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1 COSMOLOGY PHYS 3039 THE EARLY UNIVERSE Par II hp://cms.web.ce ern.ch Gampaolo Psano - Jodrell Bank Cenre for Asrophyscs The Unversy of Mancheser - Aprl 013 hp:// gampaolo.psano@mancheser.ac.uk

2 The Ho Bg Bang Model: Unfcaon of forces hp://cms.web.cern.ch/ Number of forces Theory of Everyhng (TOE Tme afer Bg Bang s s 10-1 s 10-6 s 5x10-17 s Temperaure 10 3 K 10 8 K K K 3K Energy GeV GeV 10 3 GeV 1GeV 10-4 ev (Today

3 THE EARLY UNIVERSE - Par II Baryosynhess (and Leposynhess Inflaon Planck era References: Ryden, Inroducon o Cosmology - Par Wenberg, Cosmology - Par. 3.3 Peacock, Cosmology Physcs - Par. 9.6

4 The Ho Bg Bang Model: Baryosynhess Addson-Wesley Longman CMB BBN Baryosynhess

5 Baryosynhess: Baryon-Anbaryon asymmery - Alhough BBN s well undersood, s no clear why a s begnnng: n bary << n γ Very ny # of baryons compared o phoons n anbary << n bary Very ny # of anbaryons compared o baryons n anbary << n bary << n γ - Before BBN, when he emperaure was: T >10 1 K kt >150 MeV <100 µs Quarks no confned Sea of up & down quarks ( In addon o lepons-anlepons and phoons

6 Baryosynhess: Quark and Anquark soup - These quarks and anquarks were consanly creaed and desroyed: γ γ q q γ + γ q + q - Par producon q q γ γ The numbers of each quark and anquark ype were almos equal o he number of phoons n q n q n γ - Le s assume he exsence of a ny excess of quarks over anquarks: δ q n n q q n + n q q <<1 Possbly orgnaed n he GUT era (see laer

7 Baryosynhess: Quarks-Anquarks annhlaon - As he Unverse expanded, he emperaure dropped unl he quark-anquark pars were no longer creaed: Annhlaon of quarks-anquarks Before annhlaon Afer annhlaon δ q δ q Tny excess of parcles over anparcles Only parcles lef All he anquarks dsappear leavng he small excess of quarks When proons and neurons laer form, her number wll be a ny fracon of he number of phoons n n ' q γ η ~ δ n bary n γ q

8 Leposynhess: Lepon-Anlepon asymmery - In order o manan he charge neuraly of he Unverse, s naural o assume ha: There was also a slgh excess of elecrons over posrons comparable o he quark-anquark one - Smlarly o baryosyness as he Unverse expanded, he emperaure dropped unl he dfferen lepon-anlepon pars were no longer creaed: Annhlaon of lepons-anlepons Leposynhess Curren research for a mechansm ha could produce baryon-anbaryon and lepon-anlepon asymmery a he same me

9 Baryosynhess and Leposynhess: Sakharov condons - Baryons-anbaryons and lepon-anlepon nbalances could be explaned f hey were generaed by he same process n he early unverse - Ths wll have o sasfy he: Sakharov condons 1 - B and L volaon: There mus be a process volang he conservaon of baryon and lepon numbers - C and CP volaon: The process mus volae nvarance under boh C and CP ( A unverse wh an excess of baryons-anbaryons or lepon-anlepon s no nvaran under C or CP symmeres 3 - Deparure from hermal equlbrum: The unverse mus go no a sae of non-equlbrum

10 Baryosynhess and Leposynhess: Possble scenaro 1/ - In he Grand Unfed Theores (GUT here s no dsncon beween baryons and lepons: - Heavy X parcles, wh mass ~10 15 GeV, could decay n wo channels wh branchng raos: Dfferen saes of he same Lepoquark X e + d B 1, L 1 e + X (r d X u + u B, L u X (1-r u Process where boh baryonc and leponc numbers are no conserved 1 - A he same me, X anparcles wll decay producng oppose B, L numbers: X e + X u + u d -B 1, -L 1 -B, -L ( r ( 1- r No ne asymmery creaed because: r r

11 Baryosynhess and Leposynhess: Possble scenaro / - If C and CP symmeres are volaed: r r The oal baryon and lepon numbers produced n he decay of X and X are: - However, n equlbrum he nverse processes wll erase hese asymmeres:.. X.. X.. X.. X B 0 L 0, X, X X X B B, L L,, X, X X X X X X X - As he Unverse expands, he reacons wll freeze-ou when: Γ X H - A ha me, f: kt < m X c Non-equlbrum The nverse decays were already blocked, X and X dsappeared 3 The asymmeres B 0 L 0, X, X X X wll survve

12 THE EARLY UNIVERSE - Par II Baryosynhess (and Leposynhess Inflaon Planck era References: Ryden, Inroducon o Cosmology - Par. 11.0, 1,, 3, 4, 5 Lddle, Inroducon o modern Cosmology - Par. 13., 3, 4, 5

13 The Ho Bg Bang Model: Three problems o solve - The Ho Bg Bang scenaro has hree man problems: The flaness problem The Unverse s nearly fla oday and was even flaer n he pas The horzon problem The Unverse s nearly soropc and homogeneous oday, and was even more so n he pas The monopole problem The Unverse seems o be free of magnec monopoles

14 The flaness problem: Presen and pas - When he unverse was domnaed by radaon and maer, he densy parameer evolved as: 1 Ω( (1 Ω0 a Ω + aω r,0 m,0 1 Ω a r 1 Ω a / 3 m - Radaon phase - Maer phase - If oday we say ha he densy parameer devaon form 1 s: 1 Ω In he pas, mus have been whn: Ω rm - Radaon-maer equaly Ω nuc - Nucleosynhess Ω P - Planck me ( P ~10-44 s 0 Exraordnary flaness s requred a he early sages of he Unverse ( Small devaons from hese lms would brng o a very early Bg Crunch or Bg Chll

15 The horzon problem: Las Scaerng Surface 1/ - Our presen proper dsance o he LSS s: d 0.98d ( p ( 0 hor 0 Horzon Our Las Scaerng Surface 0.98 d hor 0.98 d hor - Lookng he LSS n oppose drecons we see regons causally dsconneced: d ( d hor( 0 p They have nearly dencal properes alhough hey haven had me o ge no equlbrum

16 The horzon problem: Las Scaerng Surface / - Consder now flucuaons on he LSS; he horzon dsance a ha me was: d hor ( ls 0.4 Mpc - Knowng ha he angular dsance o he LSS s: d A 13 Mpc - LSS regons a a horzon dsance appear separaed by an angle: θ hor d (( d hor A ls o - We know ha he CMB ansoropes a hs scales are ~ 10-5 Agan, s no clear how regons ousde causal connecon can have such smlar properes Maybe hey have been n conac before!?

17 The monopole problem: Grand Unfed Theores (GUTs GUTs - Theores aempng o unfy e.m., weak and srong forces: Dfferen aspecs of he same force GUT ~ s T GUT ~ 10 8 K E GUT ~10 15 GeV Predcons - Unverse had a phase ranson as he emperaure dropped below T GUT - Phase ranson assocaed o loss of symmery: Srong and elecroweak forces separae - These ranson gve rse o opologcal defecs (msmaches a boundares - GUT phase ranson creaes pon-lke opologcal defecs: Very massve magnec monopoles (m M c ~ E GUT - A a ceran sage, hey should have domnaed he unverse energy densy Why oday we no observe magnec monopoles?

18 The Ho Bg Bang Model: Inflaon Addson-Wesley Longman CMB BBN Baryosynhess Inflaon

19 The Inflaon: The acceleraon equaon Inflaon - Hypoecal perod n he early unverse of fas accelerang expanson: a& & > 0 - Remndng he acceleraon equaon: a&& a 4π G (ε 3c + 3P - We can have posve acceleraon f P < -ε /3 P -ε w -1 Λ : Cosmologcal Consan Λ > 3 - The acceleraon equaon becomes: 0 Unverse emporarly domnaed by a posve cosmologcal consan a& & a

20 - The Fredmann equaon n hs case s: The Inflaon: The Fredmann equaon The Inflaon: The Fredmann equaon 3 a a Λ & 3 H Λ 3 H Λ The Hubble parameer durng nflaon s consan - Solvng for he scale facor: a Λ & da 3 a a Λ & H d a da H e a ( Inflaon s a perod of exponenal growh - We can magne hree phases: < < < < / ( / ( ( 1/ ( ( 1/ f H f H a e a e a a f - Radaon domnaed 1 - Λ domnaed - Radaon domnaed 3

21 The Inflaon: The scale facor expanson - Plong: a( 1/ κ 0 e H 0 ( 0 ε 0 Λ 0 w -1 1/ 1 3 f - Beween and f he scale facor ncreased by: a( a( f e H ( f e N where N H ( f - Number of e-foldngs If N was large he expanson was enormous

22 The Inflaon: In numbers - A possble model for Inflaon sars around he GUT me and lased for: GUT s 1 N 100 e-foldngs H 1 GUT s 1 - The scale facor growh was: a( a( f e The nflaon cosmologcal consan and s energy densy were: c Λ 8 π G 3c Λ 3H ε Λ H 8πG - The presen cosmologcal consan energy densy s: ε ε 43 ε Λ 3 Λ 0.7,0 0 c ~ 4 GeV m ~ TeV m The nflaon cosmologcal consan s more han 100 orders of ε Λ magnude larger han he presen one 3

23 The Inflaon: Flaness problem soluon - Recall ha he Fredmann equaon for a curved unverse can be wren as: 1 κ c Ω( R a( H ( Ω( a( H ( - Durng nflaon we saw ha: H cons e H a ( 1 Ω ( e H The dfference decreases exponenally wh me - Assumng a srongly curved nal unverse: Ω( ~ Afer 100 e-foldngs s curvaure wll be: 1 Ω( f ~ e N ~ e 00 ~ The unverse becomes exraordnarly fla (The me beween he end of nflaon and oday s no enough o change he curvaure sgnfcanly

24 The Inflaon: Horzon problem soluon 1/ - The horzon dsance a any me s: d hor ( a( c d a( 0 - Calculang jus before and jus afer nflaon we have: d d hor hor ( ( f e N The horzon sze grows exponenally durng nflaon - Usng he same parameers as before: s 1 d hor ( m N 100 f s 1 d hor ( f 0.8 pc Expanson form sub-mcroscopc o asronomcal scales

25 The Inflaon: Horzon problem soluon / - Today, he proper dsance o he LSS s: ( Mpc - The same poron of unverse afer and before nflaon were: Lddle Fg.13.3 d p ( f d p d hor ( f d ( p f 0.9 m! d ( 44 p 3 10 m!!! d p ( << dhor ( d p ( d hor ( - A small enough pach of Unverse acheves hermalsaon before nflaon Inflaon hen expands o a sze much larger han he presenly observable Unverse (CMB phoons were really a he same T because hey were once n equlbrum

26 The Inflaon: Monopole problem soluon - Le s assume monopoles o be creaed before or durng nflaon - Ther number densy wll decrease exponenally durng nflaon: n M ( e 3H Monopole number densy dluon o undececable levels - Usng he parameers se before, n numbers: The probably o fnd a sngle monopole whn he LSS s exraordnarly low

27 The Inflaon: Physcs behnd 1/ - There s no consensus on he exac mechansm drvng nflaon - However, nflaon models are based on he followng deas: - The Unverse conans a scalar feld φ(, r r - Inflaon feld - There s an assocaed poenal energy V(φ - There s a slow ranson of he nflaon feld o a value ha mnmse V(φ - The nflaon feld can drve an exponenal expanson Λ - There s a frconal force Hubble frcon ha sablses he ranson

28 The Inflaon: Physcs behnd / - The slow ranson brngs from a: Measable false vacuum sae φ 0 V(φ True vacuum sae φ φ 0 φ - Afer rollng down, he nflaon feld oscllaes around he mnmum - The frconal forces wll damp he oscllaons allowng o reach he mnmum

29 The Inflaon: Two quesons 1 - Why nflaon doesn reduce he number densy of phoons o undeecable level n he way does for monopoles? - If he nflaon feld was coupled o oher felds n he unverse: Is energy densy was convered o phoons (or relavsc parcles and carred away by hem These phoons rehea he unverse resorng s pre-nfaonary value - Why nflaon doesn flaen ou he local curvaure due o he flucuaons n energy densy? - CMB flucuaons should be smooher han hey acually are Inflaon akes submcroscopc quanum flucuaons and expands hem o macroscopc scales Presen unverse large-scale srucure from ny quanum fucuaons

30 THE EARLY UNIVERSE - Par II Baryosynhess (and Leposynhess Inflaon Planck era References: Ryden, Inroducon o Cosmology - Chap. 1 Lddle, Inroducon o modern Cosmology - Chap. 14

31 The Ho Bg Bang Model: Planck Era Addson-Wesley Longman CMB BBN Baryosynhess Inflaon Planck Era

32 Planck Era: Towards he sngulary - When he Unverse exceed a ceran densy: Quanum effecs even n gravaonal physcs! - Assocaed scales: Planck Era P 5 Gh / c s - Planck me l P 3 Gh / c m - Planck lengh M P 8 hc / G. 10 kg - Planck mass E T P P M c P E / k P ev K - Planck energy - Planck emperaure - In hese condons physcs should be descrbed wh: Quanum Gravy?

33 THE END Good luck & Cao!