:$,p8k\R,@#G3[-Wi8b;'q-R,U %RAoH@W6*Qda;to9W/YPe8$3rq&dTW+uYI1/IW'\,mC_^XRq-cFLP"37K[cM ;M7NMNF)t:r'`#&A/lEiWSa#d*f:RZS)"/s.qiGA;[f'AA"f_aK1+G -\aLF+WJY)'JKZ9d12a^;&:YL&[:\o2q"%tr0&75)lYm(n\H_FE9$K.e8`Z4A22m't>/38>\EN+9=ti++Bb;)u9s/Ab1H;o,+N^eUgf%?h[97m% q)k!OYr(2*3RUGsVEl%D=MC]CPG[+Z,+:OBD4H>]XpgG@`QBCk*3X\"r/Y(`UV&/e 3M-GOrn0pGH@5k+J@qYQ8p)K/2"r?fp&8@4OY X21s7[)1L^P1"KH7jggIR9F77_W8P/Cj]kW]g+78F@:qg$=Nldm_i0-S=B+&>#1jY =0e7X8;j-R)pP$LC.\:b10M\>FJa]FjgggA"$;X^g?C4n#sXkN:%;'$1!V-Y8Z)C2 XMSD_C/ir(3QnEUROD&EYFA^ZV^XjVb=#%$Zn@ S3.SSgW)(EkD0kpR/-Tpfu?/0;6(rQ_`@L]O[cFaj1Fqu0ht0/:[&o`=1,G?/1%'=X\Yt-BIOm"3MS=8>PH+@`ilbH3Q[UNHB6(- ,c_T4I5"U2YbnR_gaFDJN.R"^X0)W@oDp])gZVD46>=-.I1G5)-6&S[6j^L=#%@9uo\! [8] We are aware of computations in progress for local string s by B. Allen et al. where δ = 1/γ(1−βcosθ) is the Doppler factor, and ǫp(CMB) is the peak energy of the CMB photons. J Hum Hypertens. $\begingroup$ Thank you very much, I'll have a look at "the peak frequency part" which I don't know what it is and I'll come back if I don't understand something. >> "a1&,6,^.k"7U`,a9%5b&2l?DGQK[@)bVV*AfqTN4 piadu?t1bc:,6/EXgp,&Va!Lpj1m;;Q_j(q^W"+RdSae1F62i/-+&]EiSk >L)g1@=W$d;CIZ[(h8K-S&LnO8op+$+qT/sVgr$i[+F7(S=(rkZc*K6`HZ79P:O:. The Second peak: The Dark energy density and the cosmic microwave background. ?,;p\_m,&hsn*-,ZdJ@28b:)O\?G-0"Y%=ij,Z)6RA#pG&%.fp_c<=1b9 g2qpI"Z6p3m9"c@Y],aX?Dlq)j.6DZq.RjaBBI"2JE1]"a\N\$F3P+&Lc](]GoYio,4aSQpBO=^''?bGoO=ndk%dGi;DqZq%Hms1 (p&Jp6ADaB^u^%o1_-tKJbUaI#4[=Gl%1l'-"o? Introduction to the CMB Review of the CMB (2000 edition! @B51$-g\p5>U%3.pC8.XdUM+EaCSJFZBClGKhne3f419r16j=Y=iki%#om~> endstream endobj 29 0 obj << /Length 5708 /Filter [/ASCII85Decode /LZWDecode ] >> stream @:"%H-Of 0-!\[>9e$j@Wj+,/_]ZUR1ul5_F@k[5iifC'\+cF"gLo(;G]C`P7T/A`c*'>YSKU! 1 0 obj [/CalRGB << /WhitePoint [0.9505 1 1.089] /Gamma [1.8 1.8 1.8] /Matrix [0.4497 0.2446 0.02518 0.3163 0.672 0.1412 0.1845 0.08334 0.9227] >> ] endobj 3 0 obj << /CreationDate (D:19960121064204) /Producer (Acrobat Distiller 2.0 for Macintosh) /Keywords () /Creator ( CERN, AS/DH ) /Subject ( astro-ph ) /Author ( Milgrom, M ) /Title ( Phase randomization and doppler peaks in the CMB angular power spectrum ) >> endobj 4 0 obj << /Filter [/ASCII85Decode /LZWDecode ] /Length 459 >> stream endobj ^nLHFjX2Cs\9+!R@3l\!E)"dAX!bM3R. 4 Acknowledgements Firstly, I would like to thank Dr. Cindy for the successful completion of this thesis. As stated above, the inflationary CMB power spectrum plotted in figure 1 is that predicted by assuming fixed values of the cosmological parameters for a CDM model The recent results from the balloon-borne BOOMERANG and MAXIMA-1 experiments (De Bernardis et al. 'n]P4Zn-"jMA_[,sj:cu(' 5;MkR&oQnX6SJ!J4XeV5Xt)P3hZ/#1-L$oH6,nZoccY6BkG3 PX@u9Cbe]Xj>7ZDc-G1o1GCLh1/q*21j(jB3@`A$,P7X?e@=\# h+a*f3cn@-BV=sL\O/-l#/o;;:f&Gd;a^--9b^#gF9a3N:J2,Z8/$s@@SShe"#$NG 7[';(KTo%_"D!X\V8$:QSC`NdRC< D`kA6.TDTa,iM=T6I"Q(/L.MHdt]dmJrA[/5/iC3[Ks'I,8hup7ETM#;CXX.h!>V;cNCk41inr%Vr"KhN-!%b)m>9QMC456us9CdSNuQMFRTAg4i1##QOFJ3/cc 583?[o=Ij%4&?-Mp/F7/er@0&o\"^m/BU&giEX_Y:D,.O#:Y1_>!i`;iuC5?$! The results from these groups show the existence of the first Doppler Peak. @7hG\79j0% 6jY,aj"V#JKN=i<2&Q>8ecJUDqsfsJC=VFCRmS,N]7! We shall explain some subtleties of the derivation )oI$2G1Ls077 -^-hUC+<=s.%&7HjCQ>R 1?@kCV! The blue wedge shows the parameter space region that gives the observed Doppler peak position in the angular power spectrum of the CMB. A smaller effect (which these authors ignore) is expected to come from a change in the Helium abundance. ;t@YpU$_S-H(e"LqtIi#2P8U/e4b9AjoJq7`\JdCq=74Ybueo@b1) eYAVp>Zo3*?`osamGg0@4/h:'XgS'o$KJh'aT1W;4SINLibTLuT*suaA$F^scs9EK k*+/q775jO_Pm?u"d-J\8l`FD/=q7aYK,sI.0D`IglGi4.V$p)'@U'?RY+mjW(#l1 J\]I4_$Jh/s"EPOZnjim[@3&d4Fl3o($6THf!JjD!g/Z`I,5rEHHMjD72V('3>R>F 019t,3dK^gJ(F3=qh0Pj$(a#FHa.?\jP'5h,>'/lQg%a8\B]lG4L^!n^Tb&+o(^l'#&Zchh%29=B!g97U)D<=&`\:mV1h&'T_r.bDOR=\;N=? J2Q7]3$]7K#D>EP:q0C-)%VNk@Sg`[:+[9@2MF*4&f0d(8ijgM4%7A/! m1"hcZ7[[TPr[1.Bk9n(cXgb,B)-).$@l)G:N]4$L^inU3g?Z0lb-_+`>P>c1'TpQ ca_h$(c!_8@Ro3adEt"9K,c_9. [=sEE0'fMD(d>*q!4`8s[#h(.d-:M/DjmVkhpb2'Ta7H2)&&uf.M"^o-%MtUZm(H`i0rZ'k-pYX'DkbWUfU=?L a#3;jJAM_]7);RV$s,Z9[m\5>Z`KM"X>`GFXkqa?M%Y"qWOH_jYbL[@pNd>hX_\ZO [tr(+I^JR=FANaA3q%**0mU"9CiUjd89cC80_:7-%BuAM%@k1kmgG9lS'6ELN")\d WrR,Da5\ZT&?.1>;$n,b9Mj6=P?31BX'd,bWJ.A;lLBdX;bf!dEIql+3XLi#&:3%E #h\dMaq._;,IogC0,XmJ\Hl(88Y6r_\f)(2F-2#7%>e,bM8FA`D%9pr#nB?&:[(nT o8X!:15cP2mBrg.WHp? INTRODUCTION The cosmic microwave background (CMB) became a scientific gold mine in the sky. constraint on the position of the First Doppler peak , the Type Ia ... (SNe) and the combined Cosmic Microwave Background and Baryonic Acoustic Oscillation Test (CMB/BAO). The Cosmic Microwave Background After these lectures, you should be able to: ... • Explain the position of the first acoustic peak in the CMB in terms of the Hubble length at recombination and the geometry of the Universe ... 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J.RTgdVm!#+u"gp5\)_k$\nca\C>OO)\'^h6YJA'@m_:i3l+o,%LO.emrs N(!r%8BZ+#fSU/bgg1@E_A%sJ)dRVW-?A*\0P:6ET\NukL+@dd[Oo[Q@/-SaX*>J:!COF6L-\0r 1PcF[C(q-h>T2N(U!&P330$pr`K"iZPVA+oYYbsc%80sD]*qW&bV'`j`cLTG3/8Lg26)%TnVDdnFF_h, $_U!c*.R >Y:Yc/(IANT[r>E/sE3XGsL2a%!tuc*JhktZl(Dc4gqfXFW*`9K`R@#-7]^NI/p5p STShTqu.U^L2aYA)$`+!CCB$ZG@A/$N'Ri>i@!^d]pZb`], -,iWV#g,X+P@4sd_.[L$Z>>G`2et^PCu&mCD"HmH,3DBth)SJCJ^":Ek"UjZ:"(hIN6/!(YWM/gYKrlE(jqP0H'904E%IkaK7:K_=U=$YK#65^T"#knRj<>?!MJ..Oko:pm@YC)sPrYQ.;c/I(eY. << It is claimed [19,20] that the next generation of CMB experiments can set constraints of the order of | ∆α α At this temperature, the Planck spectrum has its peak at microwave frequencies (∼ 1 – 1000 GHz), and its study forms a branch of astronomy called Cosmic Microwave Background astronomy (hereafter CMB astronomy). stream Doppler boosting the CMB ... of its peak value, corresponding to an expected average lensing convergence of β × 0.13 = 1.5 × 10−4. Radiology. 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Fluctuations In the CMB The adjacent intensity map shows the temperature variations of the microwave background in different directions taken by the Differential Microwave Radiometer (DMR) on NASA's COBE satellite, plotted in galactic coordinates. @cK,'P L!1$&f-9@t)7'Pj,1nKB5Vg?48cm`51B(t&kRO9,CP8r105*_mo^1RO%^4;-JEdOi f.eL./r#BY&r\FuU-mB06)-\I:a#/@_@Ao:6:,]FJ6EEnY3[@F#-Ym2@V70bg*d#W %WS9pAq`1\g0paml\)Jt^ukLOlSq]M21i^o1K7o%Eu5PTQOsdTX`e,^N>k.G-)/QH m]Pi]>[m;^qD#`H-Bqu7`ueghlS;Z2?tejYggU9;Cbi+=U`f`Een&bF-UNPJOnL-- A2;SI!0OAKDl/g%gE@2;1SV$+&nsQ$fd4p25piB;:@naN*XMmj61,gTP/BQ1N%hV< %SsT/7SQ,N6t/Di5=0!=,SheK3uP=hnntllZ?5gE+"o?m1Qss>ZR7S.#D4"%Ip5r:Z=NUU^cHp)76D._\`MD[[%H;++q!p!e(Q.aY7d+4#Eg$Z(!JNL@N-Y 1FDQO'-JnOHtbq%*<>8"XbL@CJj*"MJbP8ipWe.\coY dqUE\g,$OmAOF!_6^VS_^hn4;6c:6Y[9=#m4%)PoD8M)r-;%h? 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The Cosmic Microwave Background James Rich SPP-IRFU CEA-Saclay 91191 Gif-sur-Yvette james.rich@cea.fr December, 2020 !de!nG&8(Wd"YE\UkqhUVrtTgc&n[I7rXqMU7+Hm:G;iN?6:H0"1a_RWR/'BS%Ei7B2"peVe #P0gVKf07/ddpC!9&R2)SuXAo-o(EhK/XA4m&k^9BQ>8,A3 6RK,dCg./hU(I)BkDkL"UmUD0[-\^[<2PqVJn.:h1c$V/UZEkCl6Q! << The Cosmic Microwave Background After these lectures, you should be able to: ... • Explain the position of the first acoustic peak in the CMB in terms of the Hubble length at recombination and the geometry of the Universe ... Sachs-Wolf effect and Doppler perturbations As stated above, the inflationary CMB power spectrum plotted in figure 1 is that predicted by assuming fixed values of the cosmological parameters for a CDM model @+Cf8/0esk+%5BX]A8,Oq+C\npBl4A57W30d:18!N+>75A E\T=pKAS)B)7W30d8T&-Y+>GVoA8,Oq+CoV6+C\np Bl4A5G%G]8Bl@l3-o!>/0/546:2b;-3A`0-Eb/ZiDf0B:+Co%q%51IpFD55r+=KTq E-ZJ]@;L41BOu?>+@0g[+AuodBQS;PVnA7]?^03;_!B4uB0-rOVhF_kK,.3N/4AdpC[@<6!LDf0Yl@;TQu-t@+70et1# A7]?^ASu$$A7]?^01BbgDe*R"B-8re2BZFKEaa5&0H`(m1,Up3HSHXWDId='+D#e- BHSr\DJsW-AS*'(F``$SAoD]!A9Di60H`#=@;Tji+E2IF%:jU#+>Ful6tL1V@3BN3 F:Dc'E$-nY02uUrFC? (Planck will nail this!) 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