Tuesday, August 12, 2008

The Big Bang Model

Let's review the observational evidence:

  • Distance/velocity relationship: distant galaxies are moving away from us, with speeds which increase linearly with distance
  • Chemistry: the universe is almost entirely hydrogen and helium, in a mixture of roughly 12 H atoms to 1 He atom
  • Cosmic Microwave Background: no matter where we look in the universe, we see radio waves which look like those radiated by a blackbody at about 2.7 degrees above absolute zero. There are tiny (one part in 10,000) variations in the brightness of this radiation on scales of a degree or so

Is there any way to tie all these pieces of data together? Yes! One model which can explain them all is called the Big Bang model. The name was coined by a scientist who didn't like the theory and tried to make it sound silly.

Fundamentals of the Big Bang Model

The Big Bang is built upon three main tenets:

  1. the universe used to be very hot
  2. the universe used to be very dense
  3. the universe is expanding (which is why it isn't so hot or dense anymore)

Note that the basic Big Bang Model does NOT say anything about the following questions:

  • will the universe collapse again, or expand forever?
  • is space curved or flat?
  • how old is the universe?
  • what is the matter density in the universe?
  • what about dark matter?
  • is there some mysterious "repulsive" force on large scales?
  • how did galaxies form?

Some of these questions all depend upon the values of certain parameters in the model, which we may derive from observations. Others have nothing to do with the Big Bang itself.

Our understanding of the laws of nature permit us to track the physical state of the universe back to a certain point, when the density and temperature were REALLY high. Beyond that point, we don't know exactly how matter and radiation behave. Let's call that moment the starting point. It doesn't mean that the universe "began" at that time, it just means that we don't know what happened before that point.

Big Bang Nucleosynthesis

One of the primary successes of the Big Bang theory is its explanation for the chemical composition of the universe. Recall that the universe is mostly hydrogen and helium, with very small amounts of heavier elements. How does this relate to the Big Bang?

Well, a long time ago, the universe was hot and dense. When the temperature is high enough (a few thousand degrees), atoms lose all their electrons; we call this state of matter, a mix of nuclei and electrons, a fully-ionized plasma. If the temperature is even higher (millions of degrees), then the nuclei break up into fundamental particles, and one is left with a "soup" of fundamental particles:

  • protons
  • neutrons
  • electrons

Now, if the "soup" is very dense, then these particles will collide with each other frequently. Occasionally, groups of protons and neutrons will stick together to form nuclei of light elements ... but under extremely high pressure and temperature, the nuclei are broken up by subsequent collisions. The Big Bang theory postulates that the entire universe was so hot at one time that it was filled with this proton-neutron-electron "soup."

But the Big Bang theory then states that, as the universe expanded, both the density and temperature dropped. As the temperature and density fell, collisions between particles became less violent, and less frequent. There was a brief "window of opportunity" when protons and neutrons could collide hard enough to stick together and form light nuclei, yet not suffer so many subsequent collisions that the nuclei would be destroyed. This "window" appeared about three minutes after the starting point, and lasted for a bit less than a minute.

Which nuclei would form under these conditions? Experiments with particle colliders have shown us that most of the possible nuclei are unstable, meaning they break up all by themselves, or fragile, meaning they are easily broken by collisions.



fragile

Helium (the ordinary sort, with 2 protons and 2 neutrons) is by far the most stable and robust compound nucleus. Deuterium (one proton and one neutron) is easily destroyed, and so is helium-3 (2 protons, one neutron).

So, it seems that this period of hot, dense plasma would create a lot of helium. Could it create other, heavier elements, too?



helium

Detailed models of Big Bang nucleosynthesis predict that the brief "window of opportunity" lasted only a minute or two. After that, about three and a half minutes after the starting point, the temperature and density dropped so much that collisions between particles were rare, and of such low energy that the electric forces of repulsion between positively-charged nuclei prevented fusion. The result is

  • lots of hydrogen
  • some helium (ordinary helium-4)
  • tiny bits of deuterium
  • tiny bits of lithium
  • not much else
The Cosmic Microwave Background

So, during the first few minutes after the starting point, the universe was hot enough to fuse particles into helium nuclei. The result was a ratio of about 12 hydrogen nuclei to 1 helium nucleus; that's equivalent to saying that three quarters of the mass of the universe was hydrogen nuclei, and one quarter of the mass was helium nuclei.

But these nuclei were totally ionized: they lacked the normal collection of electrons surrounding them. The electrons were free to fly around space on their own. Free electrons are very efficient at scattering photons. Any light rays or radio waves or X-rays in this ionized plasma were scattered before they could travel far. The universe was opaque.



ionized opaque

After a few thousand years, as the universe continued to expand and cool, the temperature reached a critical point. About 100,000 years after the starting point, the temperature dropped to about 3,000 degrees Kelvin. At this point, hydrogen nuclei (protons) were able to capture electrons, and hold them against collisions. We call this process of capturing electrons recombination (even though it was really the first "combination", not a re-"combination").

The universe became largely neutral, with electrons bound into hydrogen and helium atoms. Neutral atoms are nearly transparent to light rays and radio waves. Suddenly, the universe became transparent.



neutral transition
The Distance/Velocity Connection

The Big Bang theory states that the universe is expanding, though it does not explain why the universe should behave in this way. As a result, objects which are subject to no forces should move away from each other. In a uniformly-expanding universe, the rate at which objects move away from each other depends linearly on their distance from each other.

And that linear relationship between distance and radial velocity is just what we see when we look at distant galaxies:



SBF table

But ... wait a minute. Does this expansion occur on all scales? What about

  • the distance between two people on opposite sides of the room?
  • the distance between the Earth and the Sun?
  • the distance between the Sun and the center of the Milky Way?
  • the distance between the Milky Way and the Andromeda Galaxy?

If there are "significant" attractive forces between objects, they do not move away from each other as time goes by. These attractive forces may be

  "chemical" forces between              important on microscopic,
neighboring molecules or atoms human, and planet-sized
(these are really due to scales
electric forces)

gravitational forces between important on solar-system,
large bodies of matter galaxy, and galaxy-cluster
scales

So the distance between the Earth and Sun has not increased over the past 4 billion years. Nor does the length of a meterstick grow due to the expansion of the universe.

Only on the very largest scales, distances between isolated galaxies or clusters of galaxies, are the attractive forces so weak that the expansion of the universe is able to move objects apart.

The rate of expansion depends sensitively on the exact amount of matter in the universe. If the density of matter is high, long-range gravitational forces can slow down the expansion, or even stop it. If the density of matter is very low, the expansion will go on forever.

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ஸ்ரீ இராம நாம மந்திர மகிமை

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