Wim de Boer, KarlsruheKosmologie VL, 27.11.2009 1 Vorlesung 6+7 Roter Faden: 1.Cosmic Microwave Background radiation (CMB) 2.Akustische Peaks 3.Universum

Wim de Boer, Karlsruhe Kosmologie VL, 27.11.2009 1

Vorlesung 6+7

Roter Faden:

1. Cosmic Microwave Background radiation (CMB)2. Akustische Peaks3. Universum ist flach4. Baryonic Acoustic Oscillations (BAO)5. Energieinhalt des Universums


Zum Mitnehmen

Temperaturentwicklung im frühen Universum: T = (3c2/8aG)1/4 1/t = 1,5 1010 K (1s/t) = 1,3 MeV (1s/t)

Nach der Rekombination der Protonen und Elektronen zu neutralem Wasserstoff wird das Universum transparent für Photonen und absolut dunkel bis nach 200 Myr Sterne entstehen (dark ages)

Die nach der Rekombination frei entweichende Photonen sind heute noch beobachtbar als kosmische Hintergrundstrahlung mit einer Temperatur von 2.7 K Es gilt: T 1/S für Strahlung und relativ. Materie (E>10mc2) 1/S 1+z (gilt immer) T 1/ t (wenn Strahlung und relat. Materie dominiert, gilt

nicht heute, denn zusätzliche Exp. durch Vakuumenergie)

Hiermit zu jedem Zeitpunkt Energie oder Temperatur mit Dreisatz im frühen Universum zu berechnen, wenn man weiß: zum Zeitpunkt der Rekombination: (Trec=3000 K) = 380.000 yr =(z=1100)


Nach Stefan-Boltzmann: Str T4 Es gilt auch: Str N E 1/S4

Daher gilt für die Temperatur des Strahlung: T 1/S Hiermit kann man die Fríedmann Gl. umschreiben als Funkt. von T! Es gilt: dT d(1/S) oder S/S -T/T und 1/S2 T2

Im strahlungsdominierten Universum kann man schreiben:

(S/S)2 = (T/T)2 = 8GaT4/3c2 (Str=aT4>>m und k/S2 und )

Lösung dieser DG: T = (3c2/8aG)1/4 1/t = 1,5 1010 K (1s/t) = 1,3 MeV (1s/t) In Klartext: 1 s nach dem Urknall ist die Temperatur gefallen von der Planck Temperatur von 1019 GeV auf 10-3 GeV

Temperaturentwicklung des Universums

Entkoppelung der CMB bei T= 0,3 eV = 3000 K oder t = 3.105 yr oder z = S0/S = T/T0 = 3000 / 2.7 = 1100


Nach Rekombination ‘FREE STREAMING’ der Photonen


Last Scattering Surface (LSS)


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

Patches in the brightness are about 1 part in 100,000 = a bacterium on a bowling ball = 60 meter waves on the surface of the Earth.


Temperatur-Fluktuationen = DichtefluktuationenWMAP vs COBE

7

0.2

45 times sensitivityWMAP ΔT/T200uK/2.7K


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.

Cosmology and the Cosmic Microwave Background

From Nobel prize 2006 announcement


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.

Early work

From Nobel prize 2006 announcement


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). 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.

First observations of CMB

CN=Cyan


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).

Further observations of CMB


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 tehe 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.

Dipol Anisotropy

Explanation: two effects compensate the temperature anisotropies:DM dominates the gravitational potential after str<<mso hot spots in the grav. potential wells of DM have a highertemperature, but photons climbing out of the potential wellget such a strong red shift that they are COLDER than the average temperature!


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.

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.

The COBE mission


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.

The COBE success


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).

CMB Anisotropies


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.

Outlook


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 = 2.9106/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 ~ 3106/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.

The colour of the universe


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 = 2.210-7 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 = 2.210-72.74 = 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 = 81021 W/m2 ~ 1019 Isun (you boil away in much less than a nano-second).

Light Intensity


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 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.


Lösung:Druck gering: δ=aebt , d.h. exponentielle Zunahme von δ (->Gravitationskollaps)Druck groß: δ=aeibt , d.h. Oszillation von δ (akustische Welle)

Definiere: δ=Δρ/ρ

Newton: F=maδ``+ (Druck-Gravitation) δ=0

Warum akustische Wellen im frühen Universum?

FG

PF=ma

Rücktreibende Kraft: GravitationAntreibende Kraft: Photonendruck


• Photonen, Elektronen, Baryonen wegen der starken Kopplung wie eine Flüssigkeit behandelt → ρ, v, p

• Dunkle Materie dominiert das durch die Dichtefluktuationen hervorgerufene Gravitationspotential Φ

• δρ/δt+(ρv)=0 (Kontinuitätsgleichung = Masse-Erhaltung))

• v+(v∙)v = -(Φ+p/ρ)(Euler Gleichung = Impulserhaltung)

² Φ = 4πGρ (Poissongleichung = klassische Gravitation)

• erst nach Überholen durch den akustischen Horizont Hs= csH-1 , (cs = Schallgeschwindigkeit) können die ersten beiden Gleichungen verwendet werden

• Lösung kann numerisch oder mit Vereinfachungen analytisch bestimmt werden und entspricht grob einem gedämpftem harmonischen Oszillator mit einer antreibenden Kraft

Mathematisches Modell

Tiefe des Potentialtopfs be-stimmt durch dunkle Materie


T / T

Entwicklung der Dichtefluktuationen im Universum

Man kann die Dichtefluktuationenim frühen Univ. als Temp.-Fluktuationender CMB beobachten!


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

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

rarefactioncompressioncompression

dim

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

the oscillation continues the oscillation continues sound waves are createdsound 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.• We see the bright/dim regions as patchiness on the CMB.

The first sound wavesThe first sound waves


Akustische Wellen im frühen Universum

Überdichten am Anfang: Inflation


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

Druck der akust. Welle und Gravitation verstärken die Temperaturschwankungen in der Grundwelle (im ersten Peak)


Druck der akust. Welle und Gravitation wirken gegeneinander in der Oberwelle ( im zweiten Peak)


Mark WhittleMark WhittleUniversity of VirginiaUniversity of Virginia

Viele Plots und sounds von Whittles Webseite

http://www.astro.virginia.edu/~dmw8fSee also: “full presentation”See also: “full presentation”

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


Akustische Wellen im frühen Universum

Überdichten am Anfang: Inflation

Bь Clarinet

Modern Flute

piano range

Joe Wolfe (UNSW)Flute power spectra


Lineweaver 1997

peak

trough

Sky Maps Power Spectra

We “see” the CMB sound We “see” the CMB sound as as waves on the skywaves on the sky. .

Use special methods Use special methods to measure the to measure the strengthstrength of each wavelength.of each wavelength.

Shorter wavelengthsShorter wavelengthsare smaller frequenciesare smaller frequenciesare higher pitchesare higher pitches


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

all “superimposed”all “superimposed”

Sound wavesSound waves : :red/blue = high/lowred/blue = high/lowgas & light pressuregas & light pressure

Water wavesWater waves : :high/low level ofhigh/low level ofwater surfacewater surface

Sound waves in the skySound waves in the skyThis 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.


This distribution has a lot of long wavelength power

and a little short wavelength power

Power (Leistung) pro Wellenlänge)


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

• Shortly after the big bang (eg @ CMB: 380,000 yrs)• all matter is spread out evenly spread out evenly (no stars or galaxies yet)• Universe is smaller smaller everything closer together (by ×1000)• the density is much higherdensity is much higher (by ×109 = a billion)• 7 trillion photons & 7000 protons/electrons per cubic inch• all at 5400ºF with pressure 10-7 (ten millionth) Earth’s atm.

There is a hot thin atmosphere for sound wavesThere is a hot thin atmosphere for sound waves• unusual fluid intimate mix of gas & light• sound waves propagate at ~50% speed of light

Sound in space !?!Sound in space !?!


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

Big Bang Akustikhttp://astsun.astro.virginia.edu/~dmw8f/teachco/


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 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, 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 10-9 and sound ceases. The acoustic era only lasts 400 kyr, and is then over.

Akustik Ära


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 wrong. The big bang was not 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 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 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 this framework. The most important component for generating sound is dark matter. Recall that after equality (m = r at 57 kyr) dark matter dominates the density, so it determines the gravitational landscape.

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 reverses the motion; pushing the gas back out. This time it overshoots, only to turn around and fall back in again. The cycle 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 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 lumpy gravitational field of dark matter, it falls and bounces this way and that in a continuing oscillation.

Where the sound comes from?


Consider listening to a concert on the radio:

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


Since looking in anyany direction looks back to the foggy wall we see the wall in allall directions. the entire skyentire sky glows with microwaves the flash from the Big Bang is all around usall around us!

Near

Far

Now red-shift Then

Big BangBig Bang

Far NearThen red-shift Now

Big

Ban

gB

i g B

ang

Big BangBig Bang

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


Akustische Peaks von WMAP


Line

wea

ver 2

003

Frequency (in Hz)

A220 Hz

CMB Sound Spectrum

Click forsound

acoustic

non-acoustic


Kugelflächenfunktionen

Jede Funktion kann in orthogonale Kugelflächenfkt. entwickelt werden. Große Werte von l beschreiben Korrelationen unter kleinen Winkel.

l=4

l=8

l=12


• 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

Vom Bild zum Powerspektrum


Das Leistungsspektrum (power spectrum)

ω = vk = v 2/λ


Temperaturschwankungen als Fkt. des Öffnungswinkels

Θ 180/l


Position des ersten Peaks

Berechnung der Winkel, worunter mandie maximale Temperaturschwankungen der Grundwelle beobachtet:

Maximale Ausdehnung einer akust. Wellezum 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.)

Beachte: cs2 ≡ dp/d = c2/3, da p= 1/3 c2

Raum-Zeit x

tInflation

Entkopplung

max. T / T unter 10

nλ/2=cstr


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 mitbewegende 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


Temperaturanisotropie der CMB


Position des ersten akustischen Peaks bestimmt Krümmung des Universums!


Present and projected Results from CMB

180 / l

See Wayne Hu's WWW-page: http://background.uchicago.edu/~whu/

Verhältnis peak1/peak2->BaryondichtePosition erster Peak->Flaches Univ.


Open : Ω= 0.8

Flat : Ω= 1.0

Closed: Ω=1.2

Low pitch High pitchLong wavelength Short wavelength

Geometry of the Universe


8% atoms

4% atoms

2% atoms

Low pitch High pitchLong wavelength Short wavelength

Atomic content of the Universe


= x/S(t) = x(1+z)

Raum-Zeit xt

= t / S(t) = t (1+z)

Conformal Space-Time(winkelerhaltende Raum-Zeit)

conformal=winkelerhaltendz.B. mercator Projektion

x

t

t

From Ned Wright homepage


CMB polarisiert durch Streuung an Elektronen (Thompson Streuung)

Kurz vor Entkoppelung:Streuung der CMB Photonen.Nachher nicht mehr, da mittlerefreie Weglange zu groß.Lange vor der Entkopplung:Polarisation durch Mittelungüber viele Stöße verloren.

Nach Reionisation der Baryonendurch Sternentstehung wieder Streuung.

Erwarte Polarisation also kurznach dem akust. Peak (l = 300)und auf großen Abständen (l < 10)


Entwicklung des Universums


If it is not dark,it does not matter

Woher kennt man diese Verteilung?


Beobachtungen:Ω=1, jedochAlter >>2/3H0

Alte SN dunklerals erwartet


Erste Evidenz für Vakuumenergie


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 canbe used to reconstruct x(t) =∫v(t)dt. (speed distance, for universe Hubble law)This distance can be compared laterwith distance as determined from the luminosity of lamp posts (assuming same brightness for all lamp posts)(luminosity distance, if SN1a treated as ‘standard’ candles with known luminosity)

If the very first lamp posts are further away than expected, the conclusion must be 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 energy) instead of decelaration only)


SN1a originates from double star and explodes after reachingChandrasekhar mass limit

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


Zeit

Perlmutter Perlmutter 20032003

AbstandAbstand


Vergleich mit den SN 1a Daten

SN1a empfindlich für Beschleunigung, d.h. - m

CMB empfindlich für totale Dichte d.h. + m

= (SM+ DM)


Let's consider what happens to a point-like 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.

Akustische Baryon Oszillationen I: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html


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 therefore also an initial overpressure. This pressure tries 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!

The result is that the perturbation in the gas and photon is carried outward:


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


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.


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.


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 light-years) 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.


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 lock-step with the dark matter simply because the dark matter, which has no peak initially, outweighs the gas 5 to 1.


Akustische Baryon Oszillationen VIII: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html

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.

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.


One little telltale bump !! A small excess in correlation at 150

Mpc.!SDSS survey

(astro-ph/0501171)

150 Mpc.

(Einsentein et al. 2005)

1 2( ) ( ) ( )r r r

150 Mpc =2cs tr (1+z)=akustischer Horizont


2-po

int c

o rre

latio

n of

de

nsi ty

con

tra s

t

The same CMB oscillations at

low redshifts !!!SDSS survey

(astro-ph/0501171)

150 Mpc.

(Einsentein et al. 2005)

105 h-1 ¼ 150

Akustische Baryonosz. in Korrelationsfkt. der Dichteschwankungen der Materie!


http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.0732v2.pdf

Neueste WMAP Daten (2008)


http://wmap.gsfc.nasa.gov/resources/camb_tool/index.html

WMAP analyzer tool

http://wmap.gsfc.nasa.gov/resources/camb_tool/index.html


http://nedwww.ipac.caltech.edu/level5/March08/Frieman/Frieman4.html

Combined results

http://arxiv.org/PS_cache/arxiv/pdf/0804/0804.4142v1.pdf


Neueste WMAP Daten (2008)


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

Die CMB zeigt dass

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 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.)


If it is not dark,it does not matter

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Documents

Wim de Boer, KarlsruheKosmologie VL, 27.11.2009 1 Vorlesung 6+7 Roter Faden: 1.Cosmic Microwave Background radiation (CMB) 2.Akustische Peaks 3.Universum