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