Vorlesung 6+7

1. Vorlesung 6+7 • Roter Faden: • Cosmic Microwave Background radiation (CMB) • Akustische Peaks • Universum ist flach • Baryonic Acoustic Oscillations (BAO) • Energieinhalt des Universums

2. 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)

3. 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

4. Nach Rekombination ‘FREE STREAMING’ der Photonen

5. Last Scattering Surface (LSS)

6. 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.

7. 45 times sensitivity Temperatur-Fluktuationen = DichtefluktuationenWMAP vs COBE WMAP ΔT/T200uK/2.7K

8. 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

9. 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

10. 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. CN=Cyan

11. 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).

12. 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!

13. 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.

14. 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.

15. 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.

16. 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).

17. Outlook • The 1964 discovery of the cosmic microwave background had a large impact on cosmology. The COBE results of 1992, giving strong support to the Big Bang model, gave a much more detailed view, and cosmology turned into a precision science. New ambitious experiments were started and the rate of publishing papers increased by an order of magnitude. • Our understanding of the evolution of the Universe rests on a number of observations, including (before COBE) the darkness of the night sky, the dominance of hydrogen and helium over heavier elements, the Hubble expansion and the existence of the CMB. COBE’s observation of the blackbody form of the CMB and the associated small temperature fluctuations gave very strong support to the Big Bang model in proving the cosmological origin of the CMB and finding the primordial seeds of the large structures observed today. • However, while the basic notion of an expanding Universe is well established, fundamental questions remain, especially about very early times, where a nearly exponential expansion, inflation, is proposed. This elegantly explains many cosmological questions. However, there are other competing theories. Inflation may have generated gravitational waves that in some cases could be detected indirectly by measuring the CMB polarization. Figure 8 shows the different stages in the evolution of the Universe according to the standard cosmological model. The first stages after the Big Bang are still speculations.

18. 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.

19. 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).

20. 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.

21. Warum akustische Wellen im frühen Universum? P Definiere: δ=Δρ/ρ F=ma FG Newton: F=ma δ``+ (Druck-Gravitation) δ=0 Lösung: Druck gering: δ=aebt, d.h. exponentielle Zunahme von δ (->Gravitationskollaps) Druck groß: δ=aeibt , d.h. Oszillation von δ (akustische Welle) Rücktreibende Kraft: Gravitation Antreibende Kraft: Photonendruck

22. 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

23. Entwicklung der Dichtefluktuationen im Universum -DT / T ~ Dr / r Man kann die Dichtefluktuationen im frühen Univ. als Temp.-Fluktuationen der CMB beobachten!

24. The first sound waves dim dim compression rarefaction rarefaction bright • gas falls into valleys, gets compressed, & glows brighter b) it overshoots, then rebounds out, is rarefied, & gets dimmer bright bright rarefaction compression compression dim 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.

25. Akustische Wellen im frühen Universum Überdichten am Anfang: Inflation

26. Druck der akust. Welle und Gravitation verstärken die Temperaturschwankungen in der Grundwelle (im ersten Peak) http://astron.berkeley.edu/~mwhite/sciam03_short.pdf

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

28. Mark Whittle University of Virginia Viele Plots und sounds von Whittles Webseite http://www.astro.virginia.edu/~dmw8f See also: “full presentation”

29. Joe Wolfe (UNSW) Akustische Wellen im frühen Universum Flute power spectra Bь Clarinet piano range Modern Flute Überdichten am Anfang: Inflation

30. peak trough 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

31. 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

32. Power (Leistung) pro Wellenlänge) This distribution has a lot of long wavelength power and a little short wavelength power

33. 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

34. Big Bang Akustik http://astsun.astro.virginia.edu/~dmw8f/teachco/ While the universe was still foggy, atomic matter was trapped by light's pressure and prevented from clumping up. In fact, this high-pressure gas of light and atomic matter responds to 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.

35. 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.

36. 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.

37. 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.

38. Bow+string your ears microphone & amplifier & antenna ariel & amplifier speakers radio waves sound sound few 100 miles Listener Concert hall few µsec delay sound waves glow your ears telescope computer speakers light gravity + hills/valleys sound sound microwaves very long way ! Listener Big Bang 14 Gyr delay ! How does sound get to us ? Consider listening to a concert on the radio:

39. 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

40. Akustische Peaks von WMAP

41. A 220 Hz Frequency (in Hz) CMB Sound Spectrum Click for sound acoustic non-acoustic Lineweaver 2003

42. Kugelflächenfunktionen l=4 l=8 l=12 Jede Funktion kann in orthogonale Kugelflächenfkt. entwickelt werden. Große Werte von l beschreiben Korrelationen unter kleinen Winkel.

43. Vom Bild zum Powerspektrum • Temperaturverteilung ist Funktion auf Sphäre: ΔT(θ,φ) bzw. ΔT(n) = ΔΘ(n) T T n=(sinθcosφ,sinθsinφ,cosθ) • Autokorrelationsfunktion: C(θ)=<ΔΘ(n1)∙ΔΘ(n2)>|n1-n2| =(4π)-1 Σ∞l=0 (2l+1)ClPl(cosθ) • Pl sind die Legendrepolynome: Pl(cosθ) = 2-l∙dl/d(cos θ)l(cos²θ-1)l. • Die Koeffizienten Cl bilden das Powerspektrum von ΔΘ(n). mit cosθ=n1∙n2

44. Das Leistungsspektrum (power spectrum) ω = vk= v 2/λ

45. Temperaturschwankungen als Fkt. des Öffnungswinkels Θ 180/l

46. x Raum-Zeit Inflation t Entkopplung 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 nλ/2=cstr

47. 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

48. Temperaturanisotropie der CMB

49. Position des ersten akustischen Peaks bestimmt Krümmung des Universums!

50. Present and projected Results from CMB See Wayne Hu's WWW-page: http://background.uchicago.edu/~whu/ Verhältnis peak1/peak2-> Baryondichte Position erster Peak-> Flaches Univ.