1
The Early Universe
Notes based on Teaching Company lectures, and associated undergraduate text – with some additional material added.
1) From 1 µs to 1 s: quark confinement; particle freezout. 2) From 1 s to 3 minutes: Big Bang Nucleosynthesis. 3) Before 1 ns: Supersymmetry; baryogenesis; unification.
Overview: The Early Universe
Simple Friedmann equation for the radiation era:
E(a) = Ωr,o1/2 a-2 gives (using Ωr,o = 8.4 × 10-5)
a = 2.09 × 10-10 h72
½ ts½
T = 1.31 × 1010 h72-½ ts
-½ K = 1.14 h72-½ ts
-½ MeV
Note: this relation is modified somewhat at earlier times when other species (e.g. e+, e-) are thermally produced.
t1 s!
"#
$
%&'1/2
(T
1010 K(
kBT1 MeV
( !107gm cm'3
!
"#
$
%&
1/4
(!m
1 gm cm'3
!
"#
$
%&
1/3
(1+ z1010
103 10-3 10-6 10-9
10
107
Time: t (seconds)
Tem
pera
ture
: T (b
illio
ns o
f K)
10-10 10-13
1
106
1018
1024
10-6
Scale Factor: S D
ensity: ρtot (tons/cm
3)
1
10-16
1 ms 1 µs 1 ns 1 sec
104 1012
10-12 1 ps 1 ks
Expansion
Cooling and
Thinning
103 10-3 10-6 10-9
10
107
Time: t (seconds)
Tem
pera
ture
: T (b
illio
ns o
f K)
10-10 10-13
1
106
1018
1024
10-6
Scale Factor: S
Density: ρ
tot (tons/cm3)
1
10-16
1 ms 1 µs 1 ns 1 sec
104 1012
10-12 1 ps 1 ks
Quark/gluon plasma
Quark confinement
p+ / p- annihilation
Neutrinos decouple
Helium synthesis
e+ / e- annihilation
Accelerators recreate the early universe
High temperatures = high energy collisions Particle accelerators reproduce these collisions They recreate the conditions of the early universe.
Higher Temperature Faster Motion
Lower Temperature Slower Motion
2
Electric fields accelerate the particles
Detectors are immense
Particle creation and detection
Z0 detection at UA1 detector Z0 decay at DELPHI 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!
103 10-3 10-6 10-9
10
107
Time: t (seconds)
Tem
pera
ture
: T (
billi
ons o
f K)
10-10 10-13
1
106
Scale Factor: S
Energy (MeV
)
1
10-16
1 ms 1 µs 1 ns 1 sec
104 103
10-12 1 ps 1 ks
1 MeV
1 GeV
1 TeV
1950s
1960s
1980s
1990s
2010 LHC/CERN Above/below threshold temperatures: particle creation and annihilation
With high enough energy, particle collisions can generate particle-antiparticle pairs: e.g. γ + γ x+ + x- Need thermal energy: kBT ≥ mxc2 to generate this. So kBTthreshold ~ mxc2 provides a threshold temperature. (e.g. e+/e- at 0.5 MeV = 6 GK (5s); p+/p- at 1 GeV = 1013 K (1µs)
However, at any temperature, particle-antiparticle annihilation can occur: e.g. x+ + x- γ + γ
3
Below the threshold temperature proton electron photon
Gas at 1 billion K
Photons Energy exchange
Particle KE
At LTE the photons have a planck function, with energy density: uγ = ργc2 = gγ where gγ = 2 for both spins
8π5 (kBT)4 30 (hc)3
Above the threshold temperature anti-electron electron photon
Gas at 10 billion K Photons
energy exchange
Particle KE
anni
hilat
ion
annihilation
Electrons and Anti-electrons
creation crea
tion
equilibrium
We now have γ, e+ and e- all present, with total energy density: u = ρc2 = g* where g* = 5.5 (=2 + (2+2)×⅞ )
8π5 (kBT)4 30 (hc)3
The Standard Model Particles
e νe
µ νµ
τ ντ
u d
c s
t b
Leptons Quarks
Family 1
Family 2
Family 3
Matter Particles (Fermions)
γ
Z
gs
gv
Force carriers (Bosons)
EM
Weak
Strong
Gravity
W
× 8
Higgs H
10
Num
ber o
f kin
ds o
f par
ticle
s
Temperature (billions of K)
20
30
40
50
0
1 103 106
leptons added
quarks added
1 TeV 1 MeV 1 GeV
103 10-3 10-6 10-9
Time (seconds)
1 1 ms 1 µs 1 ns 1 sec
10-12 1 ps 1 ks
all SM particles present
≈ ½g*
10
Num
ber o
f kin
ds o
f par
ticle
s
Temperature (billions of K)
20
30
40
50
0
10 104 107
1 TeV 1 MeV 1 GeV
103 10-3 10-6 10-9
Time (seconds)
1 1 ms 1 µs 1 ns 1 sec
10-12 1 ps 1 ks
Electron threshold
Protons & anti-protons annihilate
Quark confinement
Quark-gluon plasma
Higher g* shortens expansion timescale
Since tH = 1/H = (3/8πGρ)½ and ρc2 = g*
Then g* enters a(t), giving faster expansion timescales at earlier times than our simple relation. In terms of temp/energy: TMeV ~ 1.5 g*
−¼ ts−½
8π5 (kBT)4 30 (hc)3
4
Big Bang Nucleosynthesis
Near 1 minute, T ~ 108 K, and nuclear reactions can occur. Unlike stars, there are free neutrons, which can form deuterium, and then He-4. The conditions don’t allow heavier elements to form.
Late 1940s: Robert Herman George Gamow and Ralph Alpher analyze nuclear reactions in a hot big bang. Their aim was to make all the elements.
Neutron/proton equilibrium
The neutron/proton number ratio is a key parameter. Before 1 sec, an eqlm population is maintained by neutrino reactions:
Recall, neutrons are slightly heavier than protons: Δm = mn – mp = 939.6 – 938.3 = 1.3 MeV
n+!e ! p+ e" + energy
p+! e + energy! n+ e+
Hence eqlm population ratio given by Boltzmann factor:
Nn
Np
= mn
mp
!
"##
$
%&&
3/2
exp '(mn 'mp )c2
kBT
!
"##
$
%&&
So, when kBT >> 1MeV, (Nn/Np) ≈ 1. This drops below 1.0 near 1sec, as T drops below 1 MeV
Temperature (billions of K)
1000 100 10 1 0.1 0.01 Time (sec)
10 1 100
1 MeV 0.1 MeV 10 MeV
1.0
0.1
0.01
1.0
0.1
0.01
Neu
tron
/ Pro
ton
ratio
Neutron decay Half-life = 10 minutes
Thermal equilibrium
Neutrinos decouple n/p ratio frozen
He synthesis
Neutrino decoupling freezes the neutron/proton ratio
Near 1 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: treac = 1/(n<σv>) With: n ~ a-3, σW ~ T2 ~ a-2, v ~ c; so treac ~ a5 is slowing down
When treac > tH then the number of “collisions” drops to zero.
The reaction is frozen.
Expansion timescale: tH = 2tage ~ a2 is also slowing down, but not as fast.
This occurs near 1 sec (T ~ 0.8 MeV), when Nn/Np ~ 1/5. The further delay of ~5 minutes until deuterium formation brings this ratio down to 1/7.3 (neutron half-life = 10.2 min)
Making 25% Helium
12
7
7
1
1
4 75% Hydrogen 25% Helium
fusion reactions
protons neutrons Helium Abundance
In simple form, helium abundance arises from full conversion of neutrons into He-4. Hence:
NHe = ½ Nn Hence the mass fraction of helium is:
YHe = (4 × ½ Nn) / (Nn + Np) = 2/(1 + Np/Nn)
Hence, for Np/Nn = 7.3, we have YHe = 0.24
5
Making deuterium
deuterium proton neutron
Making Helium
Notice: this is a strong reaction, and quite different from the weak reaction that occurs within stars:
p + p D + e+ + νe
γ
Making Helium-4
He-3
H-3
He-3
H-3
He-4
He-4
D
p
D
n
n
p
The Deuterium Bottleneck
deuterium
proton neutron
γ-ray photon
Formation
Destruction
γ BED ~ 2.2 MeV
The deuterium bottleneck
photon
N(γ) ≈ 104 N(p) N(γ) ≈ 108 N(p)
deuterium destruction
energy needed to destroy deuterium
109 K 170 seconds
2 × 109 K 40 seconds
Photon energy: MeV 1 2 3
5 × 109 K 7 seconds N
umbe
r of p
hoto
ns
0 0
N(γ) ≈ N(p)
Number of neutrons
Num
ber o
f pro
tons
1 2 3 4 5
5
4
3
2
1 H
He
Li
Be
B
0
0
6 C
6
D
n
He-3 He-4
p H-3
Li-7
Be-9
B-10 B-11
C-12
5
8
The beryllium barrier
Li-6
5
8
+n
+p +He-4
C-13
7 10 100 1000
3.0 1.0 0.3
10-4
10-6
10-8
10-10
1.0
Temperature (billions of K)
Time (seconds)
Frac
tion
by m
ass
neutrons
protons
He-4
deuterium He-3 Li-7
neutrons
1 Hour
10-2
Li-7
He-3 D
He-4 H protons
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 Ωb
Proton + neutron density (gm/m3 at 3 minutes) 10 1 100
He-4
Deuterium
He-3
Li-7
10-4
10-6
10-8
10-10
1.0
Frac
tion
by m
ass
10-2
Element production depends on furnace density
Measuring primoridal helium
Primordial value
1 2 0 Oxygen abundance ×10-4
10%
20%
30%
Hel
ium
abu
ndan
ce
0%
Increasing contribution from stars
Measuring deuterium in the intergalactic medium
Wavelength: nm
500 600 700 Wavelength: nm
Inte
nsity
556.0 555.5
QSO 1937 - 1009 Hydrogen emission in the quasar
Hydrogen absorption in the IGM 0
Proton + neutron density (gm/m3 at 3 minutes) 10 1 100
He-4
Deuterium
He-3
Li-7
10-4
10-6
10-8
10-10
1.0
Frac
tion
by m
ass
10-2
0.001 0.01 1 0.1 Omega-atomic (today): Ωat,0
0.04 Cosmic history in a glass of water
H2O
H2O HDO
H2O H2O
H2O H2O
H2O H2O
H2O
H2O H2O
H2O
H2O
H2O
The deuterium in water is a relic from the Big Bang. It’s abundance (~10-5) reveals the conditions in the 3-minute old furnace.
7
Even Earlier Times
1) Supersymmetric particle creation and dark matter
2) Force unification: electroweak and GUT
3) Baryogenesis: matter/antimatter asymmetry.
Tem
pera
ture
: T (K
) Density: ρ
tot (tons/cm3)
10-10
10-10
1010
1020
1030
Time: t (seconds)
10-15 10-20
1
1080
1040
Scale Factor: S 10-30
1 10-20 10-30
10-25
10-40
known physics
well known physics
uncertain physics
unknown physics
(Planck era)
Tem
pera
ture
: T (K
) Density: ρ
tot (tons/cm3)
10-10
10-10
1010
1020
1030
Time: t (seconds)
10-15 10-20
1
1080
1040
Scale Factor: S 10-30
1 10-20 10-30
10-25
10-40
Electroweak Unification
Higgs Mechanism
GUT Transition?
Quark confinement
Dark Matter Freezout?
Matter Asymmetry?
Tem
pera
ture
: T (K
) Density: ρ
tot (tons/cm3)
10-10
10-10
1010
1020
1030
Time: t (seconds)
10-15 10-20
1
1080
1040
Scale Factor: S 10-30
1 10-20 10-30
10-25
10-40
Particle desert?
~1020
~1010 ~1040 Super-symmetry
8
Super-symmetric particles
Standard Model particles
Super-partner particles
Fermions Bosons
Bosons Fermions
Electron Neutrino Quark
Selectron Sneutrino Squark
Photon W & Z Gluon
Photino Wino & Zino Gluino
s-
-ino
Tem
pera
ture
: T (K
) Density: ρ
tot (tons/cm3)
10-10
10-10
1010
1020
1030
Time: t (seconds)
10-15 10-20
1
1080
1040
Scale Factor: S 10-30
1 10-20 10-30
10-25
10-40
Lightest super-partner = dark matter?
Super-partner thresholds?
Force unification
Forces depend on temperature due to vacuum polarization
The Forces of Nature
Gravity Weak Electro-
magnetism Strong
Example Planetary orbits
Radioactive decay
Electrons in atoms
Protons in nucleus
Acts on All All Charged particles
Quarks & gluons
Carrying boson Graviton W & Z Photon Gluons
Relative strength 10–38 10–4 10–2 1
Electro-weak unification
Sheldon Glashow b. 1932
Abdus Salam 1926 - 1996
Steven Weinberg b. 1933
Tem
pera
ture
: T (K
) Density: ρ
tot (tons/cm3)
10-10
10-10
1010
1020
1030
Time: t (seconds)
10-15 10-20
1
1080
1040
Scale Factor: S 10-30
1 10-20 10-30
10-25
10-40
Electroweak unification
Higgs mechanism: particles acquire mass
9
Tem
pera
ture
: T (K
) Density: ρ
tot (tons/cm3)
10-10
10-10
1010
1020
1030
Time: t (seconds)
10-15 10-20
1
1080
1040
Scale Factor: S 10-30
1 10-20 10-30
10-25
10-40
Electroweak unification
GUT transition
10-36 sec
1028 K
Baryogenesis
Conditions for matter/anti-matter asymmetry
Andrei Sakharov (1921 - 1989)
1) Quarks and leptons must be able to interconvert.
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.
Hunt for CP violation currently a primary goal of the LHC.
10
Matter/anti-matter annihilation
Before annihilation:
1,000,000,000 anti-protons 1,000,000,001 protons
After annihilation:
0 anti-protons 1 proton 2,000,000,000 photons
surviving proton
N(annihilations)N(survivors)
=N(CMB)N(baryons)
!billion1
Tem
pera
ture
: T (K
) Density: ρ
tot (tons/cm3)
10-10
10-10
1010
1020
1030
Time: t (seconds)
10-15 10-20
1
1080
1040
Scale Factor: S 10-30
1 10-20 10-30
10-25
10-40
Electroweak unification
GUT transition
Matter/anti-matter asymmetry generated
?
?
End of Early Universe