Advanced Physics Made Simple

Cosmology

          Cosmology is the study of the entire universe. Although the subject dates back to the dawn of time, when ancient philosophers looked at the night sky and sought to explain it, modern cosmology requires knowledge of general relativity.The only assumption made is that the Cosmological Principle is true:

The Cosmological Principle

           In ancient times, it was accepted that the Universe had existed forever, and that the Earth was at the center of the Universe. (Some countries went one step further and placed the center of the universe in their capital city).  Then Copernicus looked at the sky and proclaimed that the Sun was the center of the Universe, and became an outcast for his blasphemy. The Cosmological Principle goes one step further, and says the Universe has no center.

       The Cosmological Principle makes two claims.

1.  The Universe is HOMOGENOUS. This means that, as long as you look at the whole Universe, all the stuff is evenly distributed. There can be no special places in the Universe.

2. The Universe is ISOTROPIC. This means that wherever you are in the Universe, all directions look the same. This also means that in space you cannot define up, down, or any other directions.

Cosmological Models

          Before general relativity, mathematicians were the only people interested in the properties of curved surfaces. There was an unsolved problem in mathematics involving what the possible surfaces are which satisfy the conditions that no point is special, and no direction is special.  Sophus Lie solved this problem, and proved that there are only three possibilities.  Thus if the Cosmological Principle is assumed, the Universe must have one of three forms:

1.  FLAT SPACE:  This is the simplest, but least likely model of the Universe. It is difficult to imagine an infinite three dimensional surface, so we shall think of a two dimension universe. In this analogy, space is like a table top or a sheet of paper. The stars and planets would look like dots on the surfaces.

2. SPHERICAL SPACE or CLOSED SPACE:  In the two dimension analogy, this model resembles a beach ball.  Again the stars and planets are little dots on the surface of the ball. This is also the only model which does not have an infinite number of stars, which makes it a very popular model.
3. OPEN SPACE: ( There are several technical names for this model, and open model actually includes flat space as well) There is no two dimensional form of this space, but if you cut a small piece out, it would look like a saddle. The entire space would be created by gluing several saddles together and smoothing the seam.
       General Relativity also changed cosmology by not allowing the Universe to be STATIC, the Universe must change with time.  Furthermore, observations of far away stars shows the Universe is expanding. Using the equations of general relativity, it can be shown that the expansion of the Universe is slowing down, but the amount of slowing depends on the amount of stuff in the Universe.

1. FLAT SPACE: If the density of matter in the Universe is exactly right , then the Universe will be flat. In a flat Universe, space will expand forever, but will eventually reach a constant rate of expansion.

2. CLOSED SPACE: If there is more matter in the Universe, then the Universe is closed. It will continue expanding for about 15 billion years, and then begin contracting again. ( So in about 50 billion years, everything will crunch together).  This is also a good model for explaining the big bang. Imagine taking a balloon (the initial Universe) and drawing points uniformly on the surface ( stars and planets and such). Then begin inflating the balloon, (the Universe expands) and notice the points do not move on the surface, the space between them expands. This is what happens in the Universe: there is not a point from which all matter spewed forth, the matter was uniformly distributed through space while space expanded.

3. OPEN SPACE: If there is less matter in the Universe, then the Universe is open. It will expand forever, and while this may seem to be a nicer situation, more complicated calculations show that the Universe and everything in it will become too cold to support life.

Dark Matter

         You may have heard about the search for dark matter in the media and science fiction. Recall that the cosmological model depends on the density of matter in the Universe, with low densities giving an infinite universe which expands forever. Currently, astronomers have only found about 1/50 of the amount of matter required to produce a closed or flat universe, and so those who like these models are looking for more stuff. If the universe is going to contract, then 98% of the universe must not be visible. Hence it is dubbed dark matter.
 
       Some prospects for dark matter are:

1.  Neutrino Mass:  Neutrino's are extremely small  particles which are plentiful in the universe. So far no one has been able to measure the mass of the neutrino.  There are so many that even a tiny mass could give enough density to close the universe. Update: It is now known that the neutrinos have mass, but that the known types of neutrinos are far too light to explain dark matter. 

2.  Black Holes and Brown Dwarfs: These are large, high density objects which emit no light. If there are many such objects in the universe, then they could contribute enough to close the universe.
Update: More precise measurements of the relative abundances of hydrogen and helium, (and other light elements) have place severe restrictions on the amount of ordinary matter in the Universe, and have excluded it as dark matter. Therefore brown dwarfs are ruled out and black holes are very unlikely as a solution to the dark matter problem.


It is also possible that the problem is in our understanding of gravity, leading to several proposals (such as Modified Newtonian Dynamics or the TeVeS model) in which gravity is altered to reproduce the effects of matter.

*UPDATES*

Since this site was written some very important discoveries have been made:

1- The Wilkinson Microwave Anisotropy Probe (WMAP) measured the microwave radiation in space left over from the Big Bang. The results proved that space is flat,  and that only 5% of the energy in the Universe is in known forms of matter, while another 25% is in the form of dark matter.

2 - Supernovae measurements revealed the biggest surprise of the last decade, the universe is not only expanding but it is accelerating. This discovery, along with measurments by WMAP, have lead to the realization that 70% of the energy in the Universe is not any form of matter, but some mysterious DARK ENERGY.


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