1. The Thermal History of the Universe
Lecture 15
The Thermal History of the Universe
Planck’s Era
GUT Epoch
Gravitons decoupling
Inflation
Baryogenesis
Transition quarks-hadrons
Neutrino decoupling
Electron annihilation
Nucleosynthesis Primordial
Matter-Energy Equality
Recombination
Photon decoupling (CMBR)
Astronomía Extragaláctica y Cosmología Observacional
Depto. de Astronomía (UGto)

2. Planck Era ħ > 2 G m mc c2 mPl = [ħc/2G]½ = 2.210–8 kg ≈ 1019 GeV
In principle T, ρ and P → ∞ as a → 0, but there comes a point at which our knowledge of
Physics breaks down. This is where the thermal energy of typical particles is such that
their de Broglie wavelength is smaller than their Schwarzschild radius
t < tPl defines the Planck Era
Thus, it is incorrect to extend the standard model to a = 0 and conclude that the Universe
began in a singularity of infinite density!
ħ > 2 G m
mc c2
mPl = [ħc/2G]½ = 2.210–8 kg ≈ 1019 GeV
rPl = ħ/(mPlc) = [2ħG/c3]½ = 1.610–35 m
tPl = [2ħG/c5]½ = 5.410–44 s

3. The GUT Epoch
relic
If current ideas about unification are correct, the first “event” of our Universe was the
decoupling of gravitons (before that they were supposedly in thermal equilibrium with
the remainder), that occurred at about tPl
thus, their present temperature should be at most 0.91 K, corresponding to a number density
of less than about 15 cm–3
this also sets the possible first phase transition (spontaneous symmetry breaking) that
corresponds to the separation of the gravitational interaction from the GUT one
The spontaneous symmetry breakings are treated in the
Particle Physics by the Gauge theories (based on the
idea of Gauge group symmetry and Gauge boson
particles – photons, vector bosons, gluons and
gravitons – which carry the “forces”). Examples
of Gauge theories are the following
U(1) → Quantum Electrodynamics (QED)
SU(2)U(1) → Weinberg-Salaam Electroweak Theory
SU(3) → Quantum Chromodynamics
(quarks, strong interaction)
SU(3)SU(2)U(1) → The Standard Model
SU(5) → Grand Unified Theory (GUT)
O(10) → another GUT
See, for example, Roos 1999, Introduction to Cosmology, chap. 6
or Kolb & Turner 1993, The Early Universe, chap. 7

4. Inflation
At the end of GUT period supposedly occurs an exponential expansion of the Universe called
inflation (for a growing factor of about 1030), driven by a quantum scalar field (inflaton)
during the inflation, the total pressure is negative, P < –ρ/3, and the Hubble “constant” really
stays constant
at least two important things occur at the inflation period:
quantum fluctuations are taken to
astronomical scales by the inflation
expansion and become the
seeds for structure formation
at the end of the exponential expansion
the Universe is reheated to a high
temperature (~ 1015 GeV),
“recreating” the Universe (that is,
the energy of the inflaton is
converted back into conventional
matter)
The main predictions of inflation are:
k = 0 (the most natural), although there
are inflationary models for k = –1;
nearly scale-invariant (n=1), Gaussian,
adiabatic, density perturbations
nearly scale-invariant gravitational waves…

5. Inflation
The inflation is not part of the standard model. It was proposed by A. Guth [1981, Phys. Rev.
23, 347] to solve some problems of this theory (and of Particle Physics):
flatness problem – if today the Universe is close to flat, it should have been much more
close in the past (Ω = 1 is an unstable critical point)  inflation forces Ω to 1 in the
beginning
horizon problem – CMBR photons emitted from opposite sides of the sky seem to be
in thermal equilibrium, which is not expected by the standard model since these photons
did not have time to make contact (one is out of the other’s horizon)
topological defects – like initial inhomogeneities and magnetic monopoles created during
phase transitions, are diluted  during reheating the T does not get hot enough for
allowing them to form again

6. Baryogenesis
The GUT epoch ends when the strong interaction separates from the electroweak one
(second phase transition)
An important symmetry breaking that possibly occurred in this phase is the asymmetry
(1/109) between matter and anti-matter (specially quarks and anti-quarks)
this asymmetry is usually associated to the baryogenesis or baryosynthesis
A. Sakharov [1967] realized that the baryosynthesis requires 3 conditions:
baryon number (B) no conservation (from a lepton, L, asymmetry)
C (charge conjugation) and CP (charge-parity) violation
departure from equilibrium (phase transitions, p.e.)
The GUT phase transition may provide these conditions, but also the Electroweak one that
occurred after
relic

7. Eletroweak Epoch During this era occurs the condensation of quarks in
hadrons (baryons and mesons)
only nucleons (p+ and n0) are stable

8. Eletroweak Epoch relic Tγ3 = (11/4) Tν3
The decoupling of neutrinos (ν) takes place in this epoch.
if we assume the lepton number (L) conservation,
the number of ν and ν are equal for each
species (e, μ, τ)
just like radiation, we expect Tν  (1+z)
(since they also relativistic).
Prior to ν decoupling we expect Tν ~ Tγ;
after the e–/e+ annihilation we expect
At the end of this era, since the temperature cools, occurs the
annihilation e–/e+ pairs
Tγ3 = (11/4) Tν3
Tν = (4/11)1/3 (2.725) = 1.95 (1+z) K

9. Primordial Nucleosynthesis (SBBN)
relic
At a temperature from K (begins about 1s after
the BB) occurs the primordial nucleosynthesis of:
12D
23He
24He
37Li (the others are unstable…)
Since the mean T of the Universe falls down with
time, the initially equilibrium rate between
p+ and n0 changes due to decay of the second:
This happens because of the higher mass of
the n0 (and lower half-life).
After the n0 are processed into nucleons, the
their number remain constant.
(n/p) = e–Q/T
Q = mn – mp = MeV

10. Primordial Nucleosynthesis

11. Equality, Recombination and CMBR
Matter-radiation equality (zeq ~ 4000) marks the transition to the matter domination regime
it has special significance for the formation of structures that was only possible in the
matter regime
At early times, radiation and matter are
thermally and dynamically coupled
by Compton interactions (nearly in
thermal equilibrium). As the temperature
gets low, the electrons become slow
enough that they can be captured into
atomic orbits by protons, forming
stable H atoms. This is called
“recombination” of free e–, although
the e– had never being bound before.
The He recombination occurs just
a short time before.
At a redshift of zdec ~ 1100, photons finally decouple from matter
the last scattering did not occur to all photons at the same time, so this last scattering
surface is really a shell of thickness Δz ~ 0.07z
relic

12. Synthesis z Age T(K) kT Planck’s Era
Radiation Era GUT Epoch Quantum-Gravity SB 10–44s GeV
gravitons decoupling
Inflation
Electroweak Epoch GUT SB –34s GeV
Baryogenesis
Quarks Epoch Electroweak SB –10s GeV
quarks → hadrons –5s GeV
Leptons Epoch MeV
ν decoupling s MeV
e–/e+ annihilation keV
Plasma Epoch P. Nucleosynthesis s keV
Matter-radiation equality a eV
Matter Era Recombination eV
γ decoupling (CMBR) a eV
Star and galaxy formation
Reionization Epoch
Λ Era Accelerated Expansion Epoch
Now Ga 10–3eV

13. Synthesis

14. Synthesis

15. Synthesis