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Einteilung der VL

Einteilung der VL. Einführung Hubblesche Gesetz Antigravitation Gravitation Entwicklung des Universums Temperaturentwicklung Kosmische Hintergrundstrahlung CMB kombiniert mit SN1a Strukturbildung Neutrinos Grand Unified Theories -13 Suche nach DM. HEUTE. Vorlesung 8 .

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Einteilung der VL

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  1. Einteilungder VL • Einführung • HubblescheGesetz • Antigravitation • Gravitation • Entwicklung des Universums • Temperaturentwicklung • Kosmische Hintergrundstrahlung • CMB kombiniert mit SN1a • Strukturbildung • Neutrinos • Grand Unified Theories • -13 Suche nach DM HEUTE

  2. Vorlesung8 • RoterFaden: • Powerspektrumder CMB • Baryonic Acoustic Oscillations (BAO) • Energieinhalt des Universums

  3. Akustische Peaks von WMAP Ort-Zeit Diagramm

  4. Kugelflächenfunktionen l Jede Funktion kann in orthogonale Kugelflächenfkt. entwickelt werden. Große Werte von l beschreiben Korrelationen unter kleinen Winkel.

  5. 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

  6. 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 „Weißes Rauschen“: flaches Powerspektrum

  7. Temperaturschwankungen als Fkt. des Öffnungswinkels Θ 180/l Balloon exp.

  8. Das Leistungsspektrum (power spectrum) UrsachenfürTemperatur- Schwankungen: GroßeSkalen: Gravitationspotentiale KleineSkalen: AkustischeWellen l=1 nichtgezeigt, da sehr stark wegen Dipoltermdurch BewegungderGalaxie gegenüber CMB

  9. Temperaturanisotropie der CMB

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

  11. 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 109yr. Öffnungswinkel θ = cs * trec * (1+z) / c*t0 Mit (1+z)= 3000/2.7 =1100 und trec = 3,8 105yr 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

  12. CMB zeigt: Universum ist flach Erste akustische Peak unter bei einem Öffnungswinkel von 0.8 Grad oder l=220 bedeutet: das Universum ist flach oder die mittlere Dichte entspricht der kritischen Dichte von 2. 10-29 g/cm3 oder =1 und Gesamtenergie (kin. + pot. Energie) ist Null!

  13. Präzisere Berechnung des ersten Peaks Vor Entkopplung Universum teilweise strahlungsdominiert. Hier ist die Expansion  t1/2 statt t2/3 in materiedominiertes Univ. Muss Abstände nach bewährtem Rezept berechnen: Erst in mitbewegtenKoor. 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

  14. WMAP analyzer tool http://wmap.gsfc.nasa.gov/resources/camb_tool/index.html

  15. Neueste WMAP Daten (2008)

  16. Neueste WMAP Daten (2008) http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.0732v2.pdf Polarisation Reionisation nach 2.108 a Temperatur Temperatur- und Polarisationsanisotropien um 90 Grad in Phase verschoben, weilPolarisation FlussderElektronen, also wenn x cos (t), dann v  sin (t)

  17. CMB Polarisation durch Thomson Streuung (elastische Photon-Electron Streuung) Prinzip: unpolarisiertes Photon unter 90 Grad gestreut, muss immer noch E-Feld Richtunghaben, so eineKomponenteverschwindet! DaherbeiIsotropiekeine Pol. , beiDipolauchnicht, nurbeiQuadr.

  18. CMB Polarisation bei Quadrupole-Anisotropie Polarization entweder radial oder tangential um hot oder cold spots (proportional zumFlussderElektronen, also zeigtwie Plasma sich bewegtebei z=1100 and auf großeSkalenwie Plasma in Galaxien Cluster sichrelativzum CMB bewegt) http://gyudon.as.utexas.edu/~komatsu/presentation/wmap7_ias.pdf

  19. Entwicklung des Universums

  20. CMB polarisiert durch Streuung an Elektronen (Thomson Streuung) Kurz vor Entkoppelung: Streuung der CMB Photonen. Nachher nicht mehr, da mittlere freie Weglange zu groß. Lange vor der Entkopplung: Polarisation durch Mittelung über viele Stöße verloren. Nach Reionisation der Baryonen durch Sternentstehung wieder Streuung. Erwarte Polarisation also kurz nach dem akust. Peak (l = 300) und auf großen Abständen (l < 10) Instruktiv:http://background.uchicago.edu/~whu/polar/webversion/node1.html

  21. Conformal Space-Time (winkel-erhaltende Raum-Zeit) t Raum-Zeit x t From Ned Wright homepage x  = x/S(t) = x(1+z) t    = t / S(t) = t (1+z) conformal=winkelerhaltend z.B. mercator Projektion 

  22. Woher kennt man diese Verteilung? If it is not dark, it does not matter

  23.  = (SM+ DM) Vergleich mit den SN 1a Daten SN1a empfindlich für Beschleunigung a, d.h. a  - m (beachte: DM und DE unterschei- den sich im VZ der Grav. a   - m CMB empfindlich für totale Dichte d.h. tot = + m =1 tot =  + m =1

  24. 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 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.

  25. Akustische Baryon Oszillationen II: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html Now what happens? The neutrinos don't interact with anything and are too fast to be bound gravitationally, so they begin to stream away from the initial perturbation. The dark matter moves only in response to gravity and has no intrinsic motion (it's cold dark matter). So it sits still. The perturbation (now dominated by the photons and neutrinos) is overdense, so it attracts the surroundings, causing more dark matter to fall towards the center. The gas, however, is so hot at this time that it is ionized. In the resulting plasma, the cosmic microwave background photons are not able to propagate very far before they scatter off an electron. Effectively, the gas and photons are locked into a single fluid. The photons are so hot and numerous, that this combined fluid has an enormous pressure relative to its density. The initial overdensity is therefore also an initial overpressure. This pressure tries to equalize itself with the surroundings, but this simply results in an expanding spherical sound wave. This is just like a drum head pushing a sound wave into the air, but the speed of sound at this early time is 57% of the speed of light! The result is that the perturbation in the gas and photon is carried outward:

  26. Akustische Baryon Oszillationen III: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html As time goes on, the spherical shell of gas and photons continues to expand. The neutrinos spread out. The dark matter collects in the overall density perturbation, which is now considerably bigger because the photons and neutrinos have left the center. Hence, the peak in the dark matter remains centrally concentrated but with an increasing width. This is generating the familiar turnover in the cold dark matter power spectrum. Where is the extra dark matter at large radius coming from? The gravitational forces are attracting the background material in that region, causing it to contract a bit and become overdense relative to the background further away

  27. Akustische Baryon Oszillationen IV: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html The expanding universe is cooling. Around 400,000 years, the temperature is low enough that the electrons and nuclei begin to combine into neutral atoms. The photons do not scatter efficiently off of neutral atoms, so the photons begin to slip past the gas particles. This is known as Silk damping (ApJ, 151, 459, 1968). The sound speed begins to drop because of the reduced coupling between the photons and gas and because the cooler photons are no longer very heavy compared to the gas. Hence, the pressure wave slows down.

  28. Akustische Baryon Oszillationen V: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html This continues until the photons have completely leaked out of the gas perturbation. The photon perturbation begins to smooth itself out at the speed of light (just like the neutrinos did). The photons travel (mostly) unimpeded until the present-day, where we can record them as the microwave background (see below). At this point, the sound speed in the gas has dropped to much less than the speed of light, so the pressure wave stalls.

  29. Akustische Baryon Oszillationen VI: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html We are left with a dark matter perturbation around the original center and a gas perturbation in a shell about 150 Mpc (500 million light-years) in radius. As time goes on, however, these two species gravitationally attract each other. The perturbations begin to mix together. More precisely, both perturbations are growing quickly in response to the combined gravitational forces of both the dark matter and the gas. At late times, the initial differences are small compared to the later growth.

  30. Akustische Baryon Oszillationen VII: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html Eventually, the two look quite similar. The spherical shell of the gas perturbation has imprinted itself in the dark matter. This is known as the acoustic peak. The acoustic peak decreases in contrast as the gas come into lock-step with the dark matter simply because the dark matter, which has no peak initially, outweighs the gas 5 to 1.

  31. Akustische Baryon Oszillationen VIII: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html At late times, galaxies form in the regions that are overdense in gas and dark matter. For the most part, this is driven by where the initial overdensities were, since we see that the dark matter has clustered heavily around these initial locations. However, there is a 1% enhancement in the regions 150 Mpc away from these initial overdensities. Hence, there should be an small excess of galaxies 150 Mpc away from other galaxies, as opposed to 120 or 180 Mpc. We can see this as a single acoustic peak in the correlation function of galaxies. Alternatively, if one is working with the power spectrum statistic, then one sees the effect as a series of acoustic oscillations. Before we have been plotting the mass profile (density times radius squared). The density profile is much steeper, so that the peak at 150 Mpc is much less than 1% of the density near the center.

  32. One little telltale bump !! 150 Mpc. A small excess in correlation at 150 Mpc.! SDSS survey (astro-ph/0501171) (Einsentein et al. 2005) 150 Mpc =2cs tr(1+z)=akustischer Horizont

  33. 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 (astro-ph/0501171) (Eisenteinet al. 2005)

  34. Combined results http://arxiv.org/PS_cache/arxiv/pdf/0804/0804.4142v1.pdf http://nedwww.ipac.caltech.edu/level5/March08/Frieman/Frieman4.html

  35. 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 Univ. am Anfang heiß war, weil akustische Peaks, entstanden • durch akustische stehende Wellen in einem heißen Plasma, entdeckt wurden • 2. die Temperatur der Strahlung im Universum 2.7 K ist wie erwartet bei einem EXPANDIERENDEN Univ. mit Entkopplung der heißen Strahlung und Materie bei einer Temp. von 3000 K oder z=1100 (T  1+z !) • 3. das Univ. FLACH ist, weil die Photonen sich seit der letzten Streuung • zum Zeitpunkt der Entkopplung (LSS = last scatteringsurface) auf gerade • Linien bewegt haben (in comovingcoor.) • 4) BAO wichtig, weil Sie unabhängig von der akustischen Horizont in der CMB ein zweiter wohl definierter Maßstab (akustischer Horizont der Materie) bestimmt, dessen Vergrößerung heute gemessen werden kann. Dies bestätigt die Energieverteilung des Univ. unabh. von der Frage ob SN1a Standardkerzen sind. • 5) Polarisation der CMB bestätigt Natur der Dichtefluktuationen zum Zeitpunkt der Entkopplung und bestimmt Zeitpunkt der Sternbildung (Ionisation->Polarisation) • Die schnelle Sternbildung kann nur mit Potentialtöpfen der DM zum Zeitpunkt der • Entkopplung erklärt werden. (die neutrale Kerne fallen da hinein).

  36. Zum Mitnehmen If it is not dark, it does not matter

  37. Zusatzfolien mit Text der Nobelpreisankündigungen „just forfun“, kein Prüfungsstoff.

  38. 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

  39. 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

  40. 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

  41. 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).

  42. 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 theanisotropieswereexpectedtobeofthe 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!

  43. 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.

  44. 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.

  45. 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.

  46. 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).

  47. 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.

  48. 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.

  49. 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).

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