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The Physics Of the Early Universe

Fundamental Forces
Where did all the matter in the universe come from? To answer this question cosmologists have turned to the microscopic world of particle physics. Particle physics is the study of matter and energy at its most fundamental level and particle physicists seek to understand the basic structure of matter and the fundamental forces or interactions existing between matter in the universe.

There are four basic interactions that govern the interaction of matter:
(1) The gravitational interaction. Gravity attracts all matter but is too weak to have a significant affect at subatomic levels.
(2) The electromagnetic interaction. This plays an important role in forces between subatomic particles and is responsible for the phenomenon of electromagnetism.
(3) The strong interaction. It is this force that binds atomic nuclei together and stops them flying apart due to the mutual electrostatic repulsion of their protons.
(4) The weak interaction. The weak interaction is a force that is involved in the nuclear beta decay and other radioactive processes.

The CERN site with the particle accelerators clearly visible from the air

All these four forces are mediated by carrier particles which are elementary particles that 'carry' the force from one particle to another. The W and Z particles were discovered in 1984 using the Super Proton Synchrotron particle accelerator at CERN in Geneva. The Gluon has been detected by indirect methods but the graviton awaits a quantum theory of gravity and has so far not been observed.

Properties of Basic Interactions
Interaction Strength (relative to strong) Range/m Carrier Particle 
Gravitational
10-38
infinite
Graviton
Strong
1
10-15
Gluon
Electromagnetic
10-2
infinite
Photon
Weak
10-6
10-18
W and Z

Pair Production
 
Paul Dirac, theorised the existence of anti-particles years before they could be proven to exist. A biography can be found 
at the St. Andrews site. Cosmologists believe that in the universe's early history it was radiation that dominated and in order to understand why, we need to look at a key concept in particle physics called pair production We can write pair production symbolically as:

photon + photon = particle + antiparticle


 

The reverse is also possible. A particle and antiparticle can collide and annihilate each other producing two high energy gamma ray photons:
 
 

particle + antiparticle = photon + photon

For pair production to occur the following conditions must be met:

(1) The energy of the photons must be greater than the mass-energy of the created particles.

(2) Pair production must obey the law of conservation of energy.

Cosmologist's model the early universe as a hot, high energy photon gas and the kinetic energy of the photons depends on their temperature. Creation and annihilation of particles occurs in equal numbers so that as many particles are made per second as are being destroyed and the universe is in a state of thermal equilibrium. Particle physicists call this state of balance between matter and antimatter symmetry . The average energy of the photons in a gas can be approximated by the equation E = kT. It is important to understand that the creation of different types of particles by pair production depends on the temperature of the photons.

Eras of the Universe
 
Cosmologists divide the history of the universe into four periods or eras of time each one corresponding to a particular range of temperatures. These are:


(i) A heavy particle era
(ii) A light particle era
(iii) A radiation era

(iv) A matter era.

Heavy particle era: temperature of the universe: < 1033 K, time after Big Bang: > 10-43 s.
During this period the universe is hot enough for all massive elementary particles to be created by pair production. The universe is in thermal equilibrium and expands rapidly with the first stable protons being formed at about 10-6 s after the Big Bang.

Light particle era: temperature of the universe: < 1010 K, time after the Big Bang: > 10-4 s
The temperature of the universe is no longer hot enough for massive particles to be made. Lighter particles such as electrons and positrons can still be produced and protons and electrons combine to make neutrons. We live in a matter-dominated universe and for this to be the case, there must have been an excess of particles over antiparticles during the transition from the heavy to light particle eras. Particle physicists refer to this condition as a symmetry breaking.

Radiation era: temperature of the universe: < 1010 K, time after the Big Bang: > 10 s
In this era protons and neutrons left over from the heavy and light eras interact to form the first stable nuclei. The most important nucleus to form is that of deuterium 2H and, from this, stable nuclei of helium 4He and light helium 3He as well as beryllium 7Be and lithium 7Li are manufactured by fusion reactions. The manufacture of light elements from protons and neutrons formed in the heavy and light eras is called primordial nucleosynthesis (don't confuse this with stellar nucleosynthesis which is the formation of heavier elements inside stars) and about 25% to 30% of helium is formed by mass the rest being mainly hydrogen with trace amounts of beryllium and lithium. The Big Bang model predicts that the universe should contain a helium abundance of at least these percentages with more being created by nuclear reactions in stars, and observations of the chemical composition of various celestial objects tends to support this.

Matter era: temperature of the universe: < 3000 K, time after Big Bang: > 106 years 
In previous eras matter and radiation still interact with each other and are locked together. The radiation cannot escape and the universe is opaque to radiation. However when the temperature of the universe has dropped to 3000 K, the first hydrogen and helium atoms form and matter and radiation are no longer coupled together. The universe becomes transparent to radiation and cosmologists call this event decoupling. Due to local variations in density, the matter starts to clump together and material condensation occurs leading cosmologists to believe that it was from the end of this era that large scale structures such as galaxies could first start to form. The radiation that spread out after decoupling now comes to us as the 3 K cosmic background which, because of its smoothness, suggests that matter and radiation must have been uniformly distributed.

The Origin of the Four Basic Interactions
 
Particle physicists believe that, despite their different characteristics, if two particles were to collide at very high energies, these forces would be indistinguishable from each other and have the same strength. In other words, they would all be unified into a single super force and theories which attempt to unify the four interactions in this was are called Grand Unified Theories or GUT's for short.

In the 1970's particle physicists were able to show theoretically that the weak and electromagnetic force, collectively called the electroweak force, could be unified at energies of about 100 GeV corresponding to temperatures of 1015 K. The unification of the electroweak and strong forces does not occur until about 1014 GeV and, according to GUT's, all forces are unified at 1019 GeV. Particle accelerators have been built that can operated at a few 100 GeV, but is simply not possible to construct them capable of producing the full range of unification energies.

The Big Bang model though, offers a way of testing GUT's. According to GUT's during the first 10-43 s of the universe's existence when it was at a temperature exceeding 1032 K, all the forces were unified as a single force. When it cooled, the forces of nature 'froze out' to the four interactions that we know today. This would account for the balance of matter over antimatter as before the strong force froze out, equal numbers of particles and antiparticles were being created and destroyed. After the strong force froze out this symmetry was broken, leading to an excess of matter.

GUT's also predict that neutrinos created in the Big Bang should also have a small mass. If this is so then they would be a candidate for dark matter and the value of the mass-energy density might be altered so that:

Solar image taken using Neutrinos

P = Pc

Where Pc is the critical density.
Cosmologists also believe that, after decoupling, neutrinos might have aided galaxy formation within the accepted age of the universe and astrophysicists think that neutrinos with mass might help solve the solar neutrino problem.

Problems with the Big Bang
 
Despite its successes the standard big bang theory still leaves some unanswered questions. The first concern is the geometry of space and time. Observations suggest that Omega0 is very close to 1 which would suggest that we are living in a flat universe. What special conditions would have led to the mass-energy density being exactly equal to the critical density Pc?

It turns out that if the average density of matter even slightly deviated from Pc then this variation would have rapidly multiplied as the universe expanded leading to a value very far from Omega0 = 1. The fact that Omega0 is close to 1 now, means that some mechanism in the big bang ensured the near flat universe we see today. This is called the flatness problem and it is explained by introducing a concept called inflation.

Inflation explains why the cosmic microwave background is isotropic. Before inflation, the universe was small enough for all parts to reach the same temperature within the light horizon. After inflation, this uniformity of temperature is maintained at larger distances even though it now takes considerably longer for light to travel across the universe. Note that inflation does not violate special relativity's postulate that the speed of light is constant since it is the expansion of space and not expansion through space that is at work here.

Before 10-43 s - The Planck Time
 
General relativity regards space and time as linked together in a smooth continuum but, at very small scales of length and time, quantum mechanics says that this representation of space-time breaks down. Werner Heisenberg - courtesy of The St. Andrew's Website (see links) This is because of a law in quantum mechanics called the Heisenberg Uncertainty Principle named after a German physicist Werner Heisenberg (1901-1976). The uncertainty principle tells us that there always exists a degree of uncertainty between the position of a particle and its momentum. The more accurately you measure the speed of a particle the less certain you are of its position and the uncertainty principle makes it impossible to measure the exact position and the exact momentum simultaneously. The principle also extends to energy and time.

By using the uncertainty principle, cosmologists are able to arrive at an interval after which space and time are measurable called the Planck time tp which is made up of the fundamental constants G, h and c as 

tp = G1/2h1/2c-5/2 = 1.35 x 10-43 s

From the beginning of the Big Bang at t = 0 to t = tp, we do not know how the universe behaved and we have no theory that can explain what happened using quantum mechanics or general relativity. Time itself began at the Big Bang and to say what came 'before' is a meaningless statement as time didn't exist then!

Particle physicists believe that the vacuum of space is not empty but is seething with pairs of particles and antiparticles that are constantly being made and destroyed. These particles exist for so brief a time (less than 10-21 s) that they hardly exist at all, and are called virtual particles. These particles may exist for a time that satisfies the uncertainty principle , but as the universe rapidly expanded they became separated and appeared as real particles after the universe was older than the Planck time. The gravitational energy associated with the Big Bang singularity provided enough energy to fill the universe as it expanded. The main point about all these concepts is that the Planck time sets a limit to what we can know about the very early universe according to our current knowledge of physics, however theoretical particle physicists are currently working on a quantum theory of gravity and progress continues.

Link Bar

WERNER HEISENBERG
A biography of Werner Heisenberg
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Heisenberg.html

PAUL DIRAC
The St. Andrew's Paul Dirac pages.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dirac.html

FURTHER INFORMATION LINKS

Fundamental Forces
http://www.chembio.uoguelph.ca/educmat/chm386/FUNDAMNT.HTM

CERN - At the CERN homepage
http://www.cern.ch/Public/

Electro Weak Force
http://www.fnal.gov/pub/electroweak.html

Neutrinos and the Solar Neutrino Problem:
http://superk.physics.sunysb.edu/superk/physics/solar-neutrinos/


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