Chapter 27: The Early Universe

• Expansion• Fundamental forces• Creation of matter and

antimatter• Density fluctuations and

the structure of the universe

• 11 dimensions?

Cosmic microwave background

• Cosmic microwave background is evidence of Big Bang

• Temperature of CMB in all parts of the sky is very nearly the same

• Nonuniformities tell us much about the universe.– They also happen to be

difficult to explain.

Isotropy problem

• CMB photons are emitted from our cosmic light horizon– This is as far back into the past

as we can look.

• Radiation from points A and B is essentially the same.

• How is this possible?– These points are so far apart

that they haven’t had time to interact.

– This is called the isotropy problem.

Flatness problem

• Observations indicate the 0 is very close to 1 indicating a flat universe.

• If 0 is very close to 1 today then it must have been extremely close (=1 to more 50 decimal places) during the Big Bang.– If >1 then the universe would have collapsed– If <1 then universe would have expanded too rapidly

for galaxies to form

• What could have happened to ensure that 0=1 to such an astounding degree of accuracy?

The inflationary model

• Theory suggests that the universe experienced a brief period of inflation shortly after the Planck time.– Planck time: First 1.35x10-43 s

of the lifetime of the universe. Before this time the laws of physics as we know them didn’t apply.

• During inflation the universe expanded by a factor of 1050 in about 10-32 s!

Does inflation violate special relativity?

• This doesn’t violate the idea that nothing can travel faster than the speed of light. The great increase in distance between objects was not due to motion but to the expansion of space.

Solving the isotropy problem

• During inflation much of the material near our location moved to tremendous distances.– When we observe the CMB we are seeing

radiation from distant parts of the universe that were once in intimate contact.

– This explains why all parts of the sky have almost the same temperature.

Solving the flatness problem

Evidence of inflation?

Inflationary models predict that the CMB is polarized (electric fields of the light oriented in a specific direction). This is indeed what we observe.

Understanding the early universe

• What could have triggered inflation?– Inflation was one of a sequence of events in the

first 10-12 s after the Big Bang.– Each involved a fundamental transformation of

the basic physical properties of the universe.

• To understand what happened we need to know how particles interact at very high energies.

Fundamental forces of nature

Fundamental forces in the early universe

Inflation

• Just before strong force and electroweak force decoupled the universe was in an unstable “false vacuum.”

• When these forces decoupled the universe “rolled downhill” to the true vacuum (a state of lower energy).

• This transition released energy which caused the universe to expand rapidly in a short period of time.

Mass and energy from the vacuum

• Inflation helps explain where all the matter and radiation in the universe came from.

• How could a violent expansion of space create energy and matter?– To understand this we need to first talk a bit

about the branch of physics explaining nature on the atomic scale and smaller - quantum mechanics.

Heisenberg uncertainty principle

• There are fundamental limitations to how accurately we can measure stuff on the smallest scales.

• The uncertainty principle says that the more precisely you measure the position of a particle the more unsure you become of its velocity (and vice versa).– Not the result of measurement errors but a fundamental

limit imposed by the nature of the universe.

Uncertainty principle for energy and time

€

ΔE × Δt =h

2πΔE = uncertainty in energy

Δt = uncertainty in time

h = Planck's constant

Spontaneous creation of matter and antimatter

• Einstein’s special relativity tells us that mass and energy are equivalent.– There is nothing uncertain about the speed of

light, so any uncertainty in the energy of a physical system can be attributed to uncertainty in the mass.

• We can therefore write ΔE=Δm c2

• If we plug this into the previous expression for the Heisenberg uncertainty principle we get:

Uncertainty principle for mass and time

€

Δm × Δt =h

2πc 2

Δm = uncertainty in mass

Δt = uncertainty in time

h = Planck's constant

c = speed of light

Astonishing results

• Over very brief intervals of time we cannot be sure of how much matter is in a particular location, even in “empty” space.– During this time matter can spontaneously

appear and then disappear.– The greater the mass the shorter it can exist.– No particle can appear by itself. Each particle

created is accompanied by its antiparticle.

Antimatter

• Antimatter is pretty much the same thing as normal matter.

• The main distinction is that a particle and antiparticle have opposite electric charge.

• Matter/antimatter pairs last for a very short time. For example the lifetime of an electron/positron pair is given by:

€

Δt =1

Δm

h

2πc 2=

6.25 ×10−34 Js

2 × 9.11 ×10−31kg( ) 2π × 3 ×108m/s( )2

( )

= 6.43×10−22s

Virtual pairs

Pair production

Inflation: From virtual to real particles

What happened after inflation?

• As soon as matter and antimatter appeared in universe collisions between particles and antiparticles released numerous high-energy gamma rays.– The rates of pair production and annihilation were the

same.

• As the universe expanded all photons became redshifted and the radiation temperature fell.– All particles (matter, antimatter and photons) were at

the same temperature.

Formation of matter

• Threshold temperature: the temperature above which photons spontaneously produce particles and antiparticles of a particular type.

• As the temperature of the universe decreased the type of matter formed through pair production changed.

Quark confinement

• First change: At t=10-6 s and T=1013 K quarks were able to stick together and form protons and neutrons.

• This is also the threshold temperature for proton/neutron production.– No new protons/neutrons formed after this point.– Annihilation of matter/antimatter proton and neutron

pairs continued however.– This lowered dramatically the matter content of the

universe while increasing the radiation content.

1 second after the Big Bang

• T=6x109 K (threshold temperature for electrons and positrons).

• Again, annihilation of electron/positron pairs increased the radiation content of the universe while decreasing the matter content.

• The universe at this point was mainly radiation.– This radiation, referred to as the primordial fireball,

dominated the universe for the next 380,000 years.

Why is there still matter?

• If there had been equal numbers of matter and antimatter particles then eventually (by t=1 s) every particle would have been annihilated leaving only radiation.– This didn’t happen. Why not?– There are roughly 109 photons for every proton or

neutron in the universe meaning for every 109 positrons there were 109+1 electrons.

– This slight imbalance is predicted by theoretical calculations.

Formation of nuclei

• Free neutrons decay quickly. This explains why we don’t observe them.

• In the first 2 seconds after the Big Bang electrons and protons collided and formed neutrons.– After this time no neutrons were being formed,

neutrons began to decay and the overall number of neutrons declined.

Nucleosynthesis

• At t=3 min the universe was cool enough for protons to combine to form helium.– Same process as in the center of a

star.

• Lithium (3 protons) and beryllium (4 protons) also formed this way.

• At t=15 min the universe was too cool for this to happen and no further nucleosynthesis occurred until stars formed.

Structure of the universe

• Matter is distributed in a lumpy manner in the universe today. This leads to several important questions:– How did this large-scale structure arise from

the primordial fireball?– When did stars first appear in the universe?– When and how did galaxies first form?

Density fluctuations

• The early universe must have been very smooth.

• Infinitesimally small quantum density fluctuations were stretched during inflation and became galaxies and clusters.

• The Jeans length is a critical length required for density fluctuations to persist against internal pressure.

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LJ =πkT

mGρ m

LJ = Jeans length

k = Boltzmann constant

T = temperature of gas (in K)

m = mass of a single particle in gas (in kg)

G = universal constant of gravitation

ρ m = average density of matter in the gas

Growth of density fluctuations

Globular clusters

• During recombination LJ was about 100 light years.

• Mass in a cube whose sides were 1 LJ long was about 5x105 M.– Equal to mass of a typical

globular cluster.

– Suggests that globular clusters were among first objects to form after recombination.

Population III stars

• Population II stars can’t be the oldest stars in the universe.– The original stars were

Population III stars.– These stars had masses

from 30 to 1000 M.– The death of these stars

provided matter incorporated into next generation of stars.

Timeline of light in the universe

Forming large-scale structure

• Once clumps the size of globular clusters formed, how did they form into galaxies, clusters of galaxies and larger structures?– Computer simulations taking into account dark

energy and dark matter consisting mainly of MACHOs and WIMPs lead to a universe that looks just like ours.

Formation of large scale structure

Bottom-up galaxy formation

A galaxy under construction

Physics before the Planck time

• Attempts to understand the universe before the Planck time require space to have up to 11 “hidden” dimensions.

• These theories are still in their early stages and much work remains to be done to understand the first 10-43 second after the Big Bang.