Einteilung der VL
1. Einführung
2. Hubblesche Gesetz
3. Antigravitation
4. Gravitation
5. Entwicklung des Universums
6. Temperaturentwicklung
7. Kosmische Hintergrundstrahlung
8. CMB kombiniert mit SN1a
HEUTE
9. Strukturbildung
10. Neutrinos
11. Grand Unified Theories
12.-13 Suche nach DM
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
1
Vorlesung 8
Roter Faden:
1. Powerspektrum der CMB
2. Baryonic Acoustic Oscillations (BAO)
3. Energieinhalt des Universums
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
2
Akustische Peaks von WMAP
Ort-Zeit
Diagramm
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
3
Kugelflächenfunktionen
l
Jede Funktion kann in orthogonale
Kugelflächenfkt. entwickelt werden. Große
Werte von l beschreiben Korrelationen unter
kleinen Winkel.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
4
Sky Maps  Power Spectra
We “see” the CMB sound
as waves on the sky.
Use special methods
to measure the strength
of each wavelength.
peak
trough
Shorter wavelengths
are smaller frequencies
are higher pitches
Lineweaver 1997
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
5
Vom Bild zum Powerspektrum
• Temperaturverteilung ist
Funktion auf Sphäre:
ΔT(θ,φ) bzw. ΔT(n) = ΔΘ(n)
T
T
n=(sinθcosφ,sinθsinφ,cosθ)
• Autokorrelationsfunktion:
C(θ)=<ΔΘ(n1)∙ΔΘ(n2)>|n1-n2|
=(4π)-1 Σ∞l=0 (2l+1)ClPl(cosθ)
• Pl sind die Legendrepolynome:
Pl(cosθ) = 2-l∙dl/d(cos θ)l(cos²θ-1)l.
• Die Koeffizienten Cl bilden das
Powerspektrum von ΔΘ(n).
mit cosθ=n1∙n2
Wim de Boer, Karlsruhe
„Weißes Rauschen“:
flaches Powerspektrum
Kosmologie VL, 13.12.2012
6
Temperaturschwankungen als Fkt. des Öffnungswinkels
Balloon exp.
Wim de Boer, Karlsruhe
Θ  180/l
Kosmologie VL, 13.12.2012
7
Das Leistungsspektrum (power spectrum)
Ursachen für Temperatur
Schwankungen:
Große Skalen:
Gravitationspotentiale
Kleine Skalen:
Akustische Wellen
l=1 nicht gezeigt, da
sehr stark wegen
Dipolterm durch
Bewegung der Galaxie
gegenüber CMB
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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Temperaturanisotropie der CMB
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
9
Position des ersten akustischen Peaks bestimmt
Krümmung des Universums!
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
10
Position des ersten Peaks
Raum-Zeit
t
x
Inflation
Berechnung der Winkel, worunter man
die maximale Temperaturschwankungen
der Grundwelle beobachtet:
Entkopplung
Maximale Ausdehnung einer akust. Welle
zum Zeitpunkt trec: cs * trec (1+z)
Beobachtung nach t0 =13.8 109 yr.
Öffnungswinkel θ = cs * trec * (1+z) / c*t0
Mit (1+z)= 3000/2.7 =1100 und
trec = 3,8 105 yr und Schallgeschwindigkeit
cs=c/3 für ein relativ. Plasma folgt:
θ = 0.0175 = 10 (plus (kleine) ART Korrekt.)
max. T / T
unter 10
Beachte: cs2 ≡ dp/d = c2/3, da p= 1/3 c2
nλ/2=cstr
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
11
CMB zeigt: Un iversum ist flach
Erste akustische Peak unter bei einem
Öffnungswinkel von 0.8 Grad oder l=220
bedeutet:
das Universum ist flach
oder die mittlere Dichte entspricht der
kritischen Dichte von 2. 10-29 g/cm3 oder =1
und
Gesamtenergie (kin. + pot. Energie) ist Null!
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
12
Präzisere Berechnung des ersten Peaks
Vor Entkopplung Universum teilweise strahlungsdominiert.
Hier ist die Expansion  t1/2 statt t2/3 in materiedominiertes Univ.
Muss Abstände nach bewährtem Rezept berechnen:
Erst in mitbewegten Koor. und dann x S(t)
Abstand < trek: S(t) c d = S(t) c dt/S(t) = 2ctrek für S  t1/2
Abstand > trek: S(t) c d =S(t)c dt/S(t) = 3ctrek für S  t2/3
Winkel θ = 2 * cs * trec * (1+z) / 3*c*t0 = 0.7 Grad
Auch nicht ganz korrekt, denn Univ. strahlungsdom. bis t=50000 a,
nicht 380000 a. Richtige Antwort: Winkel θ = 0.8 Grad oder l=180/0.8=220
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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WMAP analyzer tool
http://wmap.gsfc.nasa.gov/resources/camb_tool/index.html
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
14
Neueste WMAP Daten (2008)
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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Neueste WMAP Daten (2008)
http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.0732v2.pdf
Polarisation
Reionisation
nach 2.108 a
Temperatur
Temperatur- und Polarisationsanisotropien um 90 Grad in Phase verschoben,
weil Polarisation Fluss der Elektronen, also wenn x  cos (t), dann v  sin (t)
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
16
CMB Polarisation durch Thomson Streuung
(elastische Photon-Electron Streuung)
Prinzip: unpolarisiertes Photon unter 90 Grad gestreut, muss immer
noch E-Feld  Richtung haben, so eine Komponente verschwindet!
Daher bei Isotropie keine Pol. , bei Dipol auch nicht, nur bei Quadr.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
17
CMB Polarisation bei Quadrupole-Anisotropie
Polarization entweder radial oder tangential um hot oder cold spots
(proportional zum Fluss der Elektronen, also zeigt wie Plasma sich
bewegte bei z=1100 and auf große Skalen wie Plasma in Galaxien
Cluster sich relativ zum CMB bewegt)
http://gyudon.as.utexas.edu/~komatsu/presentation/wmap7_ias.pdf
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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Entwicklung des Universums
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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CMB polarisiert durch Streuung an Elektronen
(Thomson Streuung)
Kurz vor Entkoppelung:
Streuung der CMB Photonen.
Nachher nicht mehr, da mittlere
freie Weglange zu groß.
Lange vor der Entkopplung:
Polarisation durch Mittelung
über viele Stöße verloren.
Nach Reionisation der Baryonen
durch Sternentstehung wieder
Streuung.
Erwarte Polarisation also kurz
nach dem akust. Peak (l = 300)
und auf großen Abständen (l < 10)
Instruktiv:http://background.uchicago.edu/~whu/polar/webversion/node1.htm
20
l
Wim de Boer, Karlsruhe Kosmologie VL, 13.12.2012
Conformal Space-Time
(winkel-erhaltende Raum-Zeit)
t
Raum-Zeit
t
x
x
From Ned Wright homepage
 = x/S(t) = x(1+z)
t



Wim de Boer, Karlsruhe
 = t / S(t) = t (1+z)
conformal=winkelerhaltend
z.B. mercator Projektion
Kosmologie VL, 13.12.2012
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Woher kennt man diese Verteilung?
If it is not dark,
it does not matter
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
22
Vergleich mit den SN 1a Daten
SN1a empfindlich für
Beschleunigung a, d.h.
a   - m (beachte:
DM und DE unterscheiden sich im VZ der Grav.

CMB empfindlich für
totale Dichte d.h.
tot =  + m =1
= (SM+ DM)
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
23
Akustische Baryon Oszillationen I:
http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html
Let's consider what happens to a pointlike initial perturbation. In other words,
we're going to take a little patch of space
and make it a little denser. Of course, the
universe has many such patchs, some
overdense, some underdense. We're just
going to focus on one. Because the
fluctuations are so small, the effects of
many regions just sum linearly.
The relevant components of the universe
are the dark matter, the gas (nuclei and
electrons),
the
cosmic
microwave
background photons, and the cosmic
background neutrinos.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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Akustische Baryon Oszillationen II:
http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html
Now what happens?
The neutrinos don't interact with anything and are too fast
to be bound gravitationally, so they begin to stream away
from the initial perturbation.
The dark matter moves only in response to gravity and has
no intrinsic motion (it's cold dark matter). So it sits still.
The perturbation (now dominated by the photons and
neutrinos) is overdense, so it attracts the surroundings,
causing more dark matter to fall towards the center.
The gas, however, is so hot at this time that it is ionized. In
the resulting plasma, the cosmic microwave background
photons are not able to propagate very far before they
scatter off an electron. Effectively, the gas and photons are
locked into a single fluid. The photons are so hot and
numerous, that this combined fluid has an enormous
pressure relative to its density. The initial overdensity is
The result is that the perturbation in therefore also an initial overpressure. This pressure tries
the gas and photon is carried outward: to equalize itself with the surroundings, but this simply
results in an expanding spherical sound wave. This is just
like a drum head pushing a sound wave into the air, but
the speed of sound at this early time is 57% of the speed of
light!
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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Akustische Baryon Oszillationen III:
http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html
As time goes on, the spherical shell of gas
and photons continues to expand. The
neutrinos spread out. The dark matter
collects in the overall density perturbation,
which is now considerably bigger because
the photons and neutrinos have left the
center. Hence, the peak in the dark matter
remains centrally concentrated but with an
increasing width. This is generating the
familiar turnover in the cold dark matter
power spectrum.
Where is the extra dark matter at large
radius coming from? The gravitational
forces are attracting the background
material in that region, causing it to contract
a bit and become overdense relative to the
background further away
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
26
Akustische Baryon Oszillationen IV:
http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html
The expanding universe is cooling.
Around
400,000
years,
the
temperature is low enough that the
electrons and nuclei begin to combine
into neutral atoms. The photons do
not scatter efficiently off of neutral
atoms, so the photons begin to slip
past the gas particles. This is known
as Silk damping (ApJ, 151, 459, 1968).
The sound speed begins to drop
because of the reduced coupling
between the photons and gas and
because the cooler photons are no
longer very heavy compared to the
gas. Hence, the pressure wave slows
down.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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Akustische Baryon Oszillationen V:
http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html
This continues until the photons have
completely leaked out of the gas
perturbation. The photon perturbation
begins to smooth itself out at the speed
of light (just like the neutrinos did).
The
photons
travel
(mostly)
unimpeded until the present-day,
where we can record them as the
microwave background (see below).
At this point, the sound speed in the
gas has dropped to much less than the
speed of light, so the pressure wave
stalls.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
28
Akustische Baryon Oszillationen VI:
http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html
We are left with a dark matter
perturbation around the original
center and a gas perturbation in a shell
about 150 Mpc (500 million lightyears) in radius.
As time goes on, however, these two
species gravitationally attract each
other. The perturbations begin to mix
together.
More
precisely,
both
perturbations are growing quickly in
response to the combined gravitational
forces of both the dark matter and the
gas. At late times, the initial
differences are small compared to the
later growth.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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Akustische Baryon Oszillationen VII:
http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html
Eventually, the two look quite
similar. The spherical shell of the
gas perturbation has imprinted
itself in the dark matter. This is
known as the acoustic peak.
The acoustic peak decreases in
contrast as the gas come into lockstep with the dark matter simply
because the dark matter, which has
no peak initially, outweighs the gas
5 to 1.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
30
Akustische Baryon Oszillationen VIII:
http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html
Before we have been plotting the mass profile
(density times radius squared). The density
profile is much steeper, so that the peak at 150
Mpc is much less than 1% of the density near
the center.
Wim de Boer, Karlsruhe
At late times, galaxies form in the
regions that are overdense in gas and
dark matter. For the most part, this is
driven
by
where
the
initial
overdensities were, since we see that the
dark matter has clustered heavily
around these initial locations. However,
there is a 1% enhancement in the
regions 150 Mpc away from these
initial overdensities. Hence, there
should be an small excess of galaxies
150 Mpc away from other galaxies, as
opposed to 120 or 180 Mpc. We can see
this as a single acoustic peak in the
correlation function of galaxies.
Alternatively, if one is working with the
power spectrum statistic, then one sees
the effect as a series of acoustic
oscillations.
Kosmologie VL, 13.12.2012
31
One little telltale bump !!
 (r )   (r1 ) (r2 )
A small excess in
correlation at 150 Mpc.!
SDSS survey
(astro-ph/0501171)
(Einsentein et al. 2005)
150 Mpc.
150 Mpc =2cs tr (1+z)=akustischer Horizont
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
32
Akustische Baryonosz. in Korrelationsfkt. der
Dichteschwankungen der Materie!
150 Mpc.
105 h-1 ¼ 150
The same CMB
oscillations at
low redshifts !!!
SDSS survey
(astro-ph/0501171)
(Eisentein et al. 2005)
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
33
Combined results
http://arxiv.org/PS_cache/arxiv/pdf/0804/0804.4142v1.pdf
http://nedwww.ipac.caltech.edu/level5/March08/Frieman/Frieman4.html
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
34
Zum Mitnehmen
Die CMB gibt ein Bild des frühen Universums 380.000 yr nach dem Urknall und zeigt
die Dichteschwankungen  T/T, woraus später die Galaxien entstehen.
Die CMB zeigt dass
1. 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  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.)
4) BAO wichtig, weil Sie unabhängig von der akustischen Horizont in der CMB ein
zweiter wohl definierter Maßstab (akustischer Horizont der Materie) bestimmt,
dessen Vergrößerung heute gemessen werden kann. Dies bestätigt die
Energieverteilung des Univ. unabh. von der Frage ob SN1a Standardkerzen sind.
5) Polarisation der CMB bestätigt Natur der Dichtefluktuationen zum Zeitpunkt der
Entkopplung und bestimmt Zeitpunkt der Sternbildung (Ionisation->Polarisation)
Die schnelle Sternbildung kann nur mit Potentialtöpfen der DM zum Zeitpunkt der
Entkopplung erklärt werden. (die neutrale Kerne fallen da hinein).
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
35
Zum Mitnehmen
If it is not dark,
it does not matter
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
36
Zusatzfolien mit Text der Nobelpreisankündigungen
„just for fun“, kein Prüfungsstoff.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
37
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
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 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
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
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
38
Early work
The discovery of the cosmic microwave background radiation has an
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
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
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.
From Nobel prize 2006 announcement
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
39
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
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
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
explain energy level transitions in interstellar molecules (McKellar 1941). CN=Cyan
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
is discussed by Alpher, Herman and Gamow 1967, Penzias 1979, Wilkinson and
Peebles 1983, Weinberg 1993, and Herman 1997.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
40
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
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
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
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
Wolfe 1967).
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
41
Dipol Anisotropy
Because the earth moves relative to the CMB, a dipole temperature
anisotropy of the level of ΔT/T = 10-3 is expected. This was observed in the
1970’s (Conklin 1969, Henry 1971, Corey and Wilkinson 1976 and Smoot,
Gorenstein and Muller 1977). During the 1970-tis the anisotropies were
expected to be of the order of 10-2 – 10-4, but were not observed
experimentally. When dark matter was taken into account in the 1980-ties,
the predicted level of the fluctuations was lowered to about 10-5, thereby
posing a great experimental challenge.
Explanation: two effects compensate the temperature anisotropies:
DM dominates the gravitational potential after str<< m
so hot spots in the grav. potential wells of DM have a higher
temperature, but photons climbing out of the potential well
get such a strong red shift that they are COLDER than the
average temperature!
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
42
The COBE mission
Because of e.g. atmospheric absorption, it was long realized that
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
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
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
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
leader from the start. He was also responsible for the FIRAS instrument. George
Smoot was the DMR principal investigator and Mike Hauser was the DIRBE principal
investigator.
43
Wim de Boer, Karlsruhe Kosmologie VL, 13.12.2012
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
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
the objective was to measure the spectral distribution of the
CMB in the range 0.1 – 10 mm and compare it with the
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,
respectively.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
44
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
cosmology a precision science. Predictions of the Big
Bang model were confirmed: temperature
fluctuations of the order of 10-5 were found and the
background radiation with a temperature of 2.725 K
followed very precisely a blackbody spectrum.
DIRBE made important observations of the infrared
background. The announcement of the discovery of
the anisotropies was met with great enthusiasm
worldwide.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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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
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.
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
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
the 1° resolution WMAP (Wilkinson Microwave Anisotropy Probe) satellite, launched
in 2001 (Bennett et al. 2003).
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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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.
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
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
of the Universe according to the standard cosmological model. The first stages after the
Big Bang are still speculations.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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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
produced: a broad range with a peak.
The thermal spectrum’s shape depends only on temperature: Hotter objects
appear bluer: the peak shifts to shorter wavelengths, with: pk = 0.0029/TK
m = 2.9106/T nm. At 10,000K we have peak = 290 nm (blue), while at
3000K we have peak = 1000 nm (deep orange/red).
Let’s now follow through the color of the Universe during its first million
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
paints its sky with a human palette.
Quantitatively: since peak ~ 3106/T nm, and T ~ 3/S K, then peak ~ 106 /
S nm. Notice that today, S = 1 and so peak = 106 nm = 1 mm, which is, of
course, the peak of the CMB microwave spectrum.
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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Light Intensity
Hotter objects appear brighter. There are two reasons for this:
More violent particle collisions make more energetic photons. Converting pk ~
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
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 T4 Watt /m2 inside a gas at
temperature T.
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.
Float in outer space, exposed only to the CMB, and you experience a radiation
field of I3K = 2.210-72.74 = 10 W/m2 = 10-8 Isun – not much! Here on Earth at
300K we have I300K ~ 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) has I1800K = 2.3 MW/m2 = 1600 Isun (you boil away in ~1 minute).
At the time of the CMB (380 kyr), the radiation intensity was I3000K = 17 MW/m2
= 12,000 Isun – you evaporate in 10 seconds.
In the Sun’s atmosphere, we have I5800K = 250 MW/m2 = 210,000 Isun. That’s a
major city’s power usage, falling on each square meter.
Radiation in the Sun’s 14 million K core has: I = 81021 W/m2 ~ 1019 Isun (you
boil away in much less than a nano-second).
Wim de Boer, Karlsruhe
Kosmologie VL, 13.12.2012
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