University of California, San Diego Physics 7 - Introduction to Astronomy

 H. E. Smith Winter 2007

 Physics 7 - Lecture Summary #18 The Big Bang - A Brief History of the Universe

The Big Bang

Hubble's Velocity-Distance relationship

v = H.d

established that the Universe is expanding. Edwin Hubble made a plot of recession velocity vs distance for galaxies that he had observed he found a straight line relationship. The slope of this line, known as the Hubble Parameter, H 20 (km/s)/million l.y., has units of 1/time. It is easy to see that, if the Universe is expanding at the present time, then at some point in the past, all matter was once together. Thus, 1/H, called the Hubble Time is an estimate of the Age of the Universe, about 15 billion years.

If we rewind the motion picture representing the history of the Universe, we can understand a great deal about its early state, just after the Big Bang. In its early stages the Universe was simpler than it has ever been. It was very hot and in a state of Thermal Equilibrium, that is its temperature determined all its other properties. Just after the Big Bang, temperatures were so high that particle pairs could be created purely out of the heat energy present. For example, a pair of thermal photons - which would be gamma-rays at these temperatures - might react to form an electron/positron pair:

+ e+ + e-

During its early phases the Universe was radiation dominated, that is the photons dominated the energy and pressure of the Universe. As the Universe expanded, it cooled, T 1/R, where R is some measure of the "scale of the Universe".

The Big Bang (Do Not Try to Memorize This!)
Time since
Big Bang
T
(K)

(g/cm-3)

• < 10-43s
•    Quantum era
Universe consists of "soup" of leptons & quarks
• ~ 10-43s
• 1032K   Grand Unification Era
Gravity separates from other Grand Unified Forces
• ~ 10-35s
• 1027K   End of Grand Unification
Strong Force breaks symmetry w/ ElectroWeak Force.
• ~ 10-35s - 10-33s
•   Inflationary epoch
Universe inflates by a factor of 1030 or more
("observable Universe" expands from size of an atomic nucleus
to size of a cherry pit).
• ~ 10-12s
• 1015K   Particle Era
Electromagnetic force and Weak Force break symmetry.
• ~ 10-6s
• 1013K   Quark --> Hadron transition.
Protons and neutrons (plus antiprotons and anti neutrons) are formed from quarks - at this time the "matter" particles have an excess of ~ one in a billion over "antimatter" particles.
• 0.01s
• 1011K
(100 billion K)
4 x 109
(4000 Volks/cm-3)
• The Universe is expanding rapidly, scale is doubling every 0.02s.
• As Universe expands it cools, T ~ 1/R.
• Although the temperature is too low for Protons and neutrons to be created from the thermal energy of the early universe reactions such as:
+ n p+ + e-
and vice-versa, maintain an equal number of protons and neutrons.
• As the temperature decreases proton/neutron balance shifts in favor of less massive protons.
• 1s
• 1010K
(10 billion K)
4 x 105
Weakly interacting neutrinos "decouple" from the rest of the Universe.
• 15s
• 3 x 109K
(3 billion K)
4 x 104
• Temperature is below threshold for creation of electron/positron pairs.
• e+/ e- annihilate: e+ + e- +
• The Universe is "reheated" about 35% by annihilation.
• 3 min
• 109K 400 Era of Nuclear Reactions
• Nuclei can begin to hold together, e.g.
p+ + n 2H +
• At this time the baryons are divided into about 87% protons 13% neutrons.
• 3 1/2 m
• 108K  End of Nuclear Reactions
neutrons have been "used-up" forming 4He
Universe is now 90% H nuclei( p+) & 10% He nuclei
• 300,000 yr
• 4000K
Era of Recombination
nuclei & electrons "recombine to form atoms
Universe becomes transparent
• 109yr
•     Era of Galaxy Formation

The net result of the early nuclear reactions Big Bang Nucleosynthesis is to transform all of the neutrons, along with the necessary protons, into Helium nuclei plus traces of 2H (deuterium), 3He, 7Li, 6Li, 7Be.

Nuclear Reactions in the Big Bang

Why is nucleosynthesis in the Big Bang different from nucleosynthesis in stars?
The answer lies in the particles present in the early Universe and the temperatures and densities present when nuclear reactions are occurring:

• In the early Universe protons react with neutrons to form deuterium as a first step:
p+ + n 2H +
The Proton-Proton Chain has as its first step the reaction of two protons:
p+ + p+ 2H + e+
which is much more difficult to accomplish because of the repulsive charges positive charges. But there are no free neutrons in the centers of stars; they all got used up in the Big Bang (besides free neutrons decay). So stars are left with the P-P Chain (or CNO Cycle).
• Stars continue with the 3- Process and, depending upon the mass, other nuclear burning stages, but the Big Bang stops with Helium and traces of other low mass elements. This is because the Universe is expanding and the density decreasing as nuclear reactions are occurring. By the time Helium fusion has occurred in the Big Bang the density is too low for the 3-, which requires the simultaneous collision of three helium nuclei.

Evidence for the Big Bang

What a wonderful mythology! Is there any evidence beyond the hyperactive imaginations of Cosmologists that this really happened?

• The expansion of the Universe suggests that some sort of explosion or "Big Bang" took place, but any decent theoretical astrophysicist can find a way to wiggle out of the need for a Big Bang. (One theory proposed a number of years ago was called the Steady State Theory; some astrophysicists are still trying to redeem a version of the Steady State.)

• We do find that in most places in the Universe where we can measure the amount of helium that it amounts to about 10% compared with hydrogen's 90%. The helium production in the early Universe is not very sensitive to the details of the calculation

•  The strongest evidence that something like the Big Bang really happened is the Cosmic Background Radiation predicted by Cosmologist George Gamov in 1948 and discovered by Arno Penzias & Robert Wilson of Bell Labs in 1965. All those -rays described above are part of the thermal radiation present in the early Universe because it is hot. As the Universe expanded and cooled, the radiation field cooled along with it. When matter and radiation "decoupled" with the formation of atoms a million years after the Big Bang, the radiation had cooled to visible light. Although the matter distribution has become complicated with the formation of galaxies & stars since that time the light has simply continued to cool with the expansion. Gamow predicted that the Universe should be filled with this "relic radiation left over" from the Big Bang. (Gamow calculated a temperature of 15K; Dicke & Peebles at Princeton recalculated the value in 1963, predicting a Temperature near 3K.) Using the peculiar horn-shaped antenna shown in the picture to the right, Penzias & Wilson made the first glimpses of the Cosmic Background Light quite unexpectedly. Since their discovery the evidence has become stronger and stronger that we are seeing the light from the Big Bang. Penzias & Wilson received the Nobel Prize in Physics in 1978. Penzias & Wilson in 1964

• Recall that about 1s after the Big Bang, before electron-positron annihilation caused reheating, neutrinos decoupled from the rest of the matter and radiation in the Universe. There should be a Cosmic Neutrino Background with a characteristic temperature of about 2K. These neutrinos are far too low in energy to be detected by current techniques, but there should be about 300 neutrinos/cm3 around (about a factor of three less than the number of Cosmic Background photons and a billion more than the number of baryons). If neutrinos have mass, the large number of Cosmic Neutrinos may have implications for the dark matter in the Universe.

The Cosmic Background Spectrum as measured by NASA's COBE Satellite.
from Ned Wright's Cosmology Tutorial © Edward L. Wright (UCLA), used with permission.

 Tiny variations (< 10-5K) in the Cosmic Background Radiation temperature reflect small density fluctuations in the early Universe before matter and light parted company. After decoupling, the density fluctuations could grow under gravity to form the seeds for galaxies and clusters. The nature of these fluctuations agrees with current theories of the formation of structure in the Universe. Future space missions such as the Microwave Anisotropy Probe (MAP) have the potential of making detailed measurements of the structure of the early Universe at the time of recombination.

Cosmology   Quasars & AGN   Physics 7 Lectures   Physics 7 Home

Conducted by Gene Smith, Physics/CASS, UCSD.
Comments? You may send email to hsmith@ucsd.edu

Prof. H. E. (Gene) Smith
CASS   0424   UCSD
9500 Gilman Drive
La Jolla, CA    92093-0424

Last updated: 19 March 2000