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Vorlesung 6+7. Roter Faden: Cosmic Microwave Background radiation (CMB) Akustische Peaks Universum ist flach Baryonic Acoustic Oscillations (BAO) Energieinhalt des Universums. Zum Mitnehmen. Temperaturentwicklung im fr ühen Universum :

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Vorlesung 6+7

  • Roter Faden:
  • Cosmic Microwave Background radiation (CMB)
  • Akustische Peaks
  • Universum ist flach
  • Baryonic Acoustic Oscillations (BAO)
  • Energieinhalt des Universums

Zum Mitnehmen

Temperaturentwicklung im frühen Universum:

T = (3c2/8aG)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 (darkages)

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)


Temperaturentwicklung des Universums

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 = 8GaT4/3c2 (Str=aT4>>m und k/S2 und )

Lösung dieser DG: T = (3c2/8aG)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

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


The oval shapes show a sphericalsurface, 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.


Cosmology and the Cosmic Microwave Background

The Universeisapproximatelyabout 13.7 billionyearsold, accordingtothestandardcosmological Big Bang model. Atthis time, it was a stateofhighuniformity, was extremelyhotanddense was filledwithelementaryparticlesand was expandingveryrapidly. About 380,000 years after the Big Bang, theenergyofthephotonshaddecreasedand was not sufficienttoionise hydrogen atoms. Thereafterthephotons “decoupled” fromtheotherparticlesandcouldmovethroughtheUniverseessentiallyunimpeded. The Universehasexpandedandcooledeversince, leavingbehind a remnantofitshotpast, theCosmicMicrowave Background radiation (CMB). Weobservethistodayas a 2.7 K thermal blackbodyradiationfillingtheentireUniverse. Observationsofthe CMB give a uniqueanddetailedinformationabouttheearlyUniverse, therebypromotingcosmologyto a precisionscience. Indeed, as will bediscussed in moredetailbelow, the CMB isprobablythebestrecordedblackbodyspectrumthatexists. Removing a dipoleanisotropy, mostprobably due ourmotionthroughtheUniverse, the CMB isisotropictoaboutonepart in 100,000. The 2006 Nobel Prize in physicshighlightsdetailedobservationsofthe CMB performedwiththe COBE (COsmic Background Explorer) satellite.

From Nobel prize 2006 announcement


Early work

The discoveryofthecosmicmicrowavebackgroundradiationhas an unusualandinterestinghistory. The basictheoriesas well asthenecessary experimental techniqueswereavailablelongbeforethe experimental discovery in 1964. The theoryof an expandingUniverse was firstgivenby Friedmann (1922) andLemaître (1927). An excellentaccountisgivenby Nobel laureate Steven Weinberg (1993).

Around 1960, a fewyearsbeforethediscovery, twoscenariosfortheUniversewerediscussed. Was itexpandingaccordingtothe Big Bang model, or was it in a steadystate?Bothmodelshadtheirsupportersandamongthescientistsadvocatingthelatterwere Hannes Alfvén (Nobel prize in physics 1970), Fred Hoyleand Dennis Sciama. Ifthe Big Bang model was thecorrectone, an imprintoftheradiationdominatedearlyUniverse must still exist, andseveralgroupswerelookingfor it. Thisradiation must be thermal, i.e. ofblackbody form, andisotropic.

From Nobel prize 2006 announcement


First observations of CMB

The discoveryofthecosmicmicrowavebackgroundby Penzias and Wilson in 1964 (Penzias and Wilson 1965, Penzias 1979, Wilson 1979, Dicke et al. 1965) cameas a completesurprisetothemwhiletheyweretryingto understand thesourceofunexpectednoise in theirradio-receiver (theysharedthe 1978 Nobel prize in physicsforthediscovery). The radiationproducedunexpectednoise in theirradioreceivers. Some 16 yearsearlierAlpher, Gamow and Herman (Alpherand Herman 1949, Gamow 1946), hadpredictedthatthereshouldbe a relicradiationfieldpenetratingtheUniverse. Ithadbeenshownalready in 1934 byTolman (Tolman 1934) thatthecoolingblackbodyradiation in an expandingUniverseretainsitsblackbody form. ItseemsthatneitherAlpher, Gamow nor Herman succeeded in convincingexperimentaliststousethecharacteristicblackbody form oftheradiationto find it. In 1964, however, DoroshkevichandNovikov (DoroshkevichandNovikov 1964) published an articlewheretheyexplicitlysuggested a searchfortheradiationfocusing on itsblackbodycharacteristics. Onecannotethatsomemeasurementsasearlyas 1940 hadfoundthat a radiationfield was necessarytoexplainenergyleveltransitions in interstellar molecules (McKellar 1941). Followingthe 1964 discoveryofthe CMB, many, but not all, ofthesteadystateproponentsgaveup, acceptingthehot Big Bang model. The earlytheoreticalworkisdiscussedbyAlpher, Herman and Gamow 1967, Penzias 1979, Wilkinson andPeebles 1983, Weinberg 1993, and Herman 1997.



Further observations of CMB

Followingthe 1964 discovery, severalindependentmeasurementsoftheradiationweremadeby Wilkinson andothers, usingmostlyballoon-borne, rocket-borneorgroundbasedinstruments. The intensityoftheradiationhasitsmaximumfor a wavelengthofabout 2 mm wheretheabsorption in theatmosphereis strong. Althoughmostresultsgavesupporttotheblackbody form, fewmeasurementswereavailable on thehighfrequency (lowwavelength) sideofthepeak. Somemeasurementsgaveresultsthatshowedsignificantdeviationsfromtheblackbody form (Matsumoto et al. 1988).

The CMB was expectedtobelargelyisotropic. However, in order toexplainthe large scalestructures in the form ofgalaxiesandclustersofgalaxiesobservedtoday, smallanisotropiesshouldexist. Gravitation canmakesmalldensityfluctuationsthatarepresent in theearlyUniversegrowandmakegalaxyformationpossible. A veryimportantanddetailedgeneralrelativisticcalculationby Sachs and Wolfe showedhowthree-dimensional densityfluctuationscangiverisetotwo-dimensional large angle (> 1°) temperatureanisotropies in thecosmicmicrowavebackgroundradiation (Sachs and Wolfe 1967).


Dipol Anisotropy

Becausetheearthmoves relative tothe CMB, a dipoletemperatureanisotropyofthelevelof ΔT/T = 10-3isexpected. This was observed in the 1970’s (Conklin 1969, Henry 1971, Corey and Wilkinson 1976 andSmoot, Gorensteinand Muller 1977). Duringthe 1970-tis teheanisotropieswereexpectedtobeofthe order of 10-2 – 10-4, but were not observedexperimentally. Whendark matter was takenintoaccount in the 1980-ties, thepredictedlevelofthefluctuations was loweredtoabout 10-5, therebyposing 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!


The COBE mission

        • Becauseof e.g. atmosphericabsorption, it was longrealizedthatmeasurementsofthehighfrequencypartofthe CMB spectrum (wavelengthsshorterthanabout 1 mm) shouldbeperformedfromspace. A satelliteinstrument also givesfullskycoverageand a longobservation time. The latterpointisimportantforreducingsystematicerrors in theradiationmeasurements. A detailedaccountofmeasurementsofthe CMB isgiven in a reviewbyWeiss (1980).
  • The COBE storybegins in 1974 when NASA made an announcementofopportunityforsmallexperiments in astronomy. Followinglengthydiscussionswith NASA Headquartersthe COBE project was bornandfinally, on 18 November 1989,the COBE satellite was successfullylaunchedintoorbit. More than 1,000 scientists, engineersandadministratorswereinvolved in themission. COBE carriedthreeinstrumentscoveringthewavelengthrange 1 μmto 1 cm tomeasuretheanisotropyandspectrumofthe CMB as well asthe diffuse infraredbackgroundradiation: DIRBE (Diffuse InfraRed Background Experiment), DMR (Differential Microwave Radiometer) and FIRAS (FarInfraRed Absolute Spectrophotometer). COBE’smission was tomeasurethe CMB overtheentiresky, which was possiblewiththechosensatelliteorbit. All previousmeasurementsfromgroundweredonewith limited skycoverage. John Mather was the COBE PrincipalInvestigatorandtheprojectleaderfromthestart. He was also responsibleforthe FIRAS instrument. George Smoot was the DMR principalinvestigatorand Mike Hauser was the DIRBE principalinvestigator.

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 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.


CMB Anisotropies

        • The DMR instrument (Smoot et al. 1990) measuredtemperaturefluctuationsofthe order of 10-5forthree CMB frequencies, 90, 53 and 31.5 GHz (wavelengths 3.3, 5.7 and 9.5 mm), chosennearthe CMB intensitymaximumandwherethegalacticbackground was low. The angular resolution was about 7°. After a carefuleliminationof instrumental background, thedatashowed a backgroundcontributionfromtheMilky Way, theknowndipoleamplitude ΔT/T = 10-3probablycausedbytheEarth’smotion in the CMB, and a significantlongsought after quadrupoleamplitude, predicted in 1965 by Sachs and Wolfe. The firstresultswerepublished in 1992.The datashowedscaleinvariancefor large angles, in agreementwithpredictionsfrominflationmodels.
  • Figure 5 showsthemeasuredtemperaturefluctuations in galacticcoordinates, a figurethathasappeared in slightly different forms in manyjournals. The RMS cosmicquadrupoleamplitude was estimatedat 13 ± 4 μK (ΔT/T = 5×10-6) with a systematicerrorofatmost 3 μK (Smoot et al. 1992). The DMR anisotropieswerecomparedandfoundtoagreewithmodelsofstructureformationby Wright et al. 1992. The full 4 year DMR observationswerepublished in 1996 (see Bennett et al. 1996). COBE’sresultsweresoonconfirmedby a numberofballoon-borneexperiments, and, morerecently, bythe 1° resolution WMAP (Wilkinson MicrowaveAnisotropy Probe) satellite, launched in 2001 (Bennett et al. 2003).


      • 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.

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.

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 = 10-8Isun – 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).

Warum ist die CMB so wichtig in der Kosmologie?

  • 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.


Warum akustische Wellen im frühen Universum?


Definiere: δ=Δρ/ρ



Newton: F=ma

δ``+ (Druck-Gravitation) δ=0


Druck gering: δ=aebt,

d.h. exponentielle Zunahme von δ


Druck groß: δ=aeibt ,

d.h. Oszillation von δ

(akustische Welle)

Rücktreibende Kraft: Gravitation

Antreibende Kraft: Photonendruck


Mathematisches Modell

  • 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

Tiefe des Potentialtopfs be-

stimmt durch dunkle Materie


Entwicklung der Dichtefluktuationen im Universum

-DT / T ~ Dr / r

Man kann die Dichtefluktuationen

im frühen Univ. als Temp.-Fluktuationen

der CMB beobachten!


The first sound waves







  • gas falls into valleys, gets compressed, & glows brighter

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







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

 the oscillation continues sound waves are created

  • Gravity drives the growth of sound in the early Universe.
  • The gas must also feel pressure, so it rebounds out of the valleys.
  • We see the bright/dim regions as patchiness on the CMB.

Akustische Wellen im frühen Universum

Überdichten am Anfang: Inflation


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 Whittle

University of Virginia

Viele Plots und sounds von Whittles Webseite

See also: “full presentation”

flute power spectra

Joe Wolfe (UNSW)

Akustische Wellen im frühen Universum

Flute power spectra

Bь Clarinet

piano range

Modern Flute

Überdichten am Anfang: Inflation




Lineweaver 1997

Sky Maps  Power Spectra

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

Use special methods

to measure the strength

of each wavelength.

Shorter wavelengths

are smaller frequencies

are higher pitches

sound waves in the sky
Sound waves in the sky

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

Water waves :

high/low level of

water surface

many waves of different sizes, directions & phases

all “superimposed”

Sound waves :

red/blue = high/low

gas & light pressure


Power (Leistung) pro Wellenlänge)

This distribution has a lot of long wavelength power

and a little short wavelength power


Sound in space !?!

  • Surely, the vacuum of “space” must be silent ?
    •  Not for the young Universe:
  • Shortly after the big bang (eg @ CMB: 380,000 yrs)
    • all matter is spread out evenly (no stars or galaxies yet)
    • Universe is smaller everything closer together (by ×1000)
    • the density 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 waves
    • unusual fluid  intimate mix of gas & light
    • sound waves propagate at ~50% speed of light

Big Bang Akustik

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.


Akustik Ära

  • Since it is light which provides the pressure, the speed of pressure waves (sound) is incredibly fast: vs ~ 0.6c! This makes sense: the gas is 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.

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, 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.





& amplifier

& antenna

ariel &



radio waves



few 100 miles


Concert hall

few µsec delay










gravity +





very long way !


Big Bang

14 Gyr delay !

How does sound get to us ?

Consider listening to a concert on the radio:


The Big Bang is all around us !

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

Big Bang

Near Far

Now red-shift Then

Far Near

Big Bang

Then red-shift Now

Big Bang

cmb sound spectrum


220 Hz

Frequency (in Hz)

CMB Sound Spectrum

Click for




Lineweaver 2003






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


Vom Bild zum Powerspektrum

  • Temperaturverteilung ist

Funktion auf Sphäre:

ΔT(θ,φ) bzw. ΔT(n) = ΔΘ(n)



  • Autokorrelationsfunktion:


=(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







max. T / T

unter 10

Position des ersten Peaks

Berechnung der Winkel, worunter man

die maximale Temperaturschwankungen

der Grundwelle beobachtet:

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.)

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



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 Gradoder l=180/0.8=220

present and projected results from cmb
Present and projected Results from CMB

See Wayne Hu's WWW-page:

Verhältnis peak1/peak2->


Position erster Peak->

Flaches Univ.

geometry of the universe
Geometry of the Universe

Open :Ω= 0.8

Flat : Ω= 1.0

Closed: Ω=1.2

High pitch

Low pitch

Short wavelength

Long wavelength

atomic content of the universe
Atomic content of the Universe

2% atoms

4% atoms

8% atoms

Low pitch

High pitch

Long wavelength

Short wavelength


Conformal Space-Time

(winkelerhaltende Raum-Zeit)





From Ned Wright homepage


 = x/S(t) = x(1+z)


 = t / S(t) = t (1+z)


z.B. mercator Projektion


CMB polarisiert durch Streuung an Elektronen

(Thompson 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


Erwarte Polarisation also kurz

nach dem akust. Peak (l = 300)

und auf großen Abständen (l < 10)


Woher kennt man diese Verteilung?

If it is not dark,

it does not matter



Ω=1, jedoch

Alter >>2/3H0

Alte SN dunkler

als erwartet


SNIa compared with Porsche rolling up a hill

SNIa data very similar to a dark Porsche rolling up a hill and reading speedometer regularly, i.e. determining v(t), which can

be used to reconstruct x(t) =∫v(t)dt.

(speed  distance, for universe Hubble law)

This distance can be compared later

with 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)


SN Type 1a wachsen bis Chandrasekhar Grenze

Dann Explosion mit ≈ konstanter Leuchtkraft

SN1a originates from double star

and explodes after reaching

Chandrasekhar mass limit




Perlmutter 2003



= (SM+ DM)

Vergleich mit den SN 1a Daten

SN1a empfindlich für

Beschleunigung, d.h.

 - m

CMB empfindlich für

totale Dichte d.h.

 + m


Akustische Baryon Oszillationen I:

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 II:

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:

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:

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:

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:

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:

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:

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 !!

150 Mpc.

A small excess in correlation at 150 Mpc.!

SDSS survey


(Einsentein et al. 2005)

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


Akustische Baryonosz. in Korrelationsfkt. der

Dichteschwankungen der Materie!

150 Mpc.

105 h-1¼ 150

2-point correlation of density contrast

The same CMB oscillations at low redshifts !!!

SDSS survey


(Einsentein et al. 2005)


Neueste WMAP Daten (2008)


WMAP analyzer tool


Combined results


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
  • 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.)

Zum Mitnehmen

If it is not dark,

it does not matter