Cosmology: Structure, Origin and Fate of the Universe

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay

Clusters of Galaxies

Galaxies occur in clusters. Our own Milky Way is a member of a sparse group called the Local Cluster, which includes two other large spiral galaxies about 2.5 million light years away and about 20 dwarf galaxies, with up to a few billion stars. Dwarf galaxies are so small and faint that they could not be seen at all if they were not nearby. Many of the dwarf galaxies appear to be satellite galaxies of the large spirals. Our own Galaxy has two bright satellite galaxies, the Magellanic Clouds. These small galaxies, about 150,000 light years away, are prominent in the skies of the Southern Hemisphere, where they look like detached pieces of Milky Way. The Milky way also has several smaller and much fainter satellite galaxies.

Other galactic groupings have hundreds or thousands of galaxies within a domain perhaps 50 million light years across. The nearest such grouping, the Virgo Supercluster, is about 40 million light years away. Our local cluster appears to be an outlying fringe of this supercluster. (Almost as if to humble us for our primitive Earth-centered views of the Universe, our Earth seems not to be near the center of anything!)

On a very large scale, galaxies appear to be clustered into great interconnected filaments separated by voids hundreds of millions of light years across. There are so many galaxies that we have nothing like a complete inventory of them, and research on the large-scale structure of the Universe is still very new.

Curved Space?

Many books on astronomy refer to "curvature of space" or space having more than three physical directions. It's my experience that this imagery confuses non-scientists more than it helps.

What is really involved is something called a metric; the rules for measuring distance. The rule for measuring distance for most circumstances is given by the Pythagorean theorem. If we measure position in terms of east-west and north-south, the rule is:
distance2 = (east-west)2 + (north-south)2. For our purposes, we'll confine ourselves to a small area so as not to get involved with the Earth's curvature. This conventional, or Euclidean metric isn't the only possible one, however.

The Urban Metric

In midtown Manhattan, it doesn't make the slightest difference that a point 3 kilometers east of you and 4 kilometers north is 5 kilometers away in a straight line. If you have to walk or drive the streets, the distance is 7 kilometers, period. Also it doesn't matter what route you take as long as you travel only east and north. In this metric, the urban metric, the distance rule is: distance = (east-west) + (north-south). Urban planners use the urban metric all the time because it dictates things like response times of emergency services.

                  +                          +
                 /|                          |  
                / |                          |  
      Distance /  |                          |  
              /   |N-S                       |N-S
             /    |                          |  
            /     |                          |  
           +------+                   +------+ 
              E-W                        E-W
         Euclidean Metric            Urban Metric
               2       2      2
       Distance = (E-W) +(N-S)    Distance = (E-W)+(N-S)

The San Francisco Metric

San Francisco looks eminently rational on a map - a neat grid of streets - but when you drive there you find that the grid has been laid over the landscape with complete disregard for topography. Neither the urban metric nor the Euclidean metric may really describe the driving scene in San Francisco if your concern is driving time or using a manual shift.

The Reno Metric

After a pleasant vacation in Reno, you have to leave town quickly because some nice gentlemen who loaned you funds to test your gambling strategy would like it back. Also, since your strategy ran into some unanticipated problems (it didn't work), you don't have funds to buy gas and only enough gas to get 50 miles. Where will that take you?

If you head east, the landscape is pretty flat and the roads more or less converge on Reno, so you can get nearly out to the fifty-mile circle headed east. The metric here is pretty close to Euclidean. But to the west are the Sierra Nevada, where the roads are often nonexistent or pretty crooked. Fifty miles road distance from Reno in the Sierra may not be very far in straight-line terms. The actual fifty-mile limit by road is very complicated.

Local Curvature of Space-Time

The San Francisco and Reno metrics are pretty good analogs to the idea of curved space around stars and planets, except that here there's a real third dimension to the problem. If you could imagine being a flat creature with no concept of up and down, you might decide that space in San Francisco or around Reno was distorted in weird ways. But astronomers speak of three-dimensional space being curved into a fourth spatial dimension that we can only detect by its geometric distortions. How can we picture that?

Imagine that you live in San Francisco, which is a very three-dimensional city. In addition to the normal hills, there's construction at one major intersection that slows traffic down for some distance around. Near the construction your travel time is slowed down beyond the normal effects of topography. Its as if you had to travel over an invisible steep hill superimposed on the real steep hills that are already there. Approaching the construction you slow down as congestion increases, just like going up a hill, and going away you speed up as congestion decreases, just like going down a hill. Mathematically, there are two ways you can deal with this situation. One is to go on using a normal three-dimensional conception of San Francisco but say that speed slows down near the construction. The other is to imagine that the topography and street grid are deformed into a fourth-dimensional hill near the construction; your speed stays constant but the extra distance you travel over the hill increases your travel time. You can't observe the hill in three dimensions but you can describe it mathematically.

Suppose we could somehow bury a small chunk of neutron star matter under a parking lot so that right over the neutron star matter you feel one g of gravitational pull. As you walk across that spot, you'd feel the neutron star matter pulling you toward it, then pulling you back as you walked beyond it. It would feel as if you were walking down into a small depression, then walking out again. Also, the gravitational pull of the neutron star matter would bend light rays. The spot over the neutron star matter would appear to be lower than the rest of the lot. It would look as if you are walking across a small depression as well. The gravity of the neutron star matter would attract air and create higher air pressure; an altimeter would read lower altitude. All the physical measurements you could make would be consistent with there being a depression over the neutron star matter. But if you take the neutron star matter away, the parking lot returns to being flat. The neutron star matter deforms space in its vicinity.

The Curved Earth

Imagine a planet like Earth but perpetually cloud-covered. They have all the technology we do except space travel. What shape is their world? Three of their major cities lie at the corners of an equilateral triangle 12000 kilometers on a side. That's possible on a plane. But there is a fourth city 12000 kilometers distant from each of the other three. This sort of geometry is impossible on a plane, but is possible on a sphere. Thus a high-tech civilization (or even a low-tech one) could easily deduce that its world was a sphere even if they lacked space travel and could not see the stars. A small piece of the planet's surface is nearly a plane. We can make a scale model or map of small areas, but there is no way to make a scale model of the entire planet on a small part of its surface.

Cosmic Space Curvature

Can we make a scale model of the Universe? If we could somehow determine the distances from every galaxy to every other, we might find that there are five galaxies all equidistant from each other. We cannot make a scale model of something like that in normal space. Or we might find that on a very large scale, there can never be more than three galaxies all equidistant from one another. The rules that givern distance relationships on the very largest scales might be quite different from what we know on smaller scales.

Having said all that, the Universe is Euclidean on scales at least extending to many millions of light-years, and every test we have devised to look for cosmic curvature of space has been consistent with a completely Euclidean Universe within the precision of measurement.

Cosmology: The Biggest Questions Of All

The study of the origin, overall structure, and future of the Universe is called cosmology. At this time, cosmology is in perhaps its most revolutionary period. We can only touch on a few of the exciting developments in this field.

The Expanding Universe And Big Bang

For half a century, astronomers have known that galaxies everywhere are rushing away from us, and the farther away they are, the faster they are receding. One possible explanation of this expanding universe was that the Universe had begun in a Big Bang, a tremendous explosion that flung matter and energy outward. In 1965, radio astronomers detected faint microwave background radiation filling all of space, the echo of the initial explosion.

Note that the expansion of the Universe does not mean we are at the center. All galaxies are receding from one another, and any observer on any galaxy would see the same pattern we do. Astronomers use the "raisin bread" analogy to illustrate the expansion. In raisin bread dough, the raisins are close together. As the bread rises, the raisins spread apart, and every raini sees all the others receding.

Age Of The Universe

The Universe must be older than the Solar System, 4.6 billion years. It must be old enough for light to have travelled from the most distant objects we can see to us, at least 8 to 10 billion years. The best estimate of the age of the Universe is the time it would require for galaxies, starting from a common point and receding as they are, to reach their present positions: about 12 to 15 billion years.

Seeing the Past

Because it takes light a long time to travel from distant galaxies to us, we see galaxies as they were when light left them. When we look into space, we also look back into time. Galaxies have not changed much in the last few billion years, and galaxies farther away than a few billion light years are too faint and tiny to see in detail even with the largest telescopes. Very powerful radio sources called quasars are believed to be very young galaxies, but they are so far away it is hard to be certain. Astronomers hope that the Hubble Space Telescope, due to be placed in orbit by the Space Shuttle, might provide clearer views of quasars and even more distant objects, possibly back to the formation of the first galaxies.

If we are seeing galaxies as they were billions of years ago, then they were once much closer to us. How can they look billions of light years away? To answer this riddle, look at things from the perspective of the other galaxy. Assume our galaxy is initially a billion light years from another galaxy and the two are rushing apart at 90 per cent of the speed of light.

T = 0

New Galaxy       Newly-formed Milky Way
         @       @------>90% of speed of light
         |-------| 1 billion light years

T = 5 billion years

   Galaxy              Milky Way
         @       |-------->@ has travelled 4.5 billion light years
                             Galaxies are 5.5 billion light years apart
         @-------------> Light has travelled 5 billion light years and
                         is still 500 million light years from Milky Way

T = 10 billion years

   Galaxy              Milky Way
         @       |------------------------->@ 
                             Our galaxy has travelled 9 billion light years
                             Galaxies are 10 billion light years apart
                             Light has travelled 10 billion light years 
                             and is just arriving.

Thus, a galaxy that looks ten billion light years away really is ten billion light years away. Its light has travelled ten billion light years. However, the information carried by the light is also ten billion years old, so we see the galaxy in the condition it was in when the light left.

The "Missing" Mass

Clusters of galaxies are obviously bound by gravity, and so are the galaxies themselves, yet the visible stars are not massive enough to account for the gravity of galaxies and galaxy clusters. About 90 per cent of the mass in the Universe is "missing". Astronomers are less disturbed by this than one might expect because the possible explanations are so numerous. In roughly increasing order of exoticness, they include:

Faint intergalactic stars
Cool thin gas
Hot gas is detectable by its radio emissions but cool gas emits little or no radiation
Brown dwarfs
Interstellar planets
Planets might form from interstellar dust clouds but not as part of any planetary system. They would be extremely hard to detect.
Black Holes
Most known black hole candidates are detected by the radiation given off by matter falling into them. Isolated black holes not part of a multiple star system might be pretty quiet.
Quantum Black Holes
Just after the Big Bang matter in the universe was dense enough that it could have collapsed into microscopic black holes, as massive as mountains or planets but the size of a proton. Stephen Hawking discovered that all black holes eventually decay in a burst of radiation. Quantum black holes as massive as mountains should be decaying just about now. Physicists are looking.
Massive neutrinos
Neutrinos are generally considered massless, but some theories predict they might have a very tiny mass. These particles are so numerous that even a tiny mass would account for all the "missing" mass.
Photons with mass
There's no compelling reason in physics why photons must have exactly zero mass. If they have a very tiny mass, again it could account for all the "missing" mass.
Magnetic monopoles
Some theories in physics predict the existence of isolated north or south magnetic poles. If they exist, they are predicted to be very massive.
Exotic massive subatomic particles
Some theories in physics predict the existence of even more exotic very massive particles.
Cosmic strings
These would be linear equivalents of black holes and extremely massive.

The list includes MACHOS and WIMPS. MACHO stands for Massive Compact Halo Object. MACHO's include stars and planets that might form thin but massive halos around galaxies but be too faint to detect easily. WIMP stands for Weakly-Interacting Massive Particle and refers to some of the exotic particles predicted by some theories; these particles interact only very weakly with other matter and are thus very hard to detect if they exist. The list of possible solutions to the problem is so long that most astronomers prefer to call the undiscovered matter "nonluminous" rather than "missing". They're sure it will be found; it's just hard to see.

The Moment Of Creation

All the energy in the Universe was compressed into a tiny volume at the instant of the Big Bang. By using the principles of physics, cosmologists can estimate what conditions in the earliest Universe were like. The younger the Universe, the smaller it was, the more densely it was filled with energy, and the hotter it was. At about .001 second after the Big Bang, the Universe had expanded and cooled enough for neutrons and protons to form out of still more elementary particles. At about 3 minutes, protons and neutrons could combine to form stable nuclei. By about 500,000 years, the Universe was cool enough for atoms to form.

No GUT's, No Glory

To calculate the earliest microseconds of the Universe, we must know more about physics than we now know. Many physicists believe that all the forces of nature can be "unified" or described in terms of a single theory. For example, electricity and magnetism are quite different, but they can be described in terms of a single theory of electromagnetism. We can use this theory in a practical sense to produce magnetism using electricity (electromagnets) or electricity using magnetism (generators). More recently, physicists have unified electromagnetism and the weak nuclear force, and there are signs that these forces can be unified with the strong nuclear force.

The search for a Grand Unified Theory, or GUT, that would unify all forces has been one of the great dreams of physics. The next great cluster of Nobel Prizes will almost certainly come from this research (hence the title of this section). The GUT theories that look most promising make some astonishing predictions:

Research on these subjects is still very young, and the mathematical details are far beyond the scope of this book. But high-energy physics and cosmology are combining to offer us views of a Universe that is much stranger than even the science-fiction writers ever dreamed.

The Fate Of The Universe

What will happen to the Universe depends largely on how much matter it holds. If the Universe has enough matter, its gravitational attraction will eventually halt the expansion of the Universe, and matter will begin collapsing inward. Perhaps our Universe will end in a "Big Crunch", followed by another Big Bang and a new Universe. Or, if there is not enough matter in the Universe, the Universe will continue to expand, its stars will die out, its protons and neutrons will eventually decay, and only a thin mist of electromagnetic energy and the most elementary particles will remain. In all probability, new theories of physics will require us to alter both of these predicted fates in ways we cannot foresee. We simply do not know what the final answer will be.

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Created 26 March 1998, Last Update 10 April 1998

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