AaM2d HH $ @d HHHHff@  d Footnote TableFootnote**.\t.\t/ - :;,.!?/  `K5  `MTOCHeading1Heading2   EquationVariables9/5f5V5X5Z%5\q5^7юT6*aV61h=6?̑6G6Yz6^6g_6q6M666k6D6&66#&6%7~e7 7 C7 #o8 ! ) I > )<$lastpagenum> *<$monthname> <$daynum>, <$year> +"<$monthnum>/<$daynum>/<$shortyear> ,;<$monthname> <$daynum>, <$year> <$hour>:<$minute00> <$ampm> -"<$monthnum>/<$daynum>/<$shortyear> .<$monthname> <$daynum>, <$year> /"<$monthnum>/<$daynum>/<$shortyear> 0 <$fullfilename> 1 <$filename>t 2 <$paratext[Title]> 3 <$paratext[Heading1]> 4 <$curpagenum> 5 <$marker1> 6 <$marker2> 7 (Continued) 8+ (Sheet <$tblsheetnum> of <$tblsheetcount>) 9Heading & Page <$paratext> on page<$pagenum> :Pagepage<$pagenum>5 ;See Heading & Page%See <$paratext> on page<$pagenum>.^ < Table All*7Table<$paranumonly>, <$paratext>, on page<$pagenum> =Table Number & Page'Table<$paranumonly> on page<$pagenum>k  FFA HHA  JJ LL NN PP R A$  ~a5y  soe>5|  s > 5  ui> 5 t"5 ! u/um5 " ta5 # vn$d5 $ x se5 % w so>/5 & { s$ea5 ' y wfi5 ( w w 5 ) y w 5 *  wele5 + w wte5 , w w]5 - z wg5 .  wa5 / a5 0 z od)5 1 w w+t 5 2 w ~u<$5 3  ~n5 4  wnge5 5 { wx p5 6 w wu5 7 | ween5 8 w wHe5 9 we<5 :  e5 ; w w^5 < w*e5 = wl$p5 > w wo<5 ? w wTa5 @ w&'5 A w way>5 B { wp>k5 C w w6% D wF6& E w6+ F w62 G w w6; H  wJ6N I w w6O J { w6T K v 6U L w6Z M w6_ N wR6j O w w$ ~6k P w ws6 Q w ws6 R w wu6 S wt6 T wu6 U x wt6 V w wv6 W { wx6 X ww6 Y w{6 Z wy6 [ w ww6 \ wy6 ] w 6 ^ w6 _ x ww6 ` w wz7 a w w6 b w6 c w wz6 d ww6 e w ww7 f w w7 g w w7 h w w{7 i { ww7 j v w|7 k w ww8 l w w7 m w w7 n | ww8 o w9$ p 8 q w ww9 r w8 s 8 t w9 u {9 v w9 w 9 x } 9 y 9% z w9& { w w9- | 9. } {5 +6Tdq5PFR6jdq6wsLH6dq7xt8C6Hm3R q897 {Hm3R H RH R FootnoteHr@ q98:7 Hr@ HzHz  Single LineH'q:9<7 w;;Footnote w  5_;:     HD q<:=7 8HD HH  Double LineH q=<@78>?w Double Lines 5c>?={5e?>=9%9& wH q@=B7TAA Single Line5hA@HZqB@C7q TableFootnoteEGxR qCB7 9EGxR EPwEPw  TableFootnoteod5pDRRHH5xE5 HH Fe   HH5zFN5 HHlEE DHH5{G6 HH @>?HDoe   HH5}HJ6HHlGG HUV 5~I6 -HUV AAJUU`   HUV 5JLH6HUV lII H$ 5K6 FtnH$ ELUU` tn oH$ 5LJ6H$ lKK HUV 5M5 HUV N UUe !  HUV 5NPF5HUV lMM H$ 5O5 H$ P UUe "  H$ 5PN5H$ lOO HH5QD HHAR  ` #  The Big Bang ;` $ The Very Early Universe X` %  u` ' 5(We know the universe had a beginning. ` (  ` *  Hubble Expansion ` - $The age of the universe is  ~1/H ` / 1  It all began  10  Billion years ago ` , 5 #` . " The Cosmic Microwave Background @` 0 The flash of the big bang ]` +  Vz` 1  F` ) ,We know it looked very different back then. ` 2  ` 3 1The universe was dominated by  radiation . ` 4 +(Today it is dominated by  matter .)  HH5RDHHlUQQ d5SUUHH5TS HH|Th  ` $ V^Uly  ` 5 %The Flat Universe ;` 6 th nX h 7 nn  or   u` 8 * ` 9 on"Note:  M  is constant, but ` : 3R ,  r  and  H  change with time t 10` ; a  h < 5*Integrate the first equation and find  h = /which means that the universe grows like ] h > V@Also, if  t  is the present age of the universe, then ryW` ? en$for H 0  = 75  km/secMpc. t` @ er4  Getting hard to accomodate globular clusters! 4HH5US .)HHlRbTT |I"9@5VXSQWWT59>5WV9>9>M՜% '^equal[(*q"Blue"q*)power[(*q"Blue"q*)id[(*q"Blue"q*)over[(*q"Blue"q*)times[(*q"Blue"q*)char[(*q"Blue"q*)d],char[(*q"Blue"q*)R]],times[(*q"Blue"q*)char[(*q"Blue"q*)d],char[(*q"Blue"q*)t]]]],num[(*q"Blue"q*)2.00000000,"2"]],over[(*q"Blue"q*)times[(*q"Blue"q*)num[(*q"Blue"q*)2.00000000,"2"],char[(*q"Blue"q*)G],char[(*q"Blue"q*)M]],char[(*q"Blue"q*)R]]]T 58e5XVZSInYYT a f56e5YXh t56e56eA S''equal[(*q"Blue"q*)power[(*q"Blue"q*)char[(*q"Blue"q*)H],num[(*q"Blue"q*)2.00000000,"2"]],over[(*q"Blue"q*)times[(*q"Blue"q*)num[(*q"Blue"q*)8.00000000,"8"],char[(*q"Blue"q*)pi],char[(*q"Blue"q*)G],char[(*q"Blue"q*)rho]],num[(*q"Blue"q*)3.00000000,"3"]]])N95ZX\S[[T9YݱDu 5[ZWTYݱDu YݱDu F'atop[(*q"Magenta"q*)equal[(*q"Magenta"q*)int[(*i2iq"Magenta"q*)times[(*q"Magenta"q*)power[(*q"Magenta"q*)char[(*q"Magenta"q*)R],over[(*q"Magenta"q*)num[(*q"Magenta"q*)1.00000000,"1"],num[(*q"Magenta"q*)2.00000000,"2"]]],diff[(*q"Magenta"q*)char[(*q"Magenta"q*)R]]],num[(*q"Magenta"q*)0.00000000,"0"],char[(*q"Magenta"q*)R]],times[(*q"Magenta"q*)power[(*q"Magenta"q*)id[(*q"Magenta"q*)times[(*q"Magenta"q*)num[(*q"Magenta"q*)2.00000000,"2"],char[(*q"Magenta"q*)G],char[(*q"Magenta"q*)M]]],over[(*q"Magenta"q*)num[(*q"Magenta"q*)1.00000000,"1"],num[(*q"Magenta"q*)2.00000000,"2"]]],int[(*i2iq"Magenta"q*)diff[(*q"Magenta"q*)char[(*q"Magenta"q*)t]],num[(*q"Magenta"q*)0.00000000,"0"],char[(*q"Magenta"q*)t]]]],equal[(*q"Magenta"q*)times[(*q"Magenta"q*)over[(*q"Magenta"q*)num[(*q"Magenta"q*)2.00000000,"2"],num[(*q"Magenta"q*)3.00000000,"3"]],power[(*q"Magenta"q*)char[(*q"Magenta"q*)R],over[(*q"Magenta"q*)num[(*q"Magenta"q*)3.00000000,"3"],num[(*q"Magenta"q*)2.00000000,"2"]]]],times[(*q"Magenta"q*)power[(*q"Magenta"q*)id[(*q"Magenta"q*)times[(*q"Magenta"q*)num[(*q"Magenta"q*)2.00000000,"2"],char[(*q"Magenta"q*)G],char[(*q"Magenta"q*)M]]],over[(*q"Magenta"q*)num[(*q"Magenta"q*)1.00000000,"1"],num[(*q"Magenta"q*)2.00000000,"2"]]],char[(*q"Magenta"q*)t]]]]NH5\Z^Sn"q]]T"MenL45]\gtaL4L4$)n'equal[(*q"Magenta"q*)char[(*q"Magenta"q*)R],cross[(*q"Magenta"q*)string[(*q"Magenta"q*)"constant"],power[(*q"Magenta"q*)char[(*q"Magenta"q*)t],over[(*q"Magenta"q*)num[(*q"Magenta"q*)2.00000000,"2"],num[(*q"Magenta"q*)3.00000000,"3"]]]]]m[NBH5^\Sea"__T"qti`D<5_^("M`D<`D<$q*'equal[char[t],times[over[num[2.00000000,"2"],num[3.00000000,"3"]],over[num[1.00000000,"1"],indexes[0,1,char[H],num[0.00000000,"0"]]]],times[sn[num[8.70000000,"8.7"],num[9.00000000,"9"]],string[" years"]]]a"d5`200bba")GHH5a` ")nHH`00  a"q*)2.0fb,c  ` & The Inside of a Blackbody ;` A  X C "M/Useful model of a blackbody is a small hole in tau H C 7the side of a box (cavity) with black walls:  *q"b` D s[+What is the energy density inside the box? t"] h E "q2 The radiation per unit area out the hole is  F 001 It comes out at speed c into a solid angle and  H F 5#into a fractional solid angle  T;` G ˭ X h H    so  HH5b`eqHHlUeaa ]],d5c]umeesnumHH5dc i["HH|  2eb  ` B Matter and Radiation C ` K in the Universe  Today f` I q* 0 h L /For the local group, the matter density is dy  h M 8The density of radiation,  in mass units , is sL h N 0   and the universe is matter-dominated h i` O  " h P s[7But  there are many more photons than nucleons:  Q diXwith  < E g >= hc /l MAX  and  l MAX  from Wiens law, to@ Q /and  we assume that all matter is hydrogen. le :` R  GW` S 0  n N   / n g  10 -9 t` T 'with a very low average photon energy. HH5ecHHlbdd H5f`"@ga5ghf MaerHZp$? 5hgjfjip$?  thlop$!~!~%~(~(~/?p$c5iprf itchp/?c? $5jhkfhkisis/?c? $ h /?p$5c5c9_c<c<cCp$Cp$? 5kjlfjliCp$? 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Substitute for l h f [EPA 1/2 / R 2  using the expression for  r r  and get pht` g 00$where time  t  is in seconds. ],HH6]inHHl r[sn]!fG6]n]!fGn]!fG8.4/m'propto[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)rho],char[(*q"Green"q*)m]],fract[(*q"Green"q*)num[(*q"Green"q*)1.00000000,"1"],power[(*q"Green"q*)char[(*q"Green"q*)R],num[(*q"Green"q*)3.00000000,"3"]]]]yp]#fG6oBi agTh!fG6"=HH!fG!fGSna4As'#propto[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)rho],char[(*q"Green"q*)r]],power[(*q"Green"q*)char[(*q"Green"q*)T],num[(*q"Green"q*)4.00000000,"4"]],fract[(*q"Green"q*)num[(*q"Green"q*)1.00000000,"1"],power[(*q"Green"q*)char[(*q"Green"q*)R],num[(*q"Green"q*)4.00000000,"4"]]]]RyL#fG6  gXFX6,XFXXFX-#,in'spropto[(*q"Green"q*)char[(*q"Green"q*)T],fract[(*q"Green"q*)num[(*q"Green"q*)1.00000000,"1"],char[(*q"Green"q*)R]]]n]^ZFX6o*qn")06)],FjJuA(00'mpropto[over[indexes[0,1,char[rho],char[r]],indexes[0,1,char[rho],char[m]]],over[num[1.00000000,"1"],char[R]]]NL6gTh6fGTw>4xe'equal[(*q"Blue"q*)power[(*q"Blue"q*)id[(*q"Blue"q*)over[(*q"Blue"q*)times[(*q"Blue"q*)char[(*q"Blue"q*)d],char[(*q"Blue"q*)R]],times[(*q"Blue"q*)char[(*q"Blue"q*)d],char[(*q"Blue"q*)t]]]],num[(*q"Blue"q*)2.00000000,"2"]],over[(*q"Blue"q*)times[(*q"Blue"q*)num[(*q"Blue"q*)2.00000000,"2"],char[(*q"Blue"q*)G],char[(*q"Blue"q*)M]],char[(*q"Blue"q*)R]],times[(*q"Blue"q*)over[(*q"Blue"q*)times[(*q"Blue"q*)num[(*q"Blue"q*)8.00000000,"8"],char[(*q"Blue"q*)pi],char[(*q"Blue"q*)G]],num[(*q"Blue"q*)3.00000000,"3"]],power[(*q"Blue"q*)char[(*q"Blue"q*)R],num[(*q"Blue"q*)2.00000000,"2"]],indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)rho],char[(*q"Blue"q*)r]]]]NPe6u 00d6r]]r[]]HH6 HHm    ` j The Primordial Soup w;` a  X n eq0Particles and antiparticles in equilibrium with veu@ n s[Aphotons ( gg  p p )  if it is hot enough . "` h *) c h k ]]! When  the universe was o h m me1 A little later,  so the unverse became (HH6"ueHHl  num6qpivtw>,00'equal[(*q"Green"q*)power[(*q"Green"q*)id[(*q"Green"q*)over[(*q"Green"q*)times[(*q"Green"q*)char[(*q"Green"q*)d],char[(*q"Green"q*)R]],times[(*q"Green"q*)char[(*q"Green"q*)d],char[(*q"Green"q*)t]]]],num[(*q"Green"q*)2.00000000,"2"]],times[(*q"Green"q*)over[(*q"Green"q*)times[(*q"Green"q*)num[(*q"Green"q*)8.00000000,"8"],char[(*q"Green"q*)pi],char[(*q"Green"q*)G]],num[(*q"Green"q*)3.00000000,"3"]],power[(*q"Green"q*)char[(*q"Green"q*)R],num[(*q"Green"q*)2.00000000,"2"]],char[(*q"Green"q*)rho]]]NR6irt6pTVN9$'equal[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)rho],char[(*q"Green"q*)r]],over[(*q"Green"q*)char[(*q"Green"q*)A],power[(*q"Green"q*)char[(*q"Green"q*)R],num[(*q"Green"q*)4.00000000,"4"]]],times[(*q"Green"q*)over[(*q"Green"q*)times[(*q"Green"q*)num[(*q"Green"q*)4.00000000,"4"],char[(*q"Green"q*)sigma]],power[(*q"Green"q*)char[(*q"Green"q*)c],num[(*q"Green"q*)3.00000000,"3"]]],power[(*q"Green"q*)char[(*q"Green"q*)T],num[(*q"Green"q*)4.00000000,"4"]]]]"GN4X6eq*],m[6eq*b w>/(*'equal[(*q"Magenta"q*)int[(*i2iq"Magenta"q*)times[(*q"Magenta"q*)char[(*q"Magenta"q*)R],diff[(*q"Magenta"q*)char[(*q"Magenta"q*)R]]],num[(*q"Magenta"q*)0.00000000,"0"],char[(*q"Magenta"q*)R]],int[(*i2iq"Magenta"q*)times[(*q"Magenta"q*)power[(*q"Magenta"q*)id[(*q"Magenta"q*)over[(*q"Magenta"q*)times[(*q"Magenta"q*)num[(*q"Magenta"q*)8.00000000,"8"],char[(*q"Magenta"q*)pi],char[(*q"Magenta"q*)G],char[(*q"Magenta"q*)A]],num[(*q"Magenta"q*)3.00000000,"3"]]],over[(*q"Magenta"q*)num[(*q"Magenta"q*)1.00000000,"1"],num[(*q"Magenta"q*)2.00000000,"2"]]],diff[(*q"Magenta"q*)char[(*q"Magenta"q*)t]]],num[(*q"Magenta"q*)0.00000000,"0"],char[(*q"Magenta"q*)t]]].Na6e(*q*],7 qreU` U@B5*)'wequal[(*q"Red"q*)times[(*q"Red"q*)char[(*q"Red"q*)T],id[(*q"Red"q*)char[(*q"Red"q*)t]]],times[(*q"Red"q*)power[(*q"Red"q*)id[(*q"Red"q*)over[(*q"Red"q*)times[(*q"Red"q*)num[(*q"Red"q*)3.00000000,"3"],power[(*q"Red"q*)char[(*q"Red"q*)c],num[(*q"Red"q*)3.00000000,"3"]]],times[(*q"Red"q*)num[(*q"Red"q*)128.00000000,"128"],char[(*q"Red"q*)pi],char[(*q"Red"q*)G],char[(*q"Red"q*)sigma]]]],over[(*q"Red"q*)num[(*q"Red"q*)1.00000000,"1"],num[(*q"Red"q*)4.00000000,"4"]]],over[(*q"Red"q*)num[(*q"Red"q*)1.00000000,"1"],power[(*q"Red"q*)char[(*q"Red"q*)t],over[(*q"Red"q*)num[(*q"Red"q*)1.00000000,"1"],num[(*q"Red"q*)2.00000000,"2"]]]]],over[(*q"Red"q*)times[(*q"Red"q*)sn[(*q"Red"q*)num[(*q"Red"q*)1.50000000,"1.5"],num[(*q"Red"q*)10.00000000,"10"]],string[(*q"Red"q*)" K"]],power[(*q"Red"q*)char[(*q"Red"q*)t],over[(*q"Red"q*)num[(*q"Red"q*)1.00000000,"1"],num[(*q"Red"q*)2.00000000,"2"]]]]]eNDc7 qH7  *)< es*q[47 a(*[4[4.u4ed'Lgg[times[char[k],char[T]],times[char[m],power[char[c],num[2.00000000,"2"]]]]pod7eq*  *qed4 &0 |мZ7&[q"l( *q"d"4)L.,,4 ,pnF,F,&.4 c Z7'00!+ Red*)&.6y!a6y!a ٟ!A"| `"| `&ٽ$f-&!. мZ7(.00'#! 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