Cosmology
Master NPAC
Lesson 4 :
Universe Thermodynamics : Thermal History Primordial Nucleosynthesis
Laurent Le Guillou
2016-11-30 & 2016-12-05
Thermal History An Overview
4.1
Eras : radiation, matter, « vacuum »
● Radiation dominated
● Matter dominated
● « vacuum » dominated
Eras : radiation, matter, « vacuum »
Eras : radiation, matter, « vacuum »
Eras : radiation, matter, « vacuum »
The Universe expands...
Entropy is being conserved
any heat flow would defined a prefered direction → isotropy
Radiation
The Universe expands adiabatically, like a fluid in equilibrium
The Universe cools down while expanding...
→ hotter and denser in the past...
Cosmic Microwave Background (CMB)
A. A. Penzias & R. W. Wilson (1965)
Hot Universe in the Past
Black body spectrum emitted at the time of last ionizations (decoupling of photons and matter)
T ~ 2.73 K implies a redshift of ~1100
Confirm the « Big Bang » model Black Body spectrum (microwave)
T ~ 2.73 K (BB spectrum up to 10-5)
Predicted by the « hot Big Bang » model
Cosmic Microwave Background (CMB)
Cosmic Microwave Background (CMB)
Anisotropies reveal densities fluctuations at the time of
emission of the CMB z~1100
Age ~ 370 000 y
Planck 2009-2012
CMB
nearly perfect black body spectrum
Anisotropies at the level of 10-5 (once dipole is removed)
Hot Big Bang theory : CMB
Hot Big Bang theory : CMB
● Cosmic microwave background (CMB)
● black body (BB) spectrum at 2.7 K
→ recombination of H+ and e- around T~3000 K
● redshifted by the expansion
● BB spectrum redshifted is still a BB spectrum !
Universe : cooling history
radiation era :
matter era :
Universe : cooling history
Event T kT z t
Quantum gravity 1032 K 1019 GeV 1032 10-43 s Grand unification 1028 K 1015 GeV 1028 10-36 s E-W unification 1015.5 K 250 GeV 1015 10-12 s Nucleon pairs 1013 K 1 GeV 1013 10-7 s Neutrino decoupl. 1010 K ~1 MeV 1010 1 s Nucleosynthesis 10-0.1 MeV 10-1 – 103 s
Pairs e+ e- 109.7 K 0.5 MeV 109.5 4 s
9500 K 0.8 eV 3600 50 kyr
Recombination 3000 K 3 eV 1100 380 kyr
Reionization 11 – 4 0.4 – 0.1 Myr
First Galaxies 16 K 10-3 eV 5 1 Gyr
3 10-4 eV 0.3 10 Gyr
Now 2.7 K 2 10-4 eV 0 13.5 Gyr
Planck scales : mass, time, length, ...
● Fundamental constants :
● « Natural » units :
● Planck length
● Planck time
● Planck mass
● Planck temperature
Max particle mass
Quantum gravity
Equilibrium distributions
Studying the hot universe plasma...
4.2
Thermal equilibrium in the early universe
● Hypotheses :
● ~ Ideal gas – interactions are negligible
● Thermal equilibrium (tiny fraction of collision occurs)
● Equilibrium between radiation (dominating) ↔ matter
● As long as i.e.
● Particles stay in thermal equilibrium with the photons...
… Until they stop interacting when
… then they decouple (freeze)
Thermal equilibrium : distributions
● Density of states in 6D phase space
● Particle density (g : degrees of freedom)
Waves in a box of size L
Thermal equilibrium : distributions
● Occupation density
Thermal equilibrium : distributions
● Number density
● Energy density
● Pressure
● Entropy
● Entropy is conserved
Non relativistic matter
Cold matter Radiation, relativistic particles Hot matter
or
Relativistic / non relativistic particles
Relativistic limit
● Number density
Energy density
Useful Integrals and formulas...
For bosons For fermions
Gamma function
Riemann zeta function
Relativistic limit
● Number density
● Energy density
● Pressure
● Entropy
Relativistic and non relativistic limits
Bosons Fermions Non relativistic gas
Number density of non relativistic particles exponentially suppressed, until they decouple from thermal bath...
Number density of non relativistic particle exponentially suppressed, until they decouple from thermal bath...
Total energy density
For particles still at equilibrium with the photons (« th »), Where
Once a particle population is non relativistic, it is removed from
Entropy
Where
For particles still at equilibrium with the photons (« th »),
When a particle species decouples, its entropy is transfered to the heat bath… and drops. Total entropy is conserved.
When
All SM particles are relativistic :
Bosons : Fermions :
Decoupled species
● Before decoupling → phase space distribution (prev.)
● Decoupling when
● After decoupling : relic density (frozen)
● Relativistic species (neutrinos, …) :
● Non relativistic species :
particles per unit of comobile volume conserved particles dilute…
The remaining amount (relic density) depends
on the desintegration cross-section.
Neutrino decoupling
Equilibrium with heat bath :
Happens when
i.e.
Freeze the neutron / proton ratio
Entropy conservation :
Annihilation pairs e+ e-
It occurs around At time
Before (1) : After (2) :
Entropy conserved :
(neutrinos already decoupled) (relic e-, neutrinos already decoupled)
Primordial nucleosynthesis
How the first nuclei appeared...
4.3
Dark Energy
69
Dark Matter
26
Baryons 4.8
Now z=0
Photons 59
Neutrinos 41
BBN z=108
Big Bang nucleosynthesis
Era dominated by radiation
0 2 4 6 8 10 12 14 16 18 20
10-2 10-1 1 10
T (MeV)
g *, g * e+ e- annihil. decoupling (2-3 MeV)
n/p freeze-out (3.3 GK)
Nucleosinthesis (0.9 GK)
g* (Entropy) e
g* (Energy) e
43/4
3.36 2
11/2 s
s g
A. Coc, CSNSM, 2011
Big Bang nucleosynthesis
● Critical parameter : density of baryons
Time < 1 s Neutron/proton
freeze-out
1 – 100 s Neutrons decay
100 – 200 s Deuterium formed
Allows neutrons to survive
200 – 1000 s Deuterium burned to
produce next elements
Bh2=WMAP
10 -21 10 -19 10 -17 10 -15 10 -13 10 -11 10 -9 10 -7 10 -5 10 -3 10 -1 1
102 103 104
10 -21 10 -19 10 -17 10 -15 10 -13 10 -11 10 -9 10 -7 10 -5 10 -3 10 -1
1
102 103 104
n
p
2H
3H
16O
3He
4He
15N
14N
6Li
7Li
7Be
9Be
10B
11B
11C
12C 13C
Time (s)
Mass fraction
A. Coc, CSNSM, 2011
Etc...
0.22 0.24 0.26
Planck
Bh2
Mass fraction
4He
10 -2
10 -6 10 -5 10 -4 10 -3
3 He/H, D/H
D
3He
10 -10 10 -9
1 10
7 Li/H 7
Li
Planck
1010 A. Coc, CSNSM, 2011
http://xkcd.com/1606/
