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“ " In the beginning the Universe was created.

Fundamental Cosmology: 7. Big Bang Cosmology. PART I. “ " In the beginning the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.” The Hitch Hiker's Guide to the Galaxy — Douglas Adams (1952-2001), British writer.

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“ " In the beginning the Universe was created.

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  1. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Fundamental Cosmology: 7.Big Bang Cosmology PART I “"In the beginning the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.” The Hitch Hiker's Guide to the Galaxy — Douglas Adams (1952-2001), British writer

  2. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.1: The 4 pillars of Standard Cosmology • The story so far • Expansion of the Universe • Universe began in a BIG BANG about 13.7billion years ago • The Universe is expanding • The Universe is Isotropic and Homogeneous on the largest scales • Origin of the cosmic background radiation • The CMB is the fossil of the Hot Big Bang Fireball • The surface of last scattering is the last time the bulk of the background radiation interacted with normal matter • The temperature of that radiation has cooled from 3000K to 2.7K • Nucleosynthesis of the light elements • Nucleons synthesized into the light elements in the first few minutes of the Big Bang • The Big Bang correctly predicts the ratio of Helium to Hydrogen ~25% • Formation of galaxies and large-scale structure • Structure formation commences at the time of matter-radiation decoupling • The Big Bang provides the framework from which matter condenses to form large scale structure

  3. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 redshift Wiens Law 3 2 1 1 Energy density of radiation The Friedmann Equation for radiation dominated universe integrating 7.2: The Timeline of the Universe How does the temperature of the early Universe evolve ? THE HOT BIG BANG a= Radiation constant G= Newton’s Gravitational Constant c= speed of light Temperature evolution in early Universe depends ONLY on Nature’s fundamental constants!

  4. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 10-43s 1031K 10-35s 1027K 10-12s 1015K 10-6s 1013K 10-4s 1012K 0.01s 1011K 1s 109K 4s 5x109K 3mins 109K 3x105yrs 3000K 107yrs 300K 109yrs 30K 1010yrs 2.73K He q+ m+ n Matter Clumping W± ? n m- Zo q- n n Atoms Initial Singularity Formation of Solar System and Birth of Life Hadron-Lepton Reactions shift -> Proton First Stars and Galaxies (re-ionization) Primordial Nucleosynthesis quark - antiquark annihilation n-p ratio freezes Epoch of Galaxy Formation ne decouple, e± annihilate Epoch of Recombination E-W Phase Transition Planck Time m- m+ annihilation Inflation 7.2: The Timeline of the Universe t=0 T=∞

  5. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.2: The Timeline of the Universe Epochs of the Universe

  6. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Running Time backwards Initial singularity - The Creation Event Planck time can be defined via the Heisenberg Uncertainty Principle 7.3: The Planck Time and Initial Singularity • In the Beginning…… Planck era = 0 - 10-43 s after Big Bang • From Plank time tp define • Planck lengthlp ctp • Planck densityrp 1/Gtp2 • Planck massmp rp lp3 • t<10-43sknown as the Planck Era • Quantum Effects become important • Einstein’s Theory of gravity breaks down

  7. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 For any particle of mass, m, Scale at which quantum effects become important is given by theCompton Wavelength Scale at which self gravity of particle becomes important is theSchwarzchild Radius For a particle of mass, mP = the Planck Mass lC RS 7.3: The Planck Time and Initial Singularity • In the Beginning…… What is the Planck scale ?? Quantum fluctuations of spacetime, of scale equal to Planck length, are of cosmic magnitude Compton Wavelength & Schwarzchild Radius are comparable

  8. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.3: The Planck Time and Initial Singularity • Require Quantum Theory of Gravity ? • In the Beginning…… Before the Planck time ?? • (1) Quantum Gravity • Path Integrals (sum over possible histories) successful in Quantum Mechanics • For gravity, sum over possible geometries • Very complicated mathematical process  simplify  instantons. • Assume most of 4D geometries in the path integral  very small contributions  can be neglected • Path integral can be calculated but considering few geometries with largest contributions = instantons • (2) Super Gravity • A quantum theory of elementary particles based on particle symmetry known as supersymmetry. • Naturally includes gravity along with other fundamental forces (electromagnetic, weak & strong nuclear) • Predicts quanta of gravity - graviton with spin 2 and its fermionic partner, the gravitino, spin 3/2. • Neither has yet been observed.

  9. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 graviton quark photon 7.3: The Planck Time and Initial Singularity • In the Beginning…… Before the Planck time ?? • (3) SUPERSTRING THEORY • String theory + supersymmetry = Superstring Theory • Sub quantum scales - Universe composed of strings - fundamental building blocks • Requires ~10 dimensions with 6 being curled up at every point in space (Calabi-Yau Manifolds and Orbifolds) • Think of different modes of vibration as representing different particles • Predicts a massless spin 2 particle !

  10. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 The superstring Planetary System http://www.damtp.cam.ac.uk/ 7.3: The Planck Time and Initial Singularity • In the Beginning…… Before the Planck time ?? • (4) M THEORY • Problem with String theories are that there is simply too much freedom • Bosonic String Theory (just decribes bosons) • Superstring (1,2) fundemental building block are closed strings • Superstring (3) fundemental building blocks are open strings • Bosonic String Theory + Superstring Theory = Heterotic String Theories (4,5) • Too many parameters • Like exploring 5 different planets !! • M theory • Superstring Theories not 5 different planets … • BUT rather 5 islands on the same planet! • Different aspects of some greater underlying pattern or order • M- Theory (The Mother of all String Theories ??) formualted in 1 higher dimension ? (11 dimensions) CURRENTLY OUR BEST BET FOR A THEORY OF EVERYTHING (TOE)

  11. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.4: The Inflationary Era • Problems with the Hot Big Bang Model Inflationary Era = 10-43 - 10-35 s after Big Bang • THE HORIZON PROBLEM • the isotropy of the apparent causally disconnected regions of the CMB • THE FLATNESS PROBLEM • the apparent remarkable closeness of W to 1 • THE RELIC PROBLEM • the apparent absence of relics from the Big Bang in our Universe

  12. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 t 1800 (measure the same temperature in CMB) (surface of last scattering- last time matter and radiation were in equilibrium) Earth Recall: SR Metric x y 7.4: The Inflationary Era • The Horizon Problem Speed of light is finite - define particle HORIZON Area outside light cone: dS2<0 Events that are causally disconnected from observer. spacelike intervals  no communication possible. Area within light cone: dS2>0 This is a timelike interval  communication possible. HORIZON- distance, for a given time, over which information can be exchanged

  13. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 R-W Metric 1800 (measure the same temperature in CMB) (surface of last scattering- last time matter and radiation were in equilibrium) Horizon at the surface of last scattering (tSLS~3x105yrs ~1013s) dH (t=tSLS) ~ 0.3Mpc angular diameter distance not equal to proper distance NOW but rather the proper distance at the time the light was emitted te (for our example te=tSLS) ! 7.4: The Inflationary Era • The Horizon Problem HORIZON distance (dH) is the proper distance (dP) travelled by a photon sincet=0  tH The (angular diameter) distance to the surface of last scattering dA ~ 13Mpc

  14. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 dH (tSLS)~0.3Mpc Horizon at surface of last scattering The angular diameter distance dA~13Mpc dH The horizon distance of the surface of last scattering subtends and angle of dA qH 7.4: The Inflationary Era • The Horizon Problem 1800 • CMB is highly isotropic -looking in opposite directions To is identical to 1 part in 10,000 ) • These opposite regions appear never to have been in causal contact • But opposite points in CMB are ~90 horizon distances apart !! • So how do they know that they should be at the same temperature?? • This apparently violates causality THE HORIZON PROBLEM

  15. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Friedmann eqn. Evolution of W Matter dominated Era: Radiation dominated Era: 7.4: The Inflationary Era • The Flatness Problem WMAP CMB Observations: The Universe is almost flat today: Wo~1 0.02 How about in the past ? The Flatness Problem The Flatness Problem

  16. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 MatterRadiation Equality teq~ 106yr = 1013s  |1-W|< 5x10-7 Big Bang Nucleosynthesis tBBN~ 3mins = 180s  |1-W|< 10-18 Planck Time tP~ 10-43s  |1-W|< 10-63 7.4: The Inflationary Era • The Flatness Problem to~ 13.7Gyr=4x1017s  Wo~1 0.02 The Flatness Problem The Flatness Problem • Why is the Universe so FLAT • Fine Tuning to > 1 part in 1060 • Why did the Universe not expand - contract back to a big crunch very quickly • Why did the Universe not expand so quickly that galaxies and life were unable to form • Do we live in a very special part of the Cosmological Parameter Space • Anthropic Principle ?

  17. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Strong Nuclear Electromagnetic GUT ELECTROWEAK t=10-35s T=1027K E=1015GeV STRENGTH TOE t=10-12s T=1015K E=102GeV Weak Nuclear t=10-43s T=1031K E=1019GeV Gravity PHASE TRANSITION 7.4: The Inflationary Era • The Relic Problem • At high energies the forces of nature unify • Symmetry  Forces become indistinguishable from each other • Universe cools  temperature drops  symmetry breaks  phase transition • Like water freezing into ice  defects appear on cooling

  18. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 VERY BIG!! Magnetic Monopole rest energy ~ 1015GeV  E=mc2  mass  bacterium 7.4: The Inflationary Era • The Relic Problem • Phase transition  loss of symmetry  topological defects • Predicted for GUT (strong/electroweak unification) t=10-35s,T=1027K, E=1015GeV • Compare with freezing water • different ice nucleation sites • different axes (domains) of symmetry  topological defects • 0D point like defects = Magnetic Monopoles (isolated North/South poles) • formed when spherical symmetry is broken • 1D linear defects = Cosmic Strings • formed when axial / cylindrical symmetry is broken • 2D sheet like defects = Textures • formed when higher symmetries are broken

  19. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.4: The Inflationary Era • The Relic Problem • Magnetic Monopoles THE MAGNETIC MONOPOLE SONG Marian McKenzie, 2-01 (To the tune “Toplady”,which is usually used for the hymn “Rock of Ages”) As the day requires the night, As the left requires the right, So are north and south entwined. Then be sure to bear in mind -- As you strive for physics goals -- NO MAGNETIC MONOPOLES! Recording (As performed by the choir of St. James United Church of Christ, Havertown PA):

  20. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Horizon distance at tGUT Number density of Monopoles with energy density Still small compared to radiation energy density 7.4: The Inflationary Era • The Relic Problem • Phase Transition  symmetry breaking  topological defects • Symmetry survives were areas of Universe are in equilibrium • Therefore, expect one topological defect / horizon distance • BUT: Monopoles become non-relativistic at early times eR-3(c.f., radiation eR-4) • t~10-12s  Dominate the energy density and CLOSE the Universe • However…. We are here ….. So where are the Monopoles ???? THE RELIC PROBLEM

  21. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.4: The Inflationary Era • Problems with the Hot Big Bang Model Inflationary Era = 10-43 - 10-35 s after Big Bang • THE HORIZON PROBLEM • the isotropy of the apparent causally disconnected regions of the CMB • THE FLATNESS PROBLEM • the apparent remarkable closeness of W to 1 • THE RELIC PROBLEM • the apparent absence of relics from the Big Bang in our Universe The Cure ? INFLATION

  22. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.4: The Inflationary Era • Inflation Inflationary Era = 10-43 - 10-35 s after Big Bang Inflationary Epoch • 1980s, Alan Guth - Inflation Theory - • Period between 10-36 and 10-34 s • Small portion of Universe balloons outward to become today’s visible Universe. • Can solve horizon, flatness, relic problems !!

  23. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 De Sitter expansion 7.4: The Inflationary Era • Inflation Inflationary Era = 10-43 - 10-35 s after Big Bang • During inflation the Universe accelerates • Need negative pressure, or large, positive L Friedmann Equations become 注意: Hubble Parameter during inflation is constant=(L/3)1/2 Universe expands exponentially

  24. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 In the language of group theory: GUT QCD EW EM schematically 7.4: The Inflationary Era • Inflation - A Possible Mechanism ? • GUT symmetry breaking • t<10-36s Universe dominated by a scalar field f • GUT theories Higgs Field mediated by Higgs Boson pervades all of space-time, at high temperatures, f=0 • Higgs Boson responsible for the particle masses ? • For the symmetry to break and the forces to separate, the Higgs field must acquire a non-zero value Spontaneous Symmetry Breaking important aspect of particle physics gauge theories

  25. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.4: The Inflationary Era • In the ordinary vacuum, Higgs field is non-zero • This is lowest (degenerate) energy state or TRUE VACUUM • f=0state = meta-stable state • Shape of the Higgs field has unique characteristic • Phase transition is slow compared to cooling of Universe • Regions of Universe supercool without breaking symmetry • Like water super cooling 253K without turning to ice • Supercooled regions in a state known as FALSE VACUUM • Inflation - A Possible Mechanism ? • Higgs field finally reaches lowest state- symmetry breaks, domains of true vacuum eat into false vacuum • True vacuum represents lowest energy density state pressure =0 • For true vacuum to expand into false vacuum, pressure of false vacuum must be negative Repulsive Force • False Vacuum acts like a Cosmological Constant L • Symmetry breaks - latent heat stored in Higgs Field released and re-heats the Universe - inflation ends

  26. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Gives a pressure and a energy density of the inflation field If inflation field changes only very slowly with time 2 2 1 1 • small SEMINAR 3 :Fluid Equation Equation of motion of a particle being accelerated by a force  dV/df and being impeded by a frictional force  particle speed (the Hubble Friction) The Expansion of the Universe provides the Hubble Friction term that slows the transition of the Inflation Field 7.4: The Inflationary Era • Inflation - The Mechanics Assume an inflation scalar field f and corresponding potential V Inflation can drive expansion if there is a period of • Large V such that the potential dominates energy density of the Universe • The Higgs Mechanism

  27. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.4: The Inflationary Era • Inflation - The Cure for the Problems 1. THE HORIZON PROBLEM • the isotropy of the apparent causally disconnected regions of the CMB • Inflate from a small sub horizon region • Seemingly causally disconnected points today would’ve been in causal contact before inflation • Inflation creates bubble Universes seperated by domain walls of order of Horizon

  28. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.4: The Inflationary Era • Inflation - The Cure for the Problems 2. THE FLATNESS PROBLEM • Can make the Universe arbitrarily flat • During inflation, H is constant: W is driven relentlessly towards unity • We needed flatness to ~10-63 •  need >1031 inflation

  29. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.4: The Inflationary Era • Inflation - The Cure for the Problems 3. THE RELIC PROBLEM • the apparent absence of relics from the Big Bang in our Universe • Inflation pushes domain boundaries beyond our horizon distance • The density of relics is diluted

  30. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 40 Standard big bang 20 0 lg(R) {m} -20 During the inflationary era -40 inflation -60 -40 -30 -20 -10 0 10 lg(t) {s} But energy in Higgs Field reheats 7.4: The Inflationary Era • INFLATION - SUMMARY • Require Flatness 1031 • Require Horizon ~100 • For Relics depends on details of the physics • For inflation from t1=10-36(1/H1) to t2=10-34 s  100 e foldings ! Inflation of quantum fluctuations  macroscopic scales  the seeds of STRUCTURE FORMATION

  31. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Fundamental Cosmology: 7.Big Bang Cosmology PART II “"In the beginning the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.” The Hitch Hiker's Guide to the Galaxy — Douglas Adams (1952-2001), British writer

  32. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 e+ • Creation of particle anti-particle pair creation becomes favourable e- e- n n n g LEPTONS q q q q GUT (Higgs?) g q QUARKS g 7.5: The Evolution of the Big Bang Thermal Equilibrium in the Early Universe • For any particle X of mass, m, there will be an epoch where kT~mc2 • For kT>mc2 : number of particles ~ number of photons • For kT<mc2 : pairs can no longer be created  annihilation & freeze out

  33. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.5: The Evolution of the Big Bang THE QUARK ERA • 3 Quarks for Muster Mark (Finnegan’s Wake) Quark era = 10-34 - 10-23 s after Big Bang The Primordial Soup : • 10-34s inflationary period ends • Energy in inflation field released • Universe reheats to 1022 K •  primordial soup in thermal equilibrium • photons • free quarks, antiquarks, exchange particles

  34. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 1995年 発見した! FUNDEMENTAL 7.5: The Evolution of the Big Bang THE QUARK ERA • Brief Review of Particle Physics http://CPEPweb.org  http://www.fnal.gov/pub/inquiring/physics/discoveries/pr/top_news_release.html

  35. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.5: The Evolution of the Big Bang • THE HADRON ERA Hadron era = 10-23 - 10-4 s after Big Bang • 10-12 s ElectroWeak Symmetry breaking (g, W, Z0)  E-M and Weak Nuclear Force • 4 fundamental forces of nature now distinct • Expansion of Universe cools Big Bang Fireball ~1013K (10-6s)  1GeV • Quarks bond to form individual Baryons  Quark Confinement Baryogenesis 1) Why are there so many photons in the Universe ? 2) Why is there no antimatter in the Universe ? 1) Photon Background produced from matter/antimatter anihilation

  36. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 After matter & antimatter anihilation: small excess of quarks remain Baryons CMB 7.5: The Evolution of the Big Bang • THE HADRON ERA MATTER ANTIMATTER ASYMMETRY Assume some tiny tiny asymmetry between quarks & anti quarks (matter & antimatter) • How large is dq ? • From CMB and Wbaryonestimate Baryon to photon ratio = ~5x10-10 • Since 3 quarks bind to form a Baryon (Hadron)  dq~ 10-10

  37. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 P violated C violated CP conserved 7.5: The Evolution of the Big Bang • THE HADRON ERA ORIGIN OF MATTER ANTIMATTER ASYMMETRY • Where does the Matter - Antimatter Asymmetry come from ? • Particle Physics - Standard Model - 3 basic symmetries • ChargeConjugation (C) • Replacing a particle by its antimatter counterpart. • Parity (P) • Reverses all three coordinates. • Like a mirror where image is not only back-to-front, but also left-right swapped and upside-down. • Time Reversal (T) • Interactions are independent of the arrow of time. • Weak interactions, both P and C are individually broken. • (neutrino chirality) but CP is conserved • One case of combination of C and P also not conserved • CP-violation, detected by Cronin & Fitch in decay neutral Kaons • CPT still believed to be conserved in all reactions • i.e., antiparticle is indistinguishable from the mirror-image of a particle moving backwards in time

  38. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 CP violation  difference in kaon-antikaon deacy lifetimes Ko d 7.5: The Evolution of the Big Bang • THE HADRON ERA CP VIOLATION AND THE ORIGIN OF MATTER ANTIMATTER ASYMMETRY • 1964 Cronin and Fitch Experiment: • Measurement of decay of pions from neutral Kaon particles • Measure the decay rate at the end of 17m particle beam tube. • Kaon decay lifetimes different by factor of 100 for the two Kaon species • Expect to see only the long-lived version at the end of the beam tube, • BUT found about 1 in 500 long lived kaons decayed to 2 pions • CP violation (in K mesons due to fact that KL contain ~0.3% more Ko than anti-Ko) Neutral Kaons also have semi-leptonic decay mode (39%, compared to 34% for 3p mode) • CP transforms one set of decay products into the other  identical decay rates ? • Experiment  positron decay mode more frequent than the electron decay mode. • CP violation with fractional excess is only 3.3 x 10-3

  39. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.5: The Evolution of the Big Bang • THE HADRON ERA ORIGIN OF MATTER ANTIMATTER ASYMMETRY • 1967 Andrei Sakharov : 3 criterea for matter-antimatter assymetry • Baryon number must be violated - Proton is unstable (decays into mu-meson and two neutrinos 1030yrs) • P and CP must be violated • A departure from thermal equilibrium when the baryon number was being violated. CP violation requires 3 families of quarks  3 families of quarks imply CP violation • N.B., CP violation T violation (strong nuclear force magnetic orientation  axion dark matter)

  40. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.5: The Evolution of the Big Bang • THE LEPTON ERA Lepton era = 10-4 - 1s after Big Bang • ~ equal numbers of g, e, n in thermal equilibrium • For every 109 photons, electrons, or neutrinos, ~ 1 proton or neutron exists • Lepton Era continues until T<~1010K neutrinos decouple forming their own ghost Universe • T<~1010K neutrinos decouple • T~109K electrons and positrons annihilate • Universe gets extra source of photons (heating) which neutrinos never “see”  neutrino background colder • Can calculate difference between neutrino background and photon background temperatures • Thermal equilibrium, the second law of thermodynamics  entropy, S, of the Universe remained constant • As Universe expands SR3=constant Consider Entropy conservation before and after the electron/positron annihilation g= effective number of species in equilibrium

  41. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Therefore; before e± annihilation ge±, g=7/2 + 2 = 11/2 after e± annihilation g0, g = 2 Tn = Tg/1.4= 2.725/1.4 ~ 1.95 K anden~ 0.5eg ~ 0.11 MeV/m3 The present day Temperature of the neutrino background is given by 7.5: The Evolution of the Big Bang • THE LEPTON ERA The Neutrino Background Contributions to g calculated as product of 3 factors • 2 if particle has distinct antiparticle, 1 if not. • Number of possible orientations of the particle spin. • 7/8 if particle subject to Pauli exclusion principle, 1 if not. g (e±) = 2 x 2 x 7/8 = 7/2 g (g) = 2 x 1 x 1 = 2 Since TR(v)for the neutrinos remains equal toTR(e±, g)before the annihilation • Neutrino background very difficult detect directly • If neutrinoes have mass, then neutrinos dominate the density of the Universe

  42. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Neutron Decay Mode Number densities of nucleons given by Maxwell-Boltzmann Distribution mn/mp=1.002~1 Neutron Proton ratio is decided by the temperature (mn-mp)c2=Q=1.29MeV 7.6: Big Bang Nucleosynthesis • The Neutron - Proton ratio ~ 0.1s after Big Bang • After Quark/Hadron era - Neutrons & Protons (nucleons) present in equal numbers • T~1010K >> mec2 g + g  e- + e+ • Nucleons in thermal equilibrium with electrons and photons

  43. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 1 0.1 Neutron freezeout Nn/Np 0.01 0.001 0.0001 Thermal Equilibrium 1011 1010 109 Temperature (K) Only neutron decay mode (1) remains t ~16mins decay time of free neutron 7.6: Big Bang Nucleosynthesis • The Neutron - Proton ratio • T~9x109K : • electrons-positrons annihilate g + g  e- + e+ • neutrinos decouple from nucleons • Small neutron-proton mass difference  reactions shift in favour of the lighter Proton Neutrons are disappearing quickly !

  44. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Weak Interaction because neutrinos are involved  lower probability Can also have ….. FIRST STEP:- Deuterium 2H = D 2H 7.6: Big Bang Nucleosynthesis • The Formation of the Light Elements ~ 1s - 3 minutes after Big Bang Onset of nucleosynthesis locks up all the free neutrons in nuclei stopping the neutron decay • Nucleosynthesis of the elements begins with Deuterium and ends with Helium (+ a little Lithium, Beryllium, Boron) • Number densities too low to directly make 2p + 2n  4He • Sequence of 2 body reactions Deuterium binding energy low = mn+mp+mD=2.22MeV  Immediately destroyed Stability when ND~Nn  Temperature drops ~kT~0.07 = 7x108K (t~200s) Neutron decay mode Nn/Np~0.16 (nucleosynthesis will be quite an inefficient process)

  45. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 4He 3He 3H 2H 7.6: Big Bang Nucleosynthesis • The Formation of the Light Elements ~ 3 minutes after Big Bang • Once significant amount of Deuterium has formed the heavier elements form very fast • All post-Deuterium reactions involve strong nuclear forces, large cross sections and high reaction rates • Reactions proceed quickly to Helium

  46. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 56Fe Fusion Fission 5 8 56 4He 7Be 7Li 6Li 7.6: Big Bang Nucleosynthesis • The Formation of the Light Elements Most of 3H, 3He gets locked up in 4He - how about heavier elements ? • Binding energy/nucleon as a function of atomic number or number of nucleons per atom. • Decrease in binding energy beyond Iron as the nucleus gets bigger, strong force loses to electrostatic force. • Maximum binding energy at iron  means that elements lighter than Iron release energy when fused. • Elements heavier than iron only release energy when split • Peaks in binding energy at 4,16 & 24 nucleons from the stability of 4He combination of 2 protons/neutrons • No stable nuclei with atomic number 5 or 8 Universe runs out of steam production ceases with Helium • Unusually large binding energy of Helium

  47. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Only the very lightest elements are synthesized in the Big Bang Assumes ~5x10-10 7.6: Big Bang Nucleosynthesis • Light Element Abundances Everything Else is made in Stars 107-108 yrs later

  48. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 Mass fraction of He ~ Nn/Np~0.16 so there are ~6 protons for every neutron So for 2n + 2p 4He  10 protons leftover  H (1) (2) 4He+3H 7Be+e- Maximum allowed Mass fraction He 28% Mass fraction of Li (1) Production of 7Li from 4He+3H ~ decreasing fn() (2) Production of 7Li from 7Be+e- ~ increasing fn() 7.6: Big Bang Nucleosynthesis • Light Element Abundances Abundance depends on Baryon to photon ration () • High  higher density •  nucleosynthesis starts earlier (higher T) • Helium production more efficient • Less D & 3He leftover

  49. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 7.7: Recombination • THE RADIATION ERA Radiation era = 1s - 106yrs after Big Bang • Radiation more dense than matter, 108 kg/m3 compared to 100 kg/m3 • Temperature 1010 K • Expanding space filled mostly with protons and neutrinos • Protons and neutrons combined to produce deuterium • Helium synthesized when universe some 200 seconds old • Universe between ~105 years old • Temperature 3000o K, electrons captured by protons to form hydrogen atoms • Electrons no longer scatter photons • Universe becomes transparent to radiation; decoupling epoch when radiation decouples from matter • Fireball that flooded expanding universe for first 106 years appears as CBR Before Recombination photon mean free path is very short Radiation and matter are thermally bound together http://zebu.uoregon.edu

  50. Chris Pearson : Fundamental Cosmology 7: Big Bang Cosmology ISAS -2003 • matter in thermal equilibrium with the radiation. photons and electrons to interact via Thompson scattering e- g e- e- g p g p p g p e- • Temperature drops then p+e-H recombination recombination t z g H H g T R H g H g • Eventually interactions stop allowing the photons to flow freely on scales of the horizon de-coupling De-coupling H g H g H g g H g 7.7: Recombination • Decoupling and Recombination

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