Transcript inflation - Departamento de Astronomía

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)
Depto. de Astronomía (UGto)
Astronomía Extragaláctica y Cosmología Observacional
 Planck Era
 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
ħ > 2Gm
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
 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!
 The GUT Epoch
 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)
• SU(2)U(1)
• SU(3)
→ Quantum Electrodynamics (QED)
→ Weinberg-Salaam Electroweak Theory
→ 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
 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…
 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
 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
 Eletroweak Epoch
 During this era occurs the condensation of quarks in
hadrons (baryons and mesons)
 only nucleons (p+ and n0) are stable
 Eletroweak Epoch
 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
Tγ3 = (11/4) Tν3
Tν = (4/11)1/3 (2.725) = 1.95 (1+z) K
 At the end of this era, since the temperature cools, occurs the
annihilation e–/e+ pairs
 Primordial Nucleosynthesis (SBBN)
 At a temperature from 109-108 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).
(n/p) = e–Q/T
Q = mn – mp = 1.293 MeV
 After the n0 are processed into nucleons, the
their number remain constant.
 Primordial Nucleosynthesis
 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
 Synthesis
z
Age
T(K)
kT
Planck’s Era
Radiation Era GUT Epoch Quantum-Gravity SB
gravitons decoupling
Inflation
Electroweak Epoch GUT SB
Baryogenesis
Quarks Epoch Electroweak SB
quarks → hadrons
Leptons Epoch
ν decoupling
e–/e+ annihilation
Plasma Epoch P. Nucleosynthesis
Matter-radiation equality
Matter Era
Λ Era
1032
510–44s
1032
1019 GeV
1026
10–34s
1027
1015 GeV
1014
1012
10–10s
10–5s
1015
1013
109
1s
108-109
4000
100s
10.000a
1011
1010
108-109
62000
100 GeV
1 GeV
150 MeV
1 MeV
500 keV
300 keV
5.4 eV
380.000a
3800
3000
0.33 eV
0.26 eV
Recombination
γ decoupling (CMBR)
Star and galaxy formation
Reionization Epoch
1400
1100
10
6-15
Accelerated Expansion Epoch
Now
0.3
0
13.7Ga
3.6
2.725
2.3510–3eV
 Synthesis
 Synthesis
 Synthesis