1• Cosmic Microwave Background is smooth to a few parts in 105/~ 10-4• Yet high contrast structures (QSOs, galaxies) by z ~ 6./>> 1• Adiabatic perturbations grow as / t 2/3  R(t)  1/(1+z)• Expect onlyBlue = 0oKRed = 4oKBlue = 2.724oKRed = 2.732oKDipole Anistropy~ 1 part in 300After removing dipoleRed – blue = 0.0002oK~ 1 part in 105The Simplest Picture of Galaxy Formation and Why It Fails01.010711001)1(4CMBQSOCMBQSOzzSo where did galaxies and clusters come from?Log MJeans,bLog time [CO Fig. 30.7]CollapsesCollapsesOscillatesIn an expanding universe, will a cloud collapse?The Jeans criterion Version 2:3,4433)()(3TMTtRTtRcvbJTbs2/3,0035TMTTmkTvbJbTbHsRadiation era After decouplingTsGv4522TTTsTsTGGGMvGMvM23222543/4535353212Collapse if 2K < -U= [CO eq. 30.27]2/33,3/2.43TsbbJbbvconstMMDecouplingRadiation pressure keeps these clouds fluffed up.Radiation pressure has disappeared. Clouds now collapse.2K < -U Pressure support < gravityvs= sound speed Log T2Log MJeans,bLog time [CO Fig. 30.7]CollapsesCollapsesOscillatesQ.When do the oscillations start?DecouplingRadiation pressure keeps these clouds fluffed up.Radiation pressure has disappeared. Clouds now collapse.2K < -U Pressure support < gravityBefore decoupling:• Particle Horizondh= 2ctR(t)2T -2 (radiation era)• Proper distance containing mass M= (Mb/b)1/3Mb1/3R(t)Mb1/3T -1•Mass for which= dhMbT -3 R3t 3/2 (radiation era)MbT -3/2 (matter era)dhWhen Particle horizon = MSize scale for mass M Log T The Rest of the Story: dhLog MJeansLog time • Mass for which = dhM T -3 (rad. era)M T -3/2 (matter era)Dark MatterBaryonsDMPhotonsBaryonsDecouplingLog time Log time Log /Log /Silk Damping• But Dark Matter not subject to all this.– Does not feel radiation pressure.– Just collapses away…• Baryons fall into Dark Matter potential wells as soon as decoupling removes photon pressure support.•At tdecouplingthis mass was ~ 1016 M– M > 1016M continued growth– M < 1016M oscillations once mass scale comes into particle horizon.DecouplingLog time Log /1015Msun1017MsunBaryons3DMPhotonsBaryonsDecouplingLog time Log /CMB Fluctuations = snapshot of oscillations at tdecouplingdhLog MJeansLog time decouplingFourier analyze WMAP image: • Measures “Power” for each size scale .•= Power for each mass scale M.• But why more power for some mass scales than others?(deg)Power = Average (/)2of clouds of given size scale (predicted)What is measured?4(/)Dark Matter(/)BaryonsBaryons: Shorter spatial wavelengths oscillate with higher time frequencyFourier analyze WMAP image: • Measures “Power” for each size scale .•= Power for each mass scale M.• But why more power for some mass scales than others?(deg)Power = Average (/)2of clouds of given size scale (predicted)• All blobs of same mass M oscillate synchronously.• Peaks are for mass scales that are either fully compressed or fully rarified. 1stcompression2ndcompression1strarefaction(deg)Power = Average (/)2of clouds of given size scale (predicted)1stcompression2ndcompression1strarefactionPositive Curvature(K > 0)Negative Curvature(K < 0)Flat(K = 0)First peak:Size of “acoustic horizon”r = vs(tDecoupling– tHorizon) = c 3 t= linear size of perturbation = r/(d)= sin(d), d, sinh(d)lpeak= 220/tot1/2( l = multipole )Measured lpeak tot= 1.02.025Launch near Mt. Erebus in AntarcticaMapped Cosmic Background Radiation with far higher angular resolution than previously available.BoomerangBoomerang balloon flight (1999)Position of 1stpeak measures curvature= 1.0 0.7 0.0All models:b= .04, m= .23[CO fig 30.17]First peak:Size of “acoustic horizon”r = vs(tDecoupling– tHorizon) = c 3 t= linear size of perturbation = r/(d)= sin(d), d, sinh(d)lpeak= 220/tot1/2( l = multipole )Measured lpeak tot= 1.02.026• Type Ia Supernovae as “standard candles” accelerating expansion qo= m/2 - • CMB anisotropy  total= m+ • Can solve for m, = Cosmological Constantm= matter density/critical densityThe “Concordance” Cosmology (or CDM)Another independent measure:Rate of galaxy cluster evolution[CO