03_short.pdf

Druck der akust. Welle und Gravitation wirken

gegeneinander in der Oberwelle ( im zweiten Peak)

Akustische Wellen im frühen Universum

Flute power spectra

Bь Clarinet Bь Clarinet

piano range

M d Fl t Modern Flute

Überdichten am Anfang: Inflation

Sky Maps Æ Power Spectra

W “ ” h CMB d

W “ ” h CMB d

peak

trough

We “see” the CMB sound We “see” the CMB sound as

as waves on the sky waves on the sky. .

trough

Use special methods Use special methods to measure the

to measure the strength strength of each wavelength

of each wavelength of each wavelength.

of each wavelength.

Shorter wavelengths Shorter wavelengths

ll f i

ll f i

are smaller frequencies are smaller frequencies are higher pitches

are higher pitches

Sound waves in the sky Sound waves in the sky

Thi lid ill h i i I i l ki d h

This slide illustrates the situation. Imagine looking down on the ocean from a plane and seeing far below, surface waves. The patches on the microwave background are peaks and troughs of distant sound waves.

Water waves Water waves ::

high/low level of high/low level of

many waves of different many waves of different high/low level of

high/low level of water surface

water surface

many waves of different many waves of different sizes, directions & phases sizes, directions & phases

all “superimposed”

all “superimposed”

Sound waves Sound waves ::

red/blue = high/low

red/blue = high/low

gas & light pressure

gas & light pressure

Power (Leistung) pro Wellenlänge

Structures in 1-D

L l h

Long-wavelength

Larger amplitude/power

Short-wavelength smaller amplitude/pow

Power (Leistung) pro Wellenlänge

This distribution has a lot of long wavelength power

And a little short wavelength power

Geometry of the Universe

Open : p

Flat :

Closed:

Closed: Ω=1.2

Atomic content of the Universe

4% t

8% atoms

2% atoms 4% atoms

Low pitch High pitch

CMB Anisotropie als Fkt. der Auflösung

ΔT=0 1 K ΔT 0.1 K

The oval shapes show a spherical surface, as in a

ΔT=3300 µK

(Dipolanisotropie)

spherical surface, as in a global map. The whole sky can be thought of as the inside of a sphere.

(Dipolanisotropie)

ΔT=18 µK

(nach Subtraktion

der Dipolanisotropie)

der Dipolanisotropie)

Mark Whittle Mark Whittle Mark Whittle Mark Whittle

University of Virginia University of Virginia

http://www.astro.virginia.edu/~dmw8f http://www.astro.virginia.edu/~dmw8f

See also: “full presentation”

See also: “full presentation”

Viele Plots und sounds von Whittles Webseite

The

is highly

Three all

Three all--sky maps of the sky maps of the

uniform

uniform,, as illustrated

here. This means the young Universe is

l h

l h The oval shapes

extremely smooth

extremely smooth. show a spherical surface, as in a global map. The whole sky can be

But not completely:

COBE

’s 1992 map

COBE

s 1992 map showed patchiness

for the first time.

red

blue = tiny

red

blue tiny

differences in brightness.

Resolution ~7

.

Patches in the brightness are about 1 part in 100,000 = a b t i

WMAP

’s now famous 2003 map of

patchiness (anisotropy

bacterium on a bowling ball = 60 meter waves on the surface

patchiness (anisotropy

Sound in space !?!

Sound in space !?!

• Surely, the vacuum of “space” must be silent silent ? Æ Not for the young Universe:

Æ Not for the young Universe:

• Shortly after the big bang ( eg @ CMB: 380,000 yrs )

ll tt i d d t t l l ( t l i t)

• all matter is spread out evenly spread out evenly (no stars or galaxies yet)

• Universe is smaller smaller Æ everything closer together (by ×1000)

• the density is much higher density is much higher (by ×10

= a billion)

• 7 trillion photons & 7000 protons/electrons per cubic inch

• all at 5400ºF with pressure 10

(ten millionth) Earth’s atm.

Æ

Æ There is a hot thin atmosphere for sound waves There is a hot thin atmosphere for sound waves

• unusual fluid Æ intimate mix of gas & light g g

• sound waves propagate at ~50% speed of light

Big Bang Akustik

http://astsun.astro.virginia.edu/~dmw8f/teachco/

While the universe was still foggy, atomic matter was trapped by light's pressure and prevented from clumping up. In fact, this high-pressure gas of light and atomic matter responds to g p g g p the pull of gravity like air responds in an organ pipe – it

bounces in and out to make sound waves. This half-million year acoustic era is a truly remarkable and useful period of year acoustic era is a truly remarkable and useful period of cosmic history. To understand it better, we'll discuss the sound's pitch, volume, and spectral form, and explain how these sound waves are visible as faint patches on the Cosmic Microwave Background. Perhaps most bizarre: analyzing the CMB patchiness reveals in the primordial sound a p p

fundamental and harmonics – the young Universe behaves like a musical instrument! We will, of course, hear acoustic versions suitably modified for human ears

versions, suitably modified for human ears.

Akustik Ära

Since it is light which provides the pressure, the speed of pressure

waves (sound) is incredibly fast: vs ~ 0.6c! This makes sense: the gas is

i dibl li ht i ht d t it th f

incredibly lightweight compared to its pressure, so the pressure force moves the gas very easily. Equivalently, the photon speeds are, of

course, c – hence vs ~ c.

In summary: we have an extremely lightweight foggy gas of brilliant light and a trace of particles, all behaving as a single fluid with modest pressure and very high sound speed. With light dominating the

pressure and very high sound speed. With light dominating the

pressure, the primordial sound waves can also be thought of as great surges in light’s brilliance.

After recombination, photons and particles decouple; the pressure drops by ×10

and sound ceases. The acoustic era only lasts 400 kyr and is then over

only lasts 400 kyr, and is then over.

Where the sound comes from?

A too-quick answer might be: “of course there’s sound, it was a “big bang”

after all, and the explosion must have been very loud”. This is completely

an explosion into an atmosphere; it was an expansion of space itself. The Hubble law tells us that every point recedes from every other – there is no compression – no sound. Paradoxically, the

i

!

big bang was totally silent!

How, then, does sound get started? Later we’ll learn that although the

Universe was born silent it was also born very slightly

On all scales Universe was born silent, it was also born very slightly lumpy. On all scales, from tiny to gargantuan, there are slight variations in density, randomly scattered, everywhere – a 3D mottle of slight peaks and troughs in density.

We’ll learn how this roughness grows over time but for now just accept

We ll learn how this roughness grows over time, but for now just accept

this framework. The most important component for generating sound is

dominates the density, so it determines the gravitational landscape. y, g p

E h th h t b

Where the sound comes from?

Everywhere, the photon-baryon gas feels the pull of dark matter.

How does it respond? It begins to “fall” towards the over-dense regions, and away from the under-dense regions. Soon, however, its pressure is higher in the over dense regions and this halts and

pressure is higher in the over-dense regions and this halts and

the motion; pushing the gas back out. This time it

overshoots, only to turn around and fall back in again. The cycle repeats, and

repeats, and we have a sound wave!

The situation resembles a spherical organ pipe: gas bounces in and out of a roughly spherical region. [One caveat: “falling in” and

“bouncing out” of the regions is only relative g g y to the overall expansion, which continues throughout the acoustic era.]

Notice there is a quite different behavior between dark matter and the photon-baryon gas. Because the dark matter has no pressure (it interacts with nothing, not even itself), it is free to clump up under its own gravity. In contrast, the photon-baryon gas has pressure, which tries to keep it uniform (like air in a room). However, in the

l it ti l fi ld f d k tt it f ll d b thi

lumpy gravitational field of dark matter, it falls and bounces this

way and that in a continuing oscillation.

How does sound get to us ? How does sound get to us ?

Consider listening to a concert on the radio:

B + t i

Bow+string microphone

& amplifier

& antenna

ariel &

amplifier speakers

sound

radio waves radio waves

your your ears ears

Concert hall

Concert hall

Listener Listener

few µsec delay few µsec delay

gravity + hills/valleys

sound waves glow

glow telescope

computer k

sound

light light

your your ears

microwaves ears

microwaves

hills/valleys microwaves microwaves speakers ears ears

Li

very long way !

Li Big Bang

Big Bang

Listener Listener

The Big Bang is all around us ! The Big Bang is all around us !

Since looking in any any direction looks back to the foggy wall Æ we see the wall in all all directions.

Æ we see the wall in all all directions.

Æ the entire entire sky sky glows with microwaves

Æ the flash from the Big Bang is all all around around us us!

CMB Sound Spectrum

Click for sound

acoustic acoustic

i non-acoustic

er 2003

220 HzA

Lineweav

220 Hz

Akustische Peaks von WMAP

Kugelflächenfunktionen

l=4

l 8 l=8

Jede Funktion kann in orthogonale

Kugelflächenfkt. entwickelt werden. Große

W t

b h ib K l ti t

l=12

Werte von l beschreiben Korrelationen unter

kleinen Winkel.

• Temperaturverteilung ist

Vom Bild zum Powerspektrum

• Temperaturverteilung ist Funktion auf Sphäre:

ΔT(θ,φ) bzw. ΔT(n) = ΔΘ(n) T T

T T

n=(sinθcosφ,sinθsinφ,cosθ)

• Autokorrelationsfunktion:

C(θ)=<ΔΘ(n₁)·ΔΘ(n₂)>_|n1-n2|

=(4π)^-1 Σ^∞ (2l+1)C P (cosθ)

=(4π) ¹ Σ^∞_l=0 (2l+1)C_lP_l(cosθ)

• P_l sind die Legendrepolynome:

P_l(cosθ) = 2^-l·d^l/d(cos θ)^l(cos²θ-1)^l. P_l(cosθ) 2 d /d(cos θ) (cos θ 1) .

• Die Koeffizienten C_l bilden das Powerspektrum von ΔΘ(n).

mit cosθ=n1·n2

Das Leistungsspektrum (power spectrum)

Temperaturschwankungen als Fkt. des Öffnungswinkels

Θ ≈ 200/l

CMB Angular Power Spectrum

WMAP (2003)

current best data

×

(2006)

( model)

ACBARCBI BOOMERANG

DASI COBE

(1992) DASI

(1992)

er 2003Lineweav

Position des ersten Peaks

B h d Wi k l t

Raum Zeit x Berechnung der Winkel, worunter man die maximale Temperaturschwankungen der Grundwelle beobachtet:

Raum-Zeit x

t Inflation

Maximale Ausdehnung einer akust. Welle zum Zeitpunkt trec: c

* trec (1+z)

Beobachtung nach t

=13.8 10

yr.

Entkopplung

Beobachtung nach t

13.8 10 yr.

Öffnungswinkel θ = c

* t

* (1+z) / c*t

Mit (1+z)= 3000/2.7 =1100 und

trec = 3,8 10

yr und Schallgeschwindigkeit y g g c

=c/√3 für ein relativ. Plasma folgt:

θ

= 0.0175 = 1

(plus (kleine) ART Korrekt.)

Beachte: c

≡ dp/dρ = c

/3, da p= 1/3 ρc

max. ΔT / T

unter 1

s

p ρ , p ρ

Temperaturanisotropie der CMB

Position des ersten akustischen Peaks bestimmt

Krümmung des Universums!

Present and projected Results from CMB

See Wayne Hu's WWW-page:

See Wayne Hu s WWW-page:

http://background.uchicago.edu/~whu

180 /l θ =

t Conformal Space-Time

(winkelerhaltende Raum-Zeit)

Raum-Zeit x

t

/S(t) (1+ ) σ = x/S(t) = x(1+z)

η = t / S(t) = t (1+z) η σ

σ

CMB polarisiert durch Streuung an Elektronen (Thompson Streuung)

Kurz vor Entkoppelung:

Kurz vor Entkoppelung:

Streuung der CMB Photonen.

Nachher nicht mehr, da mittlere freie Weglange zu groß.

Lange vor der Entkopplung:

Polarisation durch Mittelung o s o du c e u g über viele Stöße verloren.

Nach Reionisation der Baryonen Nach Reionisation der Baryonen durch Sternentstehung wieder

Streuung.

Erwarte Polarisation also kurz

nach dem akust. Peak (l = 300) ( )

Entwicklung des Universums

Woher kennt man diese Verteilung?

If it is not dark,

it does not matter

it does not matter

Beobachtungen:

Ω 1 j d h

Ω=1, jedoch

Alter >>2/3H

Alte SN dunkler

als erwartet

Hubble Diagramm aus SN Ia Daten

Abstand aus dem Hubbleschen Gesetz mit Bremsparameter

q

=-0.6 und H=0.7 (100 km/s/Mpc) q

0.6 und H 0.7 (100 km/s/Mpc) z=1-> r=c/H(z+1/2(1-q

)z

)=

3 10

/(0 7 10

)(1+0 8) M 3.10

/(0.7x10

)(1+0.8) Mpc

= 7 Gpc

Abstand aus SN1a Helligkeit m Abstand aus SN1a Helligkeit m mit absoluter Helligkeit M=-19.6:

m=24.65 und log d=(m-M+5)/5) ->

Log d=(24.65+19.6+5)/5=9.85

= 7.1 Gpc p

Erste Evidenz für Vakuumenergie

Abstand Abstand

Perlmutter 2003 Perlmutter 2003

Abstand Abstand

Zeit

Zeit

SNIa compared with Porsche rolling up a hill

SNIa data very similar to a dark Porsche rolling up a hill and reading speedometer regularly, i.e. determining v(t), which can be used to reconstruct x(t) =∫v(t)dt

be used to reconstruct x(t) =∫v(t)dt.

(speed ⇒ distance, for universe Hubble law) This distance can be compared later

with distance as determined from the l i it f l t ( i

luminosity of lamp posts (assuming same brightness for all lamp posts)

(luminosity ⇒ distance, if SN1a treated as

‘standard’ candles with known luminosity)standard candles w th known lum nos ty) If the very first lamp posts are further away than expected, the conclusion must be that the Porsche instead of rolling up the that the Porsche instead of rolling up the hill used its engine, i.e. additional

acceleration instead of decelaration only.

(universe has additional acceleration (by dark

( ( y

energy) instead of decelaration only)

SN Type 1a wachsen bis Chandrasekhar Grenze Dann Explosion mit ≈ konstanter Leuchtkraft

SN1a originates from double star and explodes after reaching

and explodes after reaching Chandrasekhar mass limit

Vergleich mit den SN 1a Daten

SN1a empfindlich für Beschleunigung, d.h.

Ω Ω Ω

- Ω

Ω_Λ

CMB empfindlich für

Ω_Λ

totale Dichte d.h.

Ω

+ Ω

= (Ω_SM+ Ω_DM)

Present and projected Results from SN1a

a tellite N AP s a from S N c tations

SN I & Ω 1 & 1

Expe c

S I fi dli h fü Diff d A i h

SN Ia & Ω =1 & w=-1: Sn Ia nur empfindlich für Differenz der Anziehung

Combination of Observables

-ph/0302209 -ph/0302208el et al. astro- tt et al. astro-

The cosmological parameters describing the best fitting FRW d l

Sperge Bennet

model are:

Total density: Ω₀ = 1.02 ± 0.02

Vacuum energy density: Ω_Λ = 0.73 ± 0.04 Matter density: Ω_m = 0.27 ± 0.04 Baryon density: Ω_bb = 0.044 ± 0.004

Neutrino density: Ω_ν < 0.0147 (@ 95%CL) Hubble constant: h = 0.71 ± 0.04

Equation of state: w < -0.71 (@ 95%CL) Age of the universe: t = (13 7 ± 0 2) Gyr Age of the universe: t₀ = (13.7 ± 0.2) Gyr Baryon/Photon ratio: η = (6.1 ± 0.3) 10^-10

Resultate aus der Anisotropie der CMB kombiniert mit Abweichungen des Hubbleschen Gesetzes

The cosmological parameters describing the best fitting FRW model are:

T t l d it Ω 1 02 ± 0 02

Total density: Ω

= 1.02 ± 0.02 Vacuum energy density: Ω

= 0.73 ± 0.04 Matter density: Ω

= 0.27 ± 0.04 Baryon density: Ω

= 0.044 ± 0.004

Neutrino density: Ω

< 0.0147 (@ 95%CL) Hubble constant: h = 0.71 ± 0.04

Hubble constant: h 0.71 ± 0.04

Equation of state: w < -0.71 (@ 95%CL)

A f th i t (13 7 ± 0 2) G

Age of the universe: t

= (13.7 ± 0.2) Gyr

Baryon/Photon ratio: η = (6.1 ± 0.3) 10

Kosmologie wurde mit WMAP Satellit Präzisionsphysik in 2003

Present and projected Results from CMB

See Wayne Hu's WWW-page:

See Wayne Hu s WWW-page:

http://background.uchicago.edu/~whu

180 /l θ =

Zum Mitnehmen

Di CMB ib i Bild d f üh U i 380 000 h d U k ll d i

Die CMB gibt ein Bild des frühen Universums 380.000 yr nach dem Urknall und zeigt die Dichteschwankungen ∝ ΔT/T, woraus später die Galaxien entstehen.

Die CMB zeigt dassg

1. das das Univ. am Anfang heiß war, weil akustische Peaks, entstanden

durch akustische stehende Wellen in einem heißen Plasma, entdeckt wurden 2. die Temperatur der Strahlung im Universum 2.7 K ist wie erwartet bei einem

EXPANDIERENDEN Univ. mit Entkopplung der heißen Strahlung und Materie bei einer Temp. von 3000 K oder z=1100 (T ∝p ( 1/(1+z !)( )

3. das Univ. FLACH ist, weil die Photonen sich seit der letzten Streuung

zum Zeitpunkt der Entkopplung (LSS = last scattering surface) auf gerade Linien bewegt haben (in comoving coor )

Linien bewegt haben (in comoving coor.)

Zum Mitnehmen

If it is not dark,

it does not matter

it does not matter