Lecture 36: The First Three Minutes

Readings: Sections 29-1, 29-2, and 29-4 (29-3)

Key Ideas

Physics of the Early Universe

Informed by experimental & theoretical physics

Later stages confirmed by observations

The Cosmic Timeline:

Unification of forces until just after the Big Bang

Separation of forces as the Universe cools

Inflation explains smoothness & flatness

Emergence of matter starting at t=10^-6 sec

Recombination & emergence of visible Universe

The Big Bang’s Hot Past

The Universe Today:

Low density, dark and very cold (2.7K)

Continues to expand

14 Gyr Ago:

Universe was smaller, denser and hotter

Opaque and filled with photons

How far back can we go in cosmic history?

Binding & Loosing

Binding Energy:

Energy needed to unbind (break up) matter.

Binding Temperature:

Temperature equivalent to the binding energy

Matter at this temperature “melts” (unbinds)

Example:

In massive stars, nuclei melt at T~10 Billion K.

Typical Sizes & Binding Energies

Size Binding Energy

Atoms 10^-10 m 10³ K

Nuclei 10^-14 m 10¹⁰ K

p&n 10^-15 m 10¹¹ K

Quarks 10^-18 m 10¹³ K

Equilibrium

When there is sufficient energy, matter and anti-matter particles can annihilate and produce energetic photons and vice versa. If equilibrium exists, then for every reaction one way, there’s a reaction the other way.

When photons do not have enough energy (=2x the rest mass energy of the electron) to make electron-positron pairs, then we fall out of equilibrium and the reaction proceeds only one way. Leads to freeze-out.

Similar idea applies to electrons no longer having enough energy to combine with protons to make neutrons, etc.

Coupling and Decoupling

Matter coupled when it can switch from one form to another (such as

protons to neutrons and back)

Photons coupled when absorbed/scattered by matter

Electrons good at this

Particles can be coupled but not in equilibrium.

Fundamental Forces of Nature

Gravitation:

Long-Range Force, weakest in Nature

Electromagnetic Force:

Long-Range, 10³⁹ x stronger than gravity

Weak Nuclear Force:

Range < 10^-17 meters, 10²⁸ x stronger than gravity

Strong Nuclear Forces:

Range < 10^-15 meters, 10⁴¹ x stronger than gravity

Electromagnetism & Weak Force

At “low” energies

Electromagnetism governs reactions between charged particles, carried by massless photons

Weak force changes neutrons into protons, carried by massive W and Z bosons.

At “high” energies

Electromagnetic interactions become indistinguishable from weak interactions

W&Z Bosons lose their mass and the weak force becomes long-range as well.

Theories suggest that at high energies, the strong force has the same strength as the electromagnetic and weak as well.

Unification of the Forces

See Figure 29-4

The Cosmic Timeline

Physics gives us a framework within which to describe the Big Bang from the earliest phases to the present:

Particle accelerators probe matter at states similar to some of these early phases

Theoretical physics formulating descriptions of the interplay of forces and particles

Astronomers look for evidence in the present Universe (e.g. Cosmic Background, amounts of primordial deuterium & helium)

The Planck Epoch

Before t=10^-43 sec

All 4 forces unified into a single Superforce

1 force rules all of physics

Few details, as we do not yet have a quantum theory of gravity to guide us.

The Grand Unification Epoch

At t=10^-43 sec, T=10³²K (?)

Gravity separates from the Superforce

Strong & Electroweak Forces still unified

The Universe is a hot, dense soup of quark, anti-quarks & photons in equlibrium.

The Inflationary Epoch

At t=10^-35 sec, T=10²⁷ K:

Strong force separates from GUTs force

EM & Weak forces still unified

The rapid separation of the forces triggers a rapid “inflation” of the Universe

The Inflationary Universe

Universe grows exponentially by ~10⁴³ between 10^-36 & 10^-34 sec:

Expansion slows down to normal afterwards

Explains smoothness & flatness on large scales

Cosmic Background is smooth to 1 part in 10⁵

Observations suggest that W₀ ~ 1 (flat)

See Figure 29-3

Four Forces at Last!

At t=10^-12 sec, T=10¹⁵ K:

Electroweak separates into EM & Weak forces

All forces are now separate

Conditions becoming right for free matter to exist separately from photons

Quark Freeze-out

At t=10^-6 sec, T=10¹³ K:

Free quark combine into hadrons (primarily protons & neutrons)

Particle-antiparticle pairs & photons in equilibrium

Matter as we understand it begins to emerge.

Nucleon Freeze-out

At t=0.01 sec, T=10¹¹ K

Protons & neutrons decouple from photons

Electrons & positrons in equilibrium with photons

Neutrinos & nucleons are in equilibrium

Free neutrons are stable during this epoch

Neutrino Decoupling

At t=1 sec, T=10¹⁰ K

Neutrinos decouple from matter and stream out into space

Forms a Cosmic Neutrino Background

(predicted but not yet observed)

Free neutrons are no longer stable

Decay into protons, electrons & neutrinos

Left with 1 neutron for every 5 protons

The Epoch of Nucleosynthesis

At t=3 minutes, T=10⁹ K

Fusion of protons & remaining free neutrons

Formation of ²H (Deuterium) & ⁴He

End up with ~75% H, 25% He

Traces of D, Li, Be, B

We cannot observe this epoch directly, but we can measure the products of primordial nucleosynthesis.

The Epoch of Recombination

At t=300,000 years, T=3000 K

Electrons & nuclei combine into neutral atoms

Universe becomes transparent, photons stream out into space

Origin of the Cosmic Background Radiation

The earliest epoch we can observe directly

Recombination to Today

See Figure 29-11

What about the very Beginning?

Our physics can not yet probe earlier than the end of the Planck Epoch (t=10^-43 seconds)

The current frontier is before the Electroweak Epoch (t=10^-12 seconds), during the period of rapid inflation. There is much active research in this area.

This will be the astrophysics of the 21^st Century (or maybe the 22^nd….)