ow may utrio scis?
Two mthods for dtrmii it lium abudac i uivrs At a collidr umbr of utrio scis
Exasio of th uivrs is ovrd by th Fridma quatio R R 8G tot Kc R Whr: :ubblcostat G :Gravitatioal costat 6. 7 tot : total mass dsity of th uivrs K : curvatur costat (-,0,) 0 m k umbr of utrio scis
This mass dsity ca b ithr iv by mattr or radiatio: Th radiatio art is for istac th Cosmic Microwav Backroud Th mattr dsity will (assumi mattr to b cosrvd) bhav as R For radiatio th mass dsity is iv by th ry dsity/c This bhavs diffrtly as th umbr of hotos will rmai costat but th ma ry will dcras throuh rdshifti sam is tru for all rlativistic articls so r R So at arly tims (R small) th first trm domiats R R 8G tot Kc R umbr of utrio scis
Ad so R R As r 8G tot R r r R 8G r R From which follows by itratio (ad multilicatio by c to t Ery dsity) c r c G t umbr of utrio scis
Accordi to Stfa Boltzma a hoto as i thrmal quilibrium has a ry dsity which dds o th tmratur accordi to: r c T c kt 5 c Whr k is Boltzma s costat (=.8x0 J/K), is Stfa Boltzma s costat, ar th umbr of si drs of frdom of th hoto, h is Plack s costat (=6.6x0 Js ad h / ) From this o ts th rlatio btw tim of xasio ad tmratur 5 5 c kt G or 0 T 0 t Ks t. MVs t umbr of utrio scis
umbr of utrio scis Photos ar ot th oly radiatio i th arly uivrs Rlativistic frmios also cout. For frmios th umbr dsity is iv by: ) ( / kt E f d d Ad so for kt>>mc, E=c ad usi 5 8 7 dx x x 5 8 7 f f c kt c
umbr of utrio scis I othr words w ca dtrmi th ry dsity for th radiatio comot by rlaci by *: f b 8 7 * At vry arly tims this icludd all articls such as quarks (=6), chard ltos (=), utrios (=), hotos (=), Wak bosos (=) ad th is (=) ad aroriat ati articls. 5 * 5 t G c kt 5 * 5 ) ( ) ( kt c G T t R R t
Primordial uclosythsis Wh kt<00 MV (about ms aftr bi ba) th th oly hadros that rmai will b rotos ad utros All othrs will hav dcayd (T ot lar ouh to sustai th ivrs of th dcay) Ati rotos ad ati utros ar also rst, but thy aihilat with most of th uclos, but ot all (why????) Th ractios that dtrmi th ratio of to ar: umbr of utrio scis
As thy ar orlativistic (kt<00 MV) th quilibrium ratio of rotos to utros is iv by th ratio of thir Boltzma factors, so: Q / Q kt M M c.9mv Th itractio rat will dcras with th dsity. Th itractio rat dcrass with tmratur bcaus Tothr with W T T T * ( T ) T 5 Mas that W G F E / ~ T / * / G F T So that at a crtai tmratur W/< so that th ractio dis out (frz out) This has at kt=0.8 MV This dds o * ad so o umbr of utrio scis
At this oit th utro to roto ratio is ( 0).9/ 0. 8 (0) 0. ow oly utro dcay taks lac: ( t) ( t) (0) t / (0) (0) t / Whr is th utro liftim =887 s So t t t / 0.. 0. t /
Thr is howvr a rocss Whr th bidi ry is. MV. This is dutro roductio ad hoto disitratio. I ricil th disitratio should sto wh kt<.mv, if th umbr of hotos ad uclos would b th sam. This is ot th cas, du to th fact that thr ar 0 0 tims as may hotos th umbr dsity of hotos with E>. MV is still lar ouh tothr with th 0.mbar cross sctio to k th ractio i quilibrium util kt~0.05 MV umbr of utrio scis
umbr of utrio scis Wh dutro disitratio stos th th followi rocsss tak ovr kt=0.05 corrsods to t=00 s t kt 8 7 *. MV * This ivs: 5 0. r
umbr of utrio scis So fially almost all utros will b i so that th mass fractio will b: 0. / / r r Y This is what w masur ad it dds o th umbr of utrios (xrcis)
umbr of utrio scis
umbr of utrio scis Masurmt at a collidr 0 This is imossibl to masur dirctly howvr thr ar two ways to masur it idirctly i M M s s M s s With th sum of all th artial widths qual to th total width Th cross sctio ito utrios will ot b visibl, so dfii vis M M s M s i
Th ak cross sctio dds o th umbr of utrios: umbr is umbr of utrio scis
Of cours thr is aothr way Iitial stat radiatio at a CM ry hihr tha mass ivs: 0 So ow w ca dtct th hoto ad othi ls ad dtrmi th cross sctio. Oft masurd comard to lowr hihr 0 S ar umbr of utrio scis