Neutron decay and interconversionParticle 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+n0 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 sidep++n0 +

• Put the electron on the other side

+

e+

n0 p+ e-+• All thee processes convert neutrons to protons and vice versa

Neutron/Proton Freezeout• Weak interactions interconvert protons/neutrons• These are slow processes, so they fall out of equilibrium fairly early• At kBT = 0.71 MeV, the process stops• What is ratio of protons to neutrons at this temperature?• Non-relativistic, E = mc2.• Ratio is:

exp BP E E k T

2

2

exp

exp

n n B

p p B

P m c k T

P m c k T

2

2

exp

expn Bn

p p B

m c k Tnn m c k T

2 1.294 MeVexp exp 0.1620.71 MeVB

mck T

0.162 0.1391.162

n

n p

nn n

• This happens at about:2

eff

2.42 s MeVg B

tk T

22.42 s MeV0.71 MeV10.75

1.5 s

The Deuterium Bottleneck• The next step in making more complex

elements is to make 2H, deuterium:• This releases about 2.24 MeV of energy• Naively: this process will go ahead as soon as kBT 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+ n0+ p+n0

2

eff

2.42 s MeVg B

tk T

22.42 s MeV0.1 MeV3.36

130 s

132 s 1.5 s

130exp886

n n

n p n p

n nn n n n

0.120

• Ratio depends weakly on density of protons/neutrons – more makes it happen sooner

Making Helium• Once we make deuterium, we continue quickly to continue to helium:

p+

n0+p+n0 p+

n0n0

p+n0n0 + p+p+

n0n0

p+

n0

+p+n0 p+p+

n0

+ p+p+n0n0

p+p+n0

• For every two neutrons, there will be two protons that combine to make 4He• Mass fraction of 4He is twice that of neutron fraction

• 4He 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, YP increases weakly:

Bnn

4 He totalPY 2 n Bn n 2 0.12 0.24

100.248 0.011ln6 10PY

Making Other elements• When you run out of neutrons, 3He can still be turned into 4He via

• The last few 2H, 3He, and 3H 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, 2H, 3He, and 3H all decrease

• There are other rare processes that produce a couple of other isotopes:• 7Li and 7Be are produced

• I don’t understand how theydepend on

• Within a few hundred seconds, thebaryons are all in 1H, 2H, 3H, 3He, 4He, 7Be and 7Li

+p+p+n0 +p+p+

n0n0p+p+

n0p+ p++

+p+p+n0 p+p+

n0n0

p+n0n0 + p+p+

n0n0

p+

p+p+n0n0

n0p+

n0n0

n0p+

p+p+n0

Anything we missed?• Two of these isotopes are unstable:• Add 3H to 3He and 7Be to 7Li

• The process whereby stars make heavier elements do not work in the early universe

• Density is too low for unstable 8Be to findanother 4He to react with

• In the end, we should be able to predict abundance (compared to hydrogen) of2H, 3He, 4He, 7Li

• These have all been measured, mostly by studying light from quasars

3 3

7 7

H He

Be Lie

e

e

e

4 4 8 *

4 8 * 12

He He Be

He Be C

• 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

106.2 0.2 10Bnn

The results

106.2 0.2 10

• Predictions for 4He, 2H and 3He all work very well

• Prediction for 7Li seems to be off• The Lithium problem

• Overall, success for the model

Summary of Events:Event kBT or T TimeNeutrinos Decouple 1 MeV 0.4 sNeutron/Proton freezeout 0.7 MeV 1.5 sElectron/Positron Annihilate 170 keV 30 sPrimordial Nucleosynthesis 80 keV 200 s

Matter/Radiation Equality 0.76 eV 57 kyrRecombination 0.26 eV 380 kyr

Structure formation 30 K 500 MyrNow 2.725 K 13.75 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?

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 kBT = 35 MeV (g = 4 fermions)• Pions, mass 135-139 MeV, at about kBT = 45 MeV (g = 3 bosons)• At a temperature of about kBT = 100 MeV, we have quark deconfinement

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

ud

ug

u

• At low temperatures quarks are confined into these packets• At high temperatures, these quarks become free (deconfined)• Estimated kBT = 150 MeV

2

eff

2.42 s MeVg B

tk T

22.42 s MeV150 MeV61.75

51.4 10 s

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 kBT = 50 GeV2

eff

2.42 s MeVg B

tk T

22.42 s MeV

50,000 MeV100

1010 s

The Standard ModelParticle symbols spin g mc2 (GeV)Electron e ½ 4 0.0005Electron neutrino e ½ 2 ~0Up quark uuu ½ 12 ~0.005Down quark ddd ½ 12 ~0.010Muon ½ 4 0.1057Muon neutrino ½ 2 ~0Charm quark ccc ½ 12 1.27Strange quark sss ½ 12 ~0.10Tau ½ 4 1.777Tau neutrino ½ 2 ~0Top quark ttt ½ 12 173Bottom quark bbb ½ 12 4.7

Photon 1 2 0Gluon gggggggg 1 16 0W-boson W 1 6 80.4Z-boson Z 1 3 91.2

Higgs H 0 1 115–285

• 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

7eff 828 90 106.75g

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 kBT = 500 GeV or so.• If this is right, the LHC should discover it

2

eff

2.42 s MeVg B

tk T

2

5

2.42 s MeV5 10 MeV100

1210 s

• In most versions of supersymmetry, the lightest super partner (LSP) should be absolutely stable Could this be dark matter?

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 1016 GeV, the three forces areequal in strength• At kBT = 1016 GeV, there will be another

phase transition – the Grand Unificationtransition

No Supersymmtery

With Supersymmtery

239

19

2.42 s MeV 10 s10 MeV210

t

Baryogenesis might occur at this scale Scale could be right for inflation

Summary of Events:Event kBT or T TimeGrand Unification 1016 GeV 10-39 sSupersymmetry Scale 500 GeV 10-12 sElectroweak Scale 50 GeV 10-10 sQuark Confinement 150 MeV 1.410-5 s

Neutrinos Decouple 1 MeV 0.4 sNeutron/Proton freezeout 0.7 MeV 1.5 sElectron/Positron Annihilate 170 keV 30 sPrimordial Nucleosynthesis 80 keV 200 s

Matter/Radiation Equality 0.76 eV 57 kyrRecombination 0.26 eV 380 kyr

Structure formation 30 K 500 MyrNow 2.725 K 13.75 Gyr