Vorlesung 6+7 Roter Fadendeboer/html/Lehre/... · Peebles 1983, Weinberg 1993, and Herman 1997. Further observations of CMB Following the 1964 discovery, several independent measurements

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

Wim de Boer, Karlsruhe Kosmologie VL, 27.11.2011 1

The oval shapesshow a sphericalsurface, as in aglobal map. Theglobal map. Thewhole sky can bethought of as theinside of a sphere.

Patches in thebrightness areabout 1 part in100,000 = abacterium on a

ibowling ball =60 meter waveson the surfacef th E th


of the Earth.

Last Scattering Surface (LSS)


Temperatur-Fluktuationen = DichtefluktuationenWMAP vs COBE

7

0.2 0.2

45 times sensitivityWMAP ΔT/T 200 K/2 7K


WMAP ΔT/T200uK/2.7K

Cosmology and the Cosmic Microwave Background

The Universe is approximately about 13.7 billion years old, according to thestandard cosmological Big Bang model. At this time, it was a state of high

if i l h d d fill d i h l i luniformity, was extremely hot and dense was filled with elementary particlesand was expanding very rapidly. About 380,000 years after the Big Bang, theenergy of the photons had decreased and was not sufficient to ionise hydrogen

t Th ft th h t “d l d” f th th ti l d ldatoms. Thereafter the photons “decoupled” from the other particles and couldmove through the Universe essentially unimpeded. The Universe has expandedand cooled ever since, leaving behind a remnant of its hot past, the CosmicMicrowave Background radiation (CMB) We observe this today as a 2 7 KMicrowave Background radiation (CMB). We observe this today as a 2.7 K thermal blackbody radiation filling the entire Universe. Observations of theCMB give a unique and detailed information about the early Universe, therebypromoting cosmology to a precision science Indeed as will be discussed inpromoting cosmology to a precision science. Indeed, as will be discussed in more detail below, the CMB is probably the best recorded blackbody spectrumthat exists. Removing a dipole anisotropy, most probably due our motionthrough the Universe, the CMB is isotropic to about one part in 100,000. Thethrough 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 y gunusual and interesting history. The basic theories as well as the necessaryexperimental techniques were available long before the experimental discovery in 1964 The theory of an expanding Universe was first given bydiscovery in 1964. The theory of an expanding Universe was first given byFriedmann (1922) and Lemaître (1927). An excellent account is given byNobel laureate Steven Weinberg (1993). Around 1960 a few years before the discovery two scenarios for theAround 1960, a few years before the discovery, two scenarios for theUniverse were discussed. Was it expanding according to the Big Bang model, or was it in a steady state? Both models had their supporters and

h i i d i h l H Alf é (N b l iamong the scientists advocating the latter were Hannes Alfvén (Nobel prizein physics 1970), Fred Hoyle and Dennis Sciama. If the Big Bang model was the correct one, an imprint of the radiation dominated early Universemust 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

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 ofunexpected noise in their radio-receiver (they shared the 1978 Nobel prize in physics for the discovery). The radiation produced unexpected noise in their radioreceivers. Some 16 years earlier Alpher, Gamow and Herman (Alpher and Herman 1949, Gamow 1946), had predicted that there should be a relic radiation fieldpenetrating the Universe. It had been shown already in 1934 by Tolman (Tolman1934) that the cooling blackbody radiation in an expanding Universe retains itsbl kb d f I h i h Al h G H d d iblackbody form. It seems that neither Alpher, Gamow nor Herman succeeded in convincing experimentalists to use the characteristic blackbody form of theradiation to find it. In 1964, however, Doroshkevich and Novikov (Doroshkevich

d N ik 1964) bli h d ti l h th li itl t d h fand Novikov 1964) published an article where they explicitly suggested a search forthe radiation focusing on its blackbody characteristics. One can note that somemeasurements as early as 1940 had found that a radiation field was necessary toexplain energy level transitions in interstellar molecules (McKellar 1941) CN=Cyanexplain energy level transitions in interstellar molecules (McKellar 1941). Following the 1964 discovery of the CMB, many, but not all, of the steady stateproponents gave up, accepting the hot Big Bang model. The early theoretical workis discussed by Alpher Herman and Gamow 1967 Penzias 1979 Wilkinson and

CN=Cyan


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

Further observations of CMB

Following the 1964 discovery, several independent measurements of theradiation were made by Wilkinson and others, using mostly balloon-borne, rocket-borne or ground based instruments The intensity of the radiation hasrocket-borne or ground based instruments. The intensity of the radiation hasits maximum for a wavelength of about 2 mm where the absorption in theatmosphere is strong. Although most results gave support to the blackbodyform fe meas rements ere a ailable on the high freq enc (loform, few measurements were available on the high frequency (lowwavelength) side of the peak. Some measurements gave results that showedsignificant deviations from the blackbody form (Matsumoto et al. 1988). The CMB was expected to be largely isotropic. However, in order to explainthe large scale structures in the form of galaxies and clusters of galaxiesobserved today, small anisotropies should exist. Gravitation can make smalldensity fluctuations that are present in the early Universe grow and makegalaxy formation possible. A very important and detailed general relativisticcalculation by Sachs and Wolfe showed how three-dimensional densityy yfluctuations can give rise to two-dimensional large angle (> 1°) temperatureanisotropies in the cosmic microwave background radiation (Sachs andWolfe 1967)


Wolfe 1967).

Dipol Anisotropy

Because the earth moves relative to the CMB, a dipole temperatureanisotropy of the level of ΔT/T = 10-3 is expected This was observed in theanisotropy of the level of ΔT/T = 10 3 is expected. This was observed in the1970’s (Conklin 1969, Henry 1971, Corey and Wilkinson 1976 and Smoot, Gorenstein and Muller 1977). During the 1970-tis the anisotropies were

t d t b f th d f 10 2 10 4 b t t b dexpected to be of the order of 10-2 – 10-4, but were not observedexperimentally. When dark matter was taken into account in the 1980-ties, the predicted level of the fluctuations was lowered to about 10-5, therebyposing a great experimental challenge.

Explanation: two effects compensate the temperature anisotropies:p p p pDM 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!


average temperature!

Because of e g atmospheric absorption it was long realized that

The COBE missionBecause of e.g. atmospheric absorption, it was long realized thatmeasurements of the high frequency part of the CMB spectrum(wavelengths shorter than about 1 mm) should be performed fromspace A satellite instrument also gives full sky coverage and a longspace. A satellite instrument also gives full sky coverage and a longobservation time. The latter point is important for reducing systematicerrors in the radiation measurements. A detailed account ofmeasurements of the CMB is given in a review by Weiss (1980).measurements of the CMB is given in a review by Weiss (1980).

The COBE story begins in 1974 when NASA made an announcement of opportunityfor small experiments in astronomy. Following lengthy discussions with NASA Headquarters the COBE project was born and finally, on 18 November 1989, theq p j y, ,COBE satellite was successfully launched into orbit. More than 1,000 scientists, engineers and administrators were involved in the mission. COBE carried threeinstruments covering the wavelength range 1 μm to 1 cm to measure the anisotropyand spectrum of the CMB as well as the diffuse infrared background radiation: DIRBE (Diffuse InfraRed Background Experiment), DMR (Differential MicrowaveRadiometer) and FIRAS (Far InfraRed Absolute Spectrophotometer). COBE’smission was to measure the CMB over the entire sky, which was possible with thechosen satellite orbit. All previous measurements from ground were done with limited sky coverage. John Mather was the COBE Principal Investigator and the projectl d f h H l ibl f h FIRAS i G


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 principalinvestigator.

The COBE mission

For DMR the objective was to search for anisotropies at three l th 3 6 d 10 i th CMB ithwavelengths, 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 beexplain 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 j pCMB in the range 0.1 – 10 mm and compare it with the blackbody form expected in the Big Bang model, which is diff t f th f t d f t li htdifferent from, e.g., the forms expected from starlight or bremsstrahlung. For DIRBE, the objective was to measure the infrared background radiation The mission spacecraftthe 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 success

COBE was a success. All instruments worked very well and the results, in particular those from DMR , pand FIRAS, contributed significantly to make cosmology a precision science. Predictions of the Big B d l fi dBang model were confirmed: temperature fluctuations of the order of 10-5 were found and the background radiation with a temperature of 2 725 Kbackground radiation with a temperature of 2.725 K followed very precisely a blackbody spectrum. DIRBE made important observations of the infrared pbackground. The announcement of the discovery of the anisotropies was met with great enthusiasm

ld idworldwide.


CMB Anisotropies

The DMR instrument (Smoot et al. 1990) measured temperaturefluctuations of the order of 10-5 for three CMB frequencies, 90, 53 and31.5 GHz (wavelengths 3.3, 5.7 and 9.5 mm), chosen near the CMB31.5 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 ofinstrumental background, the data showed a background contributiong , gfrom the Milky Way, the known dipole amplitude ΔT/T = 10-3 probablycaused by the Earth’s motion in the CMB, and a significant long soughtafter quadrupole amplitude, predicted in 1965 by Sachs and Wolfe. The first results were published in 1992.The data showed scale invariance forlarge angles, in agreement with predictions from inflation models.

Figure 5 shows the measured temperature fluctuations in galactic coordinates, a figurethat has appeared in slightly different forms in many journals. The RMS cosmicquadrupole amplitude was estimated at 13 ± 4 μK (ΔT/T = 5×10-6) with a systematicerror of at most 3 μK (Smoot et al. 1992). The DMR anisotropies were compared andf d i h d l f f i b W i h l 1992 Th f ll 4found to agree with models of structure formation by Wright et al. 1992. The full 4 yearDMR observations were published in 1996 (see Bennett et al. 1996). COBE’s resultswere soon confirmed by a number of balloon-borne experiments, and, more recently, byth 1° l ti WMAP (Wilki Mi A i t P b ) t llit l h d


the 1° resolution WMAP (Wilkinson Microwave Anisotropy Probe) satellite, launchedin 2001 (Bennett et al. 2003).

OutlookThe 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, i l di (b f COBE) th d k f th i ht k th d i f h d dincluding (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 provingtemperature 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 establishedHowever, 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 maycosmological 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


of the Universe according to the standard cosmological model. The first stages after the Big Bang are still speculations.

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 g p p g gparticles 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 objectsThe 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).p ( p g )

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 colorspending ~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


course, the peak of the CMB microwave spectrum.

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

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

i l h i kT F i l llidmean 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 atdramatically with temperature Itot 2.2 10 T Watt /m 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 f lli f ti 1400 W tt/ 2 h t f l b d itfalling 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 3K 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 th ti f th CMB (380 k ) th di ti i t it I 17 MW/ 2At 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.


j y p g , g qRadiation 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).

Rotationally excited CN

The first observations of the CMB were made by McKellar usinginterstellar molecules in 1940. The image at right shows a

f h O h k i 1940 hi h h h kspectrum of the star zeta Oph taken in 1940 which shows the weakR(1) line from rotationally excited CN. The significance of thesedata was not realized at the time and there is even a line in thedata was not realized at the time, and there is even a line in the1950 book Spectra of Diatomic Molecules by the Nobel-prizewinning physicist Gerhard Herzberg, noting the 2.3 K rotationalg p y g gtemperature of the cyanogen molecule (CN) in interstellar spacebut stating that it had "only a very restricted meaning." We nowk th t thi l l i i il it d b th CMB i l iknow that this molecule is primarily excited by the CMB implyinga brightness temperature of To = 2.729 +/- 0.027 K at a wavelengthof 2 64 mm ( Roth Meyer & Hawkins 1993)of 2.64 mm ( Roth, Meyer & Hawkins 1993).

http://www.astro.ucla.edu/~wright/CMB.html


p g

Warum ist die CMB so wichtig in der Kosmologie?

) Di CMB b i d d U i f üh h ißa) Die CMB beweist, dass das Universum früher heiß warund das die Temperaturentwicklung verstanden ist

b) Alle Wellenlängen ab einer bestimmten Länge (=oberhalb denakustischen Wellenlängen) kommen allegleich stark vor, wie von der Inflation vorhergesagt.

c) Kleine Wellenlängen (akustische Wellen) zeigenc) Kleine Wellenlängen (akustische Wellen) zeigenein sehr spezifisches Leistungsspektrum der akustischen Wellenim frühen Universum, woraus man,schließen kann, dass das Universum FLACH ist unddie baryonische Dichte nur 4-5% der Gesamtdichte ausmacht.


Warum akustische Wellen im frühen Universum?

Definiere: δ=Δρ/ρ P

F=maρ ρ

Newton: F=ma oder a-F/m=0δ``+ (Druck Gravitationpotential) δ=0

FG

Lösung:

δ + (Druck-Gravitationpotential) δ=0

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

Rücktreibende Kraft: Gravitation


Rücktreibende Kraft: GravitationAntreibende Kraft: Photonendruck

Ph t El kt B g d t k K l g

Mathematisches Modell• Photonen, Elektronen, Baryonen wegen der starken Kopplung

wie eine Flüssigkeit behandelt → ρ, v, p

• Dunkle Materie dominiert das durch die Dichtefluktuationen Dunkle Materie dominiert das durch die Dichtefluktuationen hervorgerufene Gravitationspotential Φ

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

• v+(v·)v = -(Φ+p/ρ)(E l Gl i h I l h lt )(Euler Gleichung = Impulserhaltung)

• ² Φ = 4πGρ(Poissongleichung = klassische Gravitation)

Tiefe des Potentialtopfs be-stimmt durch dunkle Materie

(Poissongleichung = klassische Gravitation)

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

• Lösung kann numerisch oder mit Vereinfachungen analytisch b ti t d d t i ht b i dä ft


bestimmt werden und entspricht grob einem gedämpftem harmonischen Oszillator mit einer antreibenden Kraft

Entwicklung der Dichtefluktuationen im Universum

Man kann die Dichtefluktuationenim frühen Univ. als Temp.-Fluktuationen


im frühen Univ. als Temp. Fluktuationender CMB beobachten!

The first sound wavesThe first sound waves

compressiondim dima) gas falls into valleys, gets compressed, & glows brighter

rarefaction rarefactioncompressiondim

brighti i i i

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

) it th f ll b k i i t k d i

compressioncompressiondim

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

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.

Akustische Peaks

1. akust. Peak

t=trec

t=1/2trec t=1/2trec2 akust Peak2. akust. Peak

1/3Wim de Boer, Karlsruhe Kosmologie VL, 27.11.2011 23

t=1/3trec 3. akust. Peak

Akustische Wellen im frühen Universum

Ü


Überdichten am Anfang: Inflation

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

http://astron.berkeley.edu/~mwhite/sciam03 short.pdfp y _ p


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


Mark WhittleMark WhittleUniversity of VirginiaUniversity of Virginiay gy g

http://www.astro.virginia.edu/~dmw8fhttp://www.astro.virginia.edu/~dmw8fSee also: “full presentation”See also: “full presentation”

Viele Plots und sounds von Whittles Webseite


Akustische Wellen im frühen UniversumJoe Wolfe (UNSW)Flute power

spectra

Bь Clarinet

piano range

Modern Flute

Wim de Boer, Karlsruhe Kosmologie VL, 27.11.2011 28Überdichten am Anfang: Inflation

Sky Maps Power Spectra

peak

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

troughUse special methods Use special methods to measure theto measure the strengthstrengthto measure the to measure the strengthstrengthof each wavelength.of each wavelength.

Shorter wavelengthsShorter wavelengthsare smaller frequenciesare smaller frequencies

hi h it hhi h it hare higher pitchesare higher pitches


Lineweaver 1997

Sound waves in the skySound waves in the skyThis slide illustrates the situation. Imagine looking down on the oceanfrom a plane and seeing far below, surface waves. The patches on the

i b k d k d t h f di t t d

Water wavesWater waves ::

microwave background are peaks and troughs of distant sound waves.

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

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

all “superimposed”all “superimposed”

Sound wavesSound waves ::red/blue = high/lowred/blue = high/low

& li ht& li ht


gas & light pressuregas & light pressure

Power (Leistung) pro Wellenlänge)

This distribution has a lot of long wavelength powerand a little short a elength po er


and a little short wavelength power

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

• Surely, the vacuum of “space” must be silentsilent ? N f h U i Not for the young Universe:

• Shortly after the big bang (eg @ CMB: 380 000 rs)• 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 smallersmaller everything closer together (by ×1000)Universe is smallersmaller 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 wavesThere is a hot thin atmosphere for sound wavesThere is a hot thin atmosphere for sound waves• unusual fluid intimate mix of gas & light

d d f li h


• sound waves propagate at ~50% speed of light

Big Bang Akustikhttp://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 the pull of gravity like air responds in an organ pipe – it bounces in and out to make sound waves This half millionbounces 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 y ,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 behavesfundamental and harmonics – the young Universe behaves like a musical instrument! We will, of course, hear acoustic versions, suitably modified for human ears.


, y

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 iswaves (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

hcourse, 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 p , p g gsurges in light’s brilliance.

After recombination photons and particles decouple; theAfter 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.


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 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 randomlyfrom 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 isthis 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, itsregions, 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 cycleovershoots, 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

t f hl h i l i [O t “f lli i ” dout 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 g ) p pits 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


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:Bow+string microphone

& amplifier& antenna

ariel &amplifierspeakers

soundsound radio wavesradio waves soundsound youryourearsears& antenna speakers earsears

Concert hallConcert hall ListenerListenerfew 100 milesConcert hallConcert hall ListenerListenerfew 100 miles

few µsec delaysound

gravity +hills/valleys

wavesglowglow

telescope computerspeakers

soundsound lightlight soundsound youryourearsearsmicrowavesmicrowaves

Big BangBig Bang ListenerListenervery long way !


Big BangBig Bang ListenerListener14 Gyr delay !

The Big Bang is all around us !

Since looking in anyany direction looks back to the foggy wall we see the wall in allall directions. the entireentire skysky glows with microwaves h fl h f h Bi B i llll dd ! the flash from the Big Bang is allall aroundaround usus!


Akustische Peaks von WMAP

Ort-ZeitDiagramm


CMB Sound Spectrum

Click forsound

acoustic

non-acoustic

3ea

ver 2

003

A220 Hz

Line

we

Wim de Boer, Karlsruhe Kosmologie VL, 27.11.2011 40Frequency (in Hz)

Kugelflächenfunktionen

l=4

l=8

J d F kti k i th l l 12Jede Funktion kann in orthogonale Kugelflächenfkt. entwickelt werden. Große Werte von l beschreiben Korrelationen unter

l=12

kleinen Winkel.


Vom Bild zum Powerspektrum

• Temperaturverteilung istFunktion auf Sphäre: ΔT(θ,φ) bzw. ΔT(n) = ΔΘ(n)( ,φ) ( ) ( )

T Tn=(sinθcosφ,sinθsinφ,cosθ)

• Autokorrelationsfunktion:

C(θ)=<ΔΘ(n )·ΔΘ(n )> n nC(θ)=<ΔΘ(n1)·ΔΘ(n2)>|n1-n2|

=(4π)-1 Σ∞l=0 (2l+1)ClPl(cosθ)• Pl sind die Legendrepolynome: 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


mit cosθ=n1·n2

Temperaturschwankungen als Fkt. des Öffnungswinkels

Θ 180/lBalloon exp.


Das Leistungsspektrum (power spectrum)

Ursachen für TemperaturSchwankungen:Schwankungen:

Große Skalen:Gravitationspotentiale

Kleine Skalen:Akustische Wellen


Position des ersten Peaks

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

Raum-Zeit x

tInflation

der Grundwelle beobachtet:

Maximale Ausdehnung einer akust. Wellezum Zeitpunkt trec: c * trec (1+z)

t

Entkopplungzum Zeitpunkt trec: cs * trec (1+z)Beobachtung nach t0 =13.8 109 yr.Öffnungswinkel θ = cs * trec * (1+z) / c*t0 Mit (1+ ) 3000/2 7 1100 dMit (1+z)= 3000/2.7 =1100 und trec = 3,8 105 yr und Schallgeschwindigkeit cs=c/3 für ein relativ. Plasma folgt: max. T / Tθ = 0.0175 = 10 (plus (kleine)ART Korrekt.)

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

max. T / Tunter 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 UnivHier 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 * c * t * (1+z) / 3*c*t0 = 0 7 GradWinkel 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


nicht 380000 a. Richtige Antwort: Winkel θ 0.8 Grad oder l 180/0.8 220

Temperaturanisotropie der CMB


Position des ersten akustischen Peaks bestimmtKrümmung des Universums!


Present and projected Results from CMB

180 / l

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

180 / l

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


Flaches Univ.

Geometry of the UniverseGeometry of the Universe

Open : Ω= 0.8

Flat : Ω= 1.0

Closed: Ω=1.2

L i h High pitch


Low pitch High pitchLong wavelength Short wavelength

Atomic content of the UniverseAtomic content of the Universe

2% atoms

4% atoms

8% atoms

Low pitch High pitch


Low pitch High pitchLong wavelength Short wavelength

WMAP analyzer tool


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

Conformal Space-Time(winkel-erhaltende Raum-Zeit)

Raum-Zeit xtt

x From Ned Wright homepage

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

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

conformal=winkelerhaltend


conformal=winkelerhaltendz.B. mercator Projektion

http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.0732v2.pdfNeueste WMAP Daten (2008)

PolarisationPolarisation

Reionisationnach 2.108 a

Temperaturp

Temperatur- und Polarisationsanisotropien um 90 Grad in Phase verschoben,


Temperatur und Polarisationsanisotropien um 90 Grad in Phase verschoben,weil Polarisation Fluss der Elektronen, also wenn x cos (t), dann v sin (t)

Neueste WMAP Daten (2008)


CMB polarisiert durch Streuung an Elektronen(Thomson Streuung)

K E k lKurz vor Entkoppelung:Streuung der CMB Photonen.Nachher nicht mehr da mittlereNachher nicht mehr, da mittlerefreie Weglange zu groß.Lange vor der Entkopplung:g pp gPolarisation durch Mittelungüber viele Stöße verloren.

Nach Reionisation der Baryonendurch Sternentstehung wiederdurch Sternentstehung wiederStreuung.

Erwarte Polarisation also kurznach dem akust. Peak (l = 300)

d f ß Ab tä d (l < 10)


und auf großen Abständen (l < 10)Instruktiv:http://background.uchicago.edu/~whu/polar/webversion/node1.html

Entwicklung des Universums


Polarisation durch Thomson Streuung (elastische Photon-Electron Streuung)


CMB Polarisation durch Thomson Streuung (elastische Photon-Electron Streuung)

Prinzip: unpolarisiertes Photon unter 90 Grad gestreut, muss immernoch E-Feld Richtung haben, so eine Komponente verschwindet!


g , pDaher bei Isotropie keine Pol. , bei Dipol auch nicht, nur bei Quadr.

CMB Polarisation bei Quadrupole-Anisotropie

Polarization entweder radial oder tangential um hot oder cold spots (proportional zum Fluss der Elektronen, also zeigt wie Plasma sichbewegte bei z=1100 and auf große Skalen wie Plasma in GalaxienCluster sich relativ zum CMB bewegt)


http://gyudon.as.utexas.edu/~komatsu/presentation/wmap7_ias.pdf

CMB Polarisation bei Quadrupole-Anisotropie


http://wmap.gsfc.nasa.gov/m_ig/101079/index.htmlNo evidence for tensor perturbations fromgravitational waves yet, as expected from inflation

Woher kennt man diese Verteilung?

If it is not dark,it does not matter


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 canregularly, 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 laterpwith distance as determined from the luminosity of lamp posts (assuming same brightness for all lamp posts)p p(luminosity distance, if SN1a treated as ‘standard’ candles with known luminosity)

f h f l f h If the very first lamp posts are further away than expected, the conclusion must be that the Porsche instead of rolling up the hill d it i i ddi i l hill used its engine, i.e. additional acceleration instead of decelaration only.(universe has additional acceleration (by dark

) i t d f d l ti l )


energy) instead of decelaration only)

Perlmutter 2003Perlmutter 2003AbstandAbstand

Zeit


Vergleich mit den SN 1a Daten

SN1a empfindlich für Beschleunigung, d.h.g g, - m

CMB empfindlich für totale Dichte d.h. + m

( )


= (SM+ DM)

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

Let's consider what happens to a point-like initial perturbation. In other words,we're going to take a little patch of spacewe're going to take a little patch of spaceand make it a little denser. Of course, theuniverse has many such patchs, someoverdense some underdense We're justoverdense, some underdense. We re justgoing to focus on one. Because thefluctuations are so small, the effects ofmany regions just sum linearly.many regions just sum linearly.The relevant components of the universeare the dark matter, the gas (nuclei andelectrons), the cosmic microwavee ec o s), e cos c c ow vebackground photons, and the cosmicbackground neutrinos.


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 fastto be bound gravitationally, so they begin to stream awayfrom the initial perturbationfrom the initial perturbation.The dark matter moves only in response to gravity and hasno intrinsic motion (it's cold dark matter). So it sits still.The perturbation (now dominated by the photons andneutrinos) 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. Inthe resulting plasma the cosmic microwave backgroundthe resulting plasma, the cosmic microwave backgroundphotons are not able to propagate very far before theyscatter off an electron. Effectively, the gas and photons arelocked into a single fluid. The photons are so hot andnumerous, that this combined fluid has an enormouspressure relative to its density. The initial overdensity istherefore also an initial overpressure. This pressure triesto equalize itself with the surroundings, but this simply

The result is that the perturbation inth d h t i i d t d to equalize itself with the surroundings, but this simply

results in an expanding spherical sound wave. This is justlike a drum head pushing a sound wave into the air, butthe speed of sound at this early time is 57% of the speed of

the gas and photon is carried outward:


light!

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

As time goes on, the spherical shell of gasand photons continues to expand. Theneutrinos spread out. The dark mattercollects in the overall density perturbation,which is now considerably bigger becauseth h t d t i h l ft ththe photons and neutrinos have left thecenter. Hence, the peak in the dark matterremains centrally concentrated but with anincreasing width This is generating theincreasing width. This is generating thefamiliar turnover in the cold dark matterpower spectrum.Where is the extra dark matter at largeWhere is the extra dark matter at largeradius coming from? The gravitationalforces are attracting the backgroundmaterial in that region, causing it to contractmaterial in that region, causing it to contracta bit and become overdense relative to thebackground 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, thetemperature is low enough that thetemperature is low enough that theelectrons and nuclei begin to combineinto neutral atoms. The photons donot scatter efficiently off of neutralnot scatter efficiently off of neutralatoms, so the photons begin to slippast the gas particles. This is known

Silk d i (A J 151 459 1968)as Silk damping (ApJ, 151, 459, 1968).The sound speed begins to dropbecause of the reduced couplingbetween the photons and gas andbecause the cooler photons are nolonger very heavy compared to theg y y pgas. Hence, the pressure wave slowsdown.


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

This continues until the photons havel t l l k d t f thcompletely leaked out of the gas

perturbation. The photon perturbationbegins to smooth itself out at the speedof light (just like the neutrinos did)of light (just like the neutrinos did).The photons travel (mostly)unimpeded until the present-day,where we can record them as thewhere we can record them as themicrowave background (see below).At this point, the sound speed in thegas has dropped to much less than thegas has dropped to much less than thespeed of light, so the pressure wavestalls.


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

We are left with a dark matterperturbation around the originalcenter and a gas perturbation in a shellabout 150 Mpc (500 million light-

) i diyears) in radius.As time goes on, however, these twospecies gravitationally attract each

th Th t b ti b i t iother. The perturbations begin to mixtogether. More precisely, bothperturbations are growing quickly inresponse to the combined gravitationalresponse to the combined gravitationalforces of both the dark matter and thegas. At late times, the initialdifferences are small compared to thedifferences are small compared to thelater growth.


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

Eventually, the two look quitesimilar. The spherical shell of thegas perturbation has imprinteditself in the dark matter. This isknown as the acoustic peak.The acoustic peak decreases incontrast as the gas come into lock-contrast as the gas come into lockstep with the dark matter simplybecause the dark matter, which hasno peak initially outweighs the gasno peak initially, outweighs the gas5 to 1.


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

At late times, galaxies form in theregions that are overdense in gas anddark matter. For the most part, this isdark matter. For the most part, this isdriven by where the initialoverdensities were, since we see that thedark matter has clustered heavilyd e s c us e ed e v yaround these initial locations. However,there is a 1% enhancement in theregions 150 Mpc away from theseg p yinitial overdensities. Hence, thereshould be an small excess of galaxies150 Mpc away from other galaxies, asopposed to 120 or 180 Mpc. We can seethis as a single acoustic peak in thecorrelation function of galaxies.

B f h b l i h fil Alternatively, if one is working with thepower spectrum statistic, then one seesthe effect as a series of acoustic

ill i

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


oscillations.Mpc is much less than 1% of the density near the center.

One little telltale bump !!

A small excess in correlation at 150 Mpc.!1 2( ) ( ) ( )r r r

p

SDSS survey(astro ph/0501171)(astro-ph/0501171)

(Einsentein et al. 2005)

150 Mpc.

150 Mpc =2c t (1+z)=akustischer Horizont


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

Akustische Baryonosz. in Korrelationsfkt. der Dichteschwankungen der Materie!

150 Mpc.

105 h-1 ¼ 150

The same CMB oscillations at

low redshifts !!!

SDSS surveyy(astro-ph/0501171)

(Einsentein et al. 2005)


( )

Combined results

http://arxiv.org/PS cache/arxiv/pdf/0804/0804.4142v1.pdf


http://nedwww.ipac.caltech.edu/level5/March08/Frieman/Frieman4.htmlp g _ p p

Zum Mitnehmen

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 dass1. das das Univ. am Anfang heiß war, weil akustische Peaks, entstanden

durch akustische stehende Wellen in einem heißen Plasma, entdeckt wurden2. 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 i AC i i i i i S3. das Univ. FLACH ist, weil die Photonen sich seit der letzten Streuungzum Zeitpunkt der Entkopplung (LSS = last scattering surface) auf geradeLinien bewegt haben (in comoving coor.)

4) BAO i hti il Si bhä i d k ti h H i t i d CMB i4) BAO wichtig, weil Sie unabhängig von der akustischen Horizont in der CMB eine zweiter wohl definierter Maßstab (akustischer Horizont der Materie) darstellen, dessen Vergrößerung heute gemessen werden kann. Dies bestätigt die Energieverteilung des Univ unabh Von der Frage ob SN1a Standardkerzen sindEnergieverteilung 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


Die schnelle Sternbildung kann nur mit Potentialtöpfen der DM zum Zeitpunkt derEntkopplung erklärt werden. (die neutrale Kerne fallen da hinein).

Zum Mitnehmen

If it is not dark,it does not matter


Documents

Vorlesung 6+7 Roter Fadendeboer/html/Lehre/... · Peebles 1983, Weinberg 1993, and Herman 1997. Further observations of CMB Following the 1964 discovery, several independent measurements