1. Neutron decay and interconversion Particle processes are a lot like equations You can turn them around and they still work You can move particles to the other side by “subtracting them” This means replacing them with anti-particles p+p+ n0n0 e-e- The neutron (in isolation) is an unstable particle Decays to proton + electron + anti-neutrino Mean lifetime: 886 seconds ++ Put the neutrino on the other side p+p+ + n0n0 + Put the electron on the other side + e+e+ n0n0 p+p+ e-e- + All thee processes convert neutrons to protons and vice versa

2. Neutron/Proton Freezeout Weak interactions interconvert protons/neutrons These are slow processes, so they fall out of equilibrium fairly early At k B T = 0.71 MeV, the process stops What is ratio of protons to neutrons at this temperature? Non-relativistic, E = mc 2. Ratio is: This happens at about:

3. The Deuterium Bottleneck The next step in making more complex elements is to make 2 H, deuterium: This releases about 2.24 MeV of energy Naively: this process will go ahead as soon as k B T drops below 2.24 MeV Actually, much lower temperature is required because of very low density of nucleons Actual temperature is about factor of 20 lower: 0.1 MeV Age of universe at this time: At this point, some neutrons are gone due to decay p+p+ n0n0 + p+p+ n0n0 Ratio depends weakly on density of protons/neutrons – more makes it happen sooner

4. Making Helium Once we make deuterium, we continue quickly to continue to helium: p+p+ n0n0 + p+p+ n0n0 p+p+ n0n0 n0n0 p+p+ n0n0 n0n0 + p+p+ p+p+ n0n0 n0n0 p+p+ n0n0 + p+p+ n0n0 p+p+ p+p+ n0n0 + p+p+ p+p+ n0n0 n0n0 p+p+ p+p+ n0n0 For every two neutrons, there will be two protons that combine to make 4 He Mass fraction of 4 He is twice that of neutron fraction 4 He is extremely stable – once formed it won’t go back. The sooner it happens, the more neutrons are left over Define  as the current ratio of baryons (protons + neutrons) to photons As  increases, Y P increases weakly:

5. Making Other elements When you run out of neutrons, 3 He can still be turned into 4 He via The last few 2 H, 3 He, and 3 H nuclei will have trouble finding partners There will be small amount of each of these isotopes left The more baryons there are, the easier it is to find a partner As  increases, 2 H, 3 He, and 3 H all decrease There are other rare processes that produce a couple of other isotopes: 7 Li and 7 Be are produced I don’t understand how they depend on  Within a few hundred seconds, the baryons are all in 1 H, 2 H, 3 H, 3 He, 4 He, 7 Be and 7 Li + p+p+ p+p+ n0n0 + p+p+ p+p+ n0n0 n0n0 p+p+ p+p+ n0n0 p+p+ p+p+ + + p+p+ p+p+ n0n0 p+p+ p+p+ n0n0 n0n0 p+p+ n0n0 n0n0 + p+p+ p+p+ n0n0 n0n0 p+p+ p+p+ p+p+ n0n0 n0n0 n0n0 p+p+ n0n0 n0n0 n0n0 p+p+ p+p+ p+p+ n0n0

6. Anything we missed? Two of these isotopes are unstable: Add 3 H to 3 He and 7 Be to 7 Li The process whereby stars make heavier elements do not work in the early universe Density is too low for unstable 8 Be to find another 4 He to react with In the end, we should be able to predict abundance (compared to hydrogen) of 2 H, 3 He, 4 He, 7 Li These have all been measured, mostly by studying light from quasars Back in the good old days (the 90s), this was how we estimated  Now we have an independent way of estimating it (later lecture) We should be able to compare the results with predictions A very strong test of Big Bang theory

7. The results Predictions for 4 He, 2 H and 3 He all work very well Prediction for 7 Li seems to be off The Lithium problem Overall, success for the model

8. Summary of Events: Eventk B T or TTime Neutrinos Decouple1 MeV0.4 s Neutron/Proton freezeout0.7 MeV1.5 s Electron/Positron Annihilate170 keV30 s Primordial Nucleosynthesis80 keV200 s Matter/Radiation Equality0.76 eV57 kyr Recombination0.26 eV380 kyr Structure formation30 K500 Myr Now2.725 K13.75 Gyr Lots of unsolved problems: What is the nature of dark matter? Why is the universe flat (or nearly so)? Where did all the structure come from? What is the nature of dark energy?

9. What we know and what we don’t: Up to now, everything we have discussed is based on pretty well understood physics And the experimental results match it well! As we move earlier, we reach higher temperatures/energies, and therefore things become more uncertain For a while, we can assume we understand the physics and apply it, but we don’t have any good tests at these scales New particles appear as temperature rises: Muons, mass 105.7 MeV, at about k B T = 35 MeV (g = 4 fermions) Pions, mass 135-139 MeV, at about k B T = 45 MeV (g = 3 bosons) At a temperature of about k B T = 100 MeV, we have quark deconfinement

10. Quark Confinement There are a group of particles called baryons that have strong interactions Proton and neutron are examples There are also anti-baryons and other strong particles called mesons In all experiments we have done, the baryon number is conserved Baryon number = baryons minus anti-baryons All strongly interacting particle contain quarks or anti-quarks or both The quarks are held together by particles called “gluons” u u d ug u At low temperatures quarks are confined into these packets At high temperatures, these quarks become free (deconfined) Estimated k B T = 150 MeV

11. Electroweak Phase Transition There are three forces that particle physicist understand: Strong, electromagnetic, and weak Electromagnetic and weak forces affected by a field called the Higgs field The shape of the Higgs potential is interesting: Sometimes called a Mexican Hat potential At low temperatures (us), one direction is easy to move (EM forces) and one is very hard (weak forces) At high temperatures, (early universe) you naturally move to the middle of the potential All directions are created equal Electroweak unification becomes apparent at perhaps k B T = 50 GeV

12. The Standard Model Particlesymbolsspingmc 2 (GeV) Electrone½40.0005 Electron neutrino e ½2~0 Up quarkuuu ½12~0.005 Down quarkddd ½12~0.010 Muon  ½40.1057 Muon neutrino  ½2~0 Charm quarkccc ½121.27 Strange quarksss ½12~0.10 Tau  ½41.777 Tau neutrino  ½2~0 Top quarkttt ½12173 Bottom quarkbbb ½124.7 Photon  120 Gluon gggggggg 1160 W-bosonW1680.4 Z-bosonZ1391.2 HiggsH01115–285 Above the electroweak phase transition, all known particles of the standard model should exist with thermal densities From here on, we will be speculating on the physics Cosmology sometimes indicates we are guessing right Goal: Learn physics from cosmology

13. Supersymmetry In conventional particle physics, fermions and bosons are fundamentally different And never the twain shall meet In a hypothesis called supersymmetry, fermions and bosons are interrelated There must be a superpartner for every particle: Supersymmetry also helps solve a problem called the hierarchy problem But only if it doesn’t happen at too high an energy If supersymmetry is right, then scale of supersymmetry breaking probably around k B T = 500 GeV or so. If this is right, the LHC should discover it In most versions of supersymmetry, the lightest super partner (LSP) should be absolutely stable Could this be dark matter?

14. Grand Unification Theories (GUT’s) In the standard model, there are three fundamental forces, and three corresponding coupling constants These have rather different values But their strength changes as you change the energy of the experiment, theortically How much they change depends on whether supersymmetry is right or not If supersymmetry is right, then at an energy of about 10 16 GeV, the three forces are equal in strength At k B T = 10 16 GeV, there will be another phase transition – the Grand Unification transition No Supersymmtery With Supersymmtery Baryogenesis might occur at this scaleScale could be right for inflation

15. Summary of Events: Eventk B T or TTime Grand Unification10 16 GeV10 -39 s Supersymmetry Scale500 GeV10 -12 s Electroweak Scale 50 GeV10 -10 s Quark Confinement150 MeV1.4  10 -5 s Neutrinos Decouple1 MeV0.4 s Neutron/Proton freezeout0.7 MeV1.5 s Electron/Positron Annihilate170 keV30 s Primordial Nucleosynthesis80 keV200 s Matter/Radiation Equality0.76 eV57 kyr Recombination0.26 eV380 kyr Structure formation30 K500 Myr Now2.725 K13.75 Gyr