The Early Universe. Overview: The Early Universe. Accelerators recreate the early universe. Simple Friedmann equation for the radiation era:

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1 The Early Universe Notes based on Teaching Company lectures, and associated undergraduate text with some additional material added. ) From µs to s: quark confinement; particle freezout. 2) From s to 3 minutes: Big Bang Nucleosynthesis. 3) Before ns: Supersymmetry; baryogenesis; unification. Overview: The Early Universe Simple Friedmann equation for the radiation era:! t $ # & " s% '/2 E(a) = Ω r,o /2 a -2 gives (using Ω r,o = ) a = h 72 ½ t s ½ T =.3 h 72 -½ t s -½ K =.4 h 72 -½ t s -½ MeV T ( K ( k T B MeV (!! $ # & " 7 gm cm '3 % Note: this relation is modified somewhat at earlier times when other species (e.g. e +, e - ) are thermally produced. /4!! ( m $ # & " gm cm '3 % /3 ( + z Temperature: T (billions of K) 7 Expansion 24 Cooling 8 and 4 Thinning Temperature: T (billions of K) 7 Quark/gluon plasma 24 Helium 8 4 synthesis 2 Quark confinement p + / p - annihilation e + / e - annihilation Neutrinos decouple ps ns µs ms sec ks ps ns µs ms sec ks Accelerators recreate the early universe Lower Temperature Slower Motion Higher Temperature Faster Motion High temperatures = high energy collisions Particle accelerators reproduce these collisions They recreate the conditions of the early universe.

2 Electric fields accelerate the particles Detectors are immense Particle creation and detection Z decay at DELPHI detector Z detection at UA detector Many accelerators collide single particles head on (e+e-, pp) Fundamental laws of physics Also possible to collide whole nuclei (Pb-Pb or Au-Au) Recreates the quark gluon plasma Primary result: the quark-gluon plasma behaves like a liquid! -3 - Above/below threshold temperatures: particle creation and annihilation 2 LHC/CERN 99s TeV 98s s 4 95s -2 ps -9 ns -6 µs -3 ms sec GeV 3 MeV 3 ks Energy (MeV) Temperature: T (billions of K) -6 With high enough energy, particle collisions can generate particle-antiparticle pairs: e.g. γ + γ x+ + xneed thermal energy: kbt mxc2 to generate this. So kbtthreshold ~ mxc2 provides a threshold temperature. (e.g. e+/e- at.5 MeV = 6 GK (5s); p+/p- at GeV = 3 K (µs) However, at any temperature, particle-antiparticle annihilation can occur: e.g. x+ + x- γ + γ 2

3 Below the threshold temperature proton electron photon Above the threshold temperature anti-electron electron photon Electrons and Anti-electrons Photons Energy exchange Particle KE creation annihilation equilibrium annihilation creation Gas at billion K Gas at billion K Photons energy exchange Particle KE At LTE the photons have a planck function, with energy density: u γ = ρ γ c 2 = g γ 8π 5 (k B T) 4 3 (hc) 3 where g γ = 2 for both spins We now have γ, e + and e - all present, with total energy density: 8π u = ρc 2 = g 5 (k B T) 4 * where g * = 5.5 (=2 + (2+2) ⅞ ) 3 (hc) 3 Force carriers (Bosons) EM Weak Strong Gravity W γ g s g v The Standard Model Particles Z 8 d s b Quarks u c t Matter Particles (Fermions) Leptons ν e ν µ ν τ e µ τ Family Family 2 Family 3 ½g * 5 Number of kinds of particles all SM particles present Temperature (billions of K) 6 3 quarks added TeV MeV GeV leptons added Higgs H ps ns µs ms sec ks Time (seconds) Number of kinds of particles Temperature (billions of K) 4 TeV GeV MeV Quark-gluon plasma Quark confinement Protons & anti-protons annihilate Electron threshold Higher g * shortens expansion timescale Since t H = /H = (3/8πGρ) ½ and ρc 2 = g * 8π 5 (k B T) 4 3 (hc) 3 Then g * enters a(t), giving faster expansion timescales at earlier times than our simple relation. In terms of temp/energy: T MeV ~.5 g * ¼ t s ½ ps ns µs ms sec ks Time (seconds) 3

4 Big Bang Nucleosynthesis Neutron/proton equilibrium The neutron/proton number ratio is a key parameter. Before sec, an eqlm population is maintained by neutrino reactions: n +! e! p + e " + energy p +! e + energy! n + e + Recall, neutrons are slightly heavier than protons: Δm = m n m p = =.3 MeV Late 94s: Robert Herman George Gamow and Ralph Alpher analyze nuclear reactions in a hot big bang. Their aim was to make all the elements. Near minute, T ~ 8 K, and nuclear reactions can occur. Unlike stars, there are free neutrons, which can form deuterium, and then. The conditions don t allow heavier elements to form. Hence eqlm population ratio given by Boltzmann factor: N n N p =! # " m n m p 3/2 $! & exp ' (m n ' m p )c 2 $ # % " k B T & % So, when k B T >> MeV, (N n /N p ). This drops below. near sec, as T drops below MeV Neutron / Proton ratio... MeV. Thermal equilibrium Temperature (billions of K) Neutrinos decouple n/p ratio frozen. MeV. MeV Time (sec) Neutron decay Half-life = minutes He synthesis... Neutrino decoupling freezes the neutron/proton ratio Near sec, the neutrino s decouple and the interconversion of neutrons and protons ceases. We say the reaction freezes out. What s going on: Reaction timescale: t reac = /(n<σv>) With: n ~ a -3, σ W ~ T 2 ~ a -2, v ~ c; so t reac ~ a 5 is slowing down Expansion timescale: t H = 2t age ~ a 2 is also slowing down, but not as fast. When t reac > t H then the number of collisions drops to zero. The reaction is frozen. This occurs near sec (T ~.8 MeV), when N n /N p ~ /5. The further delay of ~5 minutes until deuterium formation brings this ratio down to /7.3 (neutron half-life =.2 min) protons Making 25% Helium neutrons Helium Abundance 7 7 In simple form, helium abundance arises from full conversion of neutrons into. Hence: fusion reactions N He = ½ N n Hence the mass fraction of helium is: Y He = (4 ½ N n ) / (N n + N p ) = 2/( + N p /N n ) 2 75% Hydrogen 25% Helium 4 Hence, for N p /N n = 7.3, we have Y He =.24 4

5 Making Helium Making Helium-4 Making deuterium p n D proton deuterium γ neutron n H-3 p Notice: this is a strong reaction, and quite different from the weak reaction that occurs within stars: p + p D + e + + ν e D H-3 Formation BE D ~ 2.2 MeV Destruction The Deuterium Bottleneck proton γ-ray photon deuterium neutron γ Number of photons 9 K 7 seconds The deuterium bottleneck 2 9 K 4 seconds 5 9 K 7 seconds energy needed to destroy deuterium deuterium destruction photon N(γ) N(p) N(γ) 4 N(p) N(γ) 8 N(p) 2 3 Photon energy: MeV Number of protons C B Be Li He H p D H-3 5 n The beryllium barrier 8 Li-6 Li-7 Be Number of neutrons 5 C-2 B- B- +p 8 +n + 6 C-3 Fraction by mass Temperature (billions of K) protons protons neutrons deuterium Li-7 7 Time (seconds) neutrons H D Li-7 Hour 5

6 The final abundances depend somewhat on the cosmic parameters, in particular the photon/nucleon ratio or, equivalently, the nucleon density. Comparison with measured primordial abundances then allows one to measure the baryon density during BBNS. Because we know the scale factor during BBNS (because we know the temperature), then we can convert the baryon density during BBNS to a baryon density today Ω b Fraction by mass Element production depends on furnace density Deuterium Li-7 Proton + neutron density (gm/m 3 at 3 minutes) Measuring primoridal helium Measuring deuterium in the intergalactic medium Helium abundance 3% 2% % Primordial value Increasing contribution from stars Intensity QSO Hydrogen emission in the quasar Hydrogen absorption in the IGM Wavelength: nm % 2 Oxygen abundance Wavelength: nm Fraction by mass Omega-atomic (today): Ω at,... Deuterium Li-7 Proton + neutron density (gm/m 3 at 3 minutes).4 Cosmic history in a glass of water The deuterium in water is a relic from the Big Bang. It s abundance (~ -5 ) reveals the conditions in the 3-minute old furnace. H 2 O HDO 6

7 Even Earlier Times ) Supersymmetric particle creation and dark matter 2) Force unification: electroweak and GUT 3) Baryogenesis: matter/antimatter asymmetry. 2 unknown physics (Planck era) uncertain physics 4 known physics well known physics Matter Asymmetry? GUT Transition? Dark Matter Freezout? Higgs Mechanism -5 Electroweak Unification - Quark confinement Particle desert? ~ ~ 4 4 Super-symmetry ~

8 Standard Model particles Super-symmetric particles Super-partner particles Super-partner thresholds? -5-8 Fermions Electron Neutrino Quark Bosons Photon W & Z Gluon s- -ino Bosons Selectron Sneutrino Squark Fermions Photino Wino & Zino Gluino Lightest super-partner = dark matter? - 4 Force unification The Forces of Nature Gravity Weak Electromagnetism Strong Forces depend on temperature due to vacuum polarization Example Planetary orbits Radioactive decay Electrons in atoms Protons in nucleus Acts on All All Charged particles Quarks & gluons Carrying boson Relative strength Graviton W & Z Photon Gluons Electro-weak unification Sheldon Glashow b. 932 Abdus Salam Steven Weinberg b Higgs mechanism: particles acquire mass Electroweak unification

9 GUT transition 28 K Electroweak unification sec Density: ρtot (tons/cm3) Conditions for matter/anti-matter asymmetry ) Quarks and leptons must be able to interconvert. Baryogenesis 2) Matter and anti-matter reactions must differ somehow 3) The process must occur in a non-equilibrium state, that happens during times of rapid change. Andrei Sakharov (92-989) Hunt for CP violation currently a primary goal of the LHC. 9

10 Matter/anti-matter annihilation Before annihilation:,,, anti-protons,,, protons surviving proton After annihilation: anti-protons proton 2,,, photons 3 2-3? -25 Matter/anti-matter asymmetry generated -2 GUT transition? -5 Electroweak unification N(annihilations) = N(CMB) N(survivors) N(baryons)! billion End of Early Universe