Astronomía Extragaláctica y Cosmología ObservacionalDepto. de Astronomía (UGto)

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)

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

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 mmc c2

mPl = [ħc/2G]½ = 2.210–8 kg ≈ 1019 GeV

rPl = ħ/(mPlc) = [2ħG/c3]½ = 1.610–35 m

tPl = [2ħG/c5]½ = 5.410–44 s

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) → 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. 6or Kolb & Turner 1993, The Early Universe, chap. 7

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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

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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

At the end of this era, since the temperature cools, occurs the annihilation e–/e+ pairs

Tγ3 = (11/4) Tν

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Tν = (4/11)1/3 (2.725) = 1.95 (1+z) K

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Primordial Nucleosynthesis (SBBN)

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(n/p) = e–Q/T

Q = mn – mp = 1.293 MeV

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

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Synthesis

z Age T(K) kT

Planck’s Era

Radiation Era GUT Epoch Quantum-Gravity SB 1032 510–44s 1032 1019 GeV gravitons decoupling Inflation Electroweak Epoch GUT SB 1026 10–34s 1027 1015 GeV Baryogenesis Quarks Epoch Electroweak SB 1014 10–10s 1015 100 GeV quarks → hadrons 1012 10–5s 1013 1 GeV Leptons Epoch 150 MeV ν decoupling 109 1s 1011 1 MeV e–/e+ annihilation 1010 500 keV Plasma Epoch P. Nucleosynthesis 108-109 100s 108-109 300 keV Matter-radiation equality 4000 10.000a 62000 5.4 eV

Matter Era Recombination 1400 3800 0.33 eV γ decoupling (CMBR) 1100 380.000a 3000 0.26 eV Star and galaxy formation 10 Reionization Epoch 6-15

Λ Era Accelerated Expansion Epoch 0.3 3.6 Now 0 13.7Ga 2.725 2.3510–3eV

Synthesis

Synthesis

Synthesis