Cosmology

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This chapter gives you the Big Picture called cosmology. Cosmology is the study of the nature, origin, and evolution of the universe as a whole. The observational aspect of cosmology deals with finding distances to galaxies which is necessary for determining the geometry of the universe. This was covered in the last chapter. Vocabulary terms in the text are in boldface.

Observations and Some Implications

At first you might think that in order to understand the structure of something as large as the universe, which by definition contains everything there is, you would need some very powerful telescope to see to the farthest reaches of space and a complex theoretical model. Actually, there are some powerful conclusions you can draw from observations with the naked eye. You will explore that first and then move on to conclusions you can draw from extending your eyesight. You will explore the basic questions that human beings have been asking themselves ever since we have walked the Earth: where did we come from and where are we going?

Universe Contains Mass---Why has the Universe Not Collapsed?

The universe is not empty. There is matter with mass, so the attraction of gravity is present. Newton knew that if the universe has existed forever and is static, that is, it has no net pattern of motion, then there must be enough time for gravity to collapse the universe, but this has clearly not happened! He knew of three ways to resolve this paradox. Either the universe is infinite in volume and mass or it is expanding fast enough to overcome the gravitational attraction or the universe has a beginning and/or an end. The last two ways violate the assumptions of an eternal and static universe, of course. So Newton chose the infinite universe option. Notice that you are able to arrive at the conclusion of an infinite universe from just one observation: the universe is not empty. No telescopes are needed, just the ability to follow a train of logical thought to its conclusion.

Olbers' Paradox and the Dark Night Sky

Another simple observation is that the visible night sky is dark. IF the universe is infinite, eternal, and static, then the sky should be as bright as the surface of the Sun all of the time! Heinrich Olbers (lived 1758--1840) popularized this paradox in 1826, but he was not the first to come up with this conclusion. Thomas Digges wrote about it in 1576, Kepler stated it in 1610, and Edmund Halley and Jean Philippe de Cheseaux talked about it in the 1720's, but Olbers stated it very clearly, so he was given credit for it. This problem is called Olbers' Paradox.

If the universe is uniformly filled with stars, then no matter which direction you look, your line of sight will eventually intersect a star (or other bright thing). Now it is known that stars are grouped into galaxies, but the paradox remains: your line of sight will eventually intersect a galaxy.

why the night sky should NOT be dark

The brightnesses of stars does decrease with greater distance (remember the inverse square law) BUT there are more stars further out. The number of stars within a spherical shell around us will increase by the same amount as their brightness decreases. Therefore, each shell of stars will have the same overall luminosity and because there are a lot of ever bigger shells in an infinite universe, there is going to be a lot of light!

Any intervening material absorbing the starlight would eventually heat up and radiate as much energy as it absorbed, so the problem remains even if you try these ``shields''. Of course, stars are not points. They do have a definite size, so they can block light from other stars. The total brightness of the universe will not be infinite, but only as bright as the surface of a star (!). You can substitute ``galaxy'' for ``star'' in the preceding paragraphs if you want to update Olbers' Paradox for modern times. The way to resolve a paradox like this is to look at the assumptions that are used (the ``if'' statements) and determine whether or not they are valid.

Universe Is Expanding

Edwin Hubble and Milton Humason discovered in the 1920's that the universe is not static---it is expanding. This is enough to resolve the paradox. As the universe expands, the light waves are stretched out and the energy is reduced. Also, the time to receive the light is also lengthened over the time it took to emit the photon. Because the luminosity = the energy/time, the apparent brightness will be reduced enough by the expansion to make the sky dark.

stretching space produces cosmological
redshift

The stretching of the light waves makes the light from galaxies appear redshifted, mimicking a redshift from the doppler effect as if the galaxies were moving through space away from us. However, the galaxies are simply being carried along with the expansion of the space between them---the whole coordinate system is expanding. The expansion of the universe means that galaxies were much closer together long ago. This implies that there is a finite age to the universe, it is not eternal. Even if the universe is infinite, the light from places very far away will not have had enough time to reach us. This will make the sky dark.

The Hubble law, speed = Ho × distance, says the expansion is uniform. The Hubble constant, Ho, is the slope of the line relating the speed of the galaxies away from each other and their distance apart from each other. It indicates the rate of the expansion. If the slope is steep (large Ho), then the expansion rate is large and the galaxies did not need much time to get to where they are now. If the slope is shallow (small Ho), then the galaxies need a lot of time to get to where they are now.

The age of the universe can be easily estimated from the simple relation of time = distance/speed. The Hubble Law can be rewritten 1/Ho = distance/speed. Notice that the expansion time interval = 1/Ho. The Hubble constant tells you the age of the universe, i.e., how long the galaxies have been expanding away from each other: Age = 1/Ho. This value for the age is an upper limit since the expansion has been slowing down due to gravity. That means that the Hubble ``constant'' actually was larger in the past. Taking the expansion slowdown into account, you get an age closer to 2/(3 Ho). Still, the age looks like a number × (1/Ho), so if the Hubble constant is large, the derived age of the universe will be small.

Universe is Uniform on Large Scales

On size scales of billions of light years, the universe is assumed to be uniform. This makes the universe models simpler and ``more reasonable''---if we lived in an unusual part of the universe, then it would be almost impossible to understand the universe as a whole from observing our surroundings. The discovery of the long superclusters may seem to endanger this assumption. On large enough scales though, the universe has many superclusters in all directions. It is like a large bowl of tapioca pudding, one spoonful of pudding looks like any other spoonful, even though, there are the small tapioca pieces.

The idea of a uniform universe is called the cosmological principle. There are two aspects of the cosmological principle:

test of homogeneity and isotropy

The cosmological principle is a Copernican idea. It means we are not in a special place. Every observer at a given cosmological time will see the same thing, such as the same Hubble law. ``Cosmological time'' in this context means the time measured from some common event like the creation of the universe. Everyone at the same cosmological time will measure the same age of the universe. The cosmological principle allows the universe to change, or evolve, throughout time.

An extension of the cosmological principle called the perfect cosmological principle says that the universe also does not change with time; there is no evolution. Therefore, in an expanding universe, new matter must be continually created. This violates a central rule of nature known as the law of the conservation of mass. This law says that the total amount of mass does not change---mass is not created from nothing or destroyed. However, the amount of new matter that would need to be created for the perfect cosmological principle to be true is quite small---only one hydrogen atom per cubic centimeter every 1015 years. This is approximately one hydrogen atom/Houston Astrodome every year---a very small amount! As described in the last chapter, the increase in the number of quasars at large distances from us, is strong evidence of a universe that DOES change, or evolve. Other evidence for a changing universe is given later in this chapter.

No Center to the Expansion in 3-D Space

When I discussed black holes, I examined the strange but accurate predictions of Einstein's Theory of General Relativity. General Relativity describes gravity as a warping or distortion of space and time near a massive object. In General Relativity, four-dimensional space-time is curved.

To help understand what curved space means, let's use the analogy of a two-dimensional world curving into the third dimension. Pretend you are confined to the surface of a balloon and you only know about ``front'', ``back'', ``left'', and ``right'', but not ``up'' and ``down''. In your 2D universe you cannot see the third dimension. Your universe appears flat. Yet you know that your 2D universe must be curved because if you walk in a straight line, you eventually arrive back at where you started! The balloon universe has a finite size but no edge. You also know that the angles of large triangles add up to a number larger than 180ƒ! For example, on the balloon the lines of longitude running north-south intercept the equator at a 90ƒ angle and converge at the poles. So a triangle made of one point on the equator + the north pole + another point on the equator will have the angles add up to more than 180ƒ. In a truly flat universe, the angles would add up to exactly 180ƒ. You would be able to deduce that your universe is positively curved.

figuring out the universe is curved

On sufficiently small scales the surface looks flat so the regular geometry rules apply. The angles in a small triangle add up to 180ƒ. Here on the surface of the Earth, the Earth looks flat to us because the curvature of the Earth is so much larger than we are. The universe does not have to curve back on itself as shown in the illustrations above. This type of positively-curved universe is usually easier to picture, but the curvature could be the opposite. In a negatively-curved universe, the universe curves away from itself. A two-dimensional analogy would look like a saddle. The angles in large triangles would add up to less than 180ƒ. Like the positively-curved universe, there would be no center on the surface and no edge.

three different possible geometries for the universe

Rather than setting up BIG triangles in the universe, astronomers can use how the number of galaxies increases with increasing distance. If the universe has zero curvature and the galaxies are spread roughly uniformily in the universe, then the number of galaxies should increase linearly with ever greater volume. Lines defining an angle spread out in straight lines. If the universe has positive curvature, then the number of galaxies increases with greater volume then decreases with very large volumes. Lines defining an angle spread out at first and then converge at great distances. If the universe has negative curvature, then the number of galaxies increases more rapidly with with ever greater volume than a flat universe. Lines defining an angle diverge at increasing angles as the lines curve away from each other.

The idea of a curved surface also explains why astronomers in every galaxy will see the other galaxies moving away from it and, therefore, derive the same Hubble Law. Go back to the balloon analogy, imagine that there are flat houses on it. As the balloon expands, the elastic material moves the houses apart from each other. A person sitting on their front porch see everybody else moving away from her and she appears to be the center of the expansion.

who is at the center?

Now add another dimension and you have our situation. Just like there is not new balloon material being created in the 2D analogy, new three-dimensional space is not being created in the expansion. Like any analogy, though, the balloon analogy has its limits. In the analogy, the balloon expands into the region around it---there is space beyond the balloon. However, with the expanding universe, space itself is expanding in three dimensions---the whole coordinate system is expanding. Our universe is NOT expanding ``into'' anything ``beyond''.

Vocabulary

cosmological principle cosmology homogeneous
Hubble constant Hubble law isotropic
Olbers' Paradox perfect cosmological principle

Review Questions

  1. What are the assumptions that Olber's Paradox is based on?
  2. Why is the night sky dark? What important conclusions can you draw from the simple observation that the night sky is dark?
  3. Will an object with a large redshift be far away or close?
  4. What can the Hubble constant constant (Ho) tell you about the age of the universe? How would the derived age of the universe change if Ho was 50 km/sec Mpc-1 instead of 100 km/sec Mpc-1?
  5. Is the Hubble constant actually constant throughout time? Why or why not?
  6. What would the relation between the radial velocity and distance be if there was no expansion? What would the relation be if the universe was contracting?
  7. Is there a center to the expansion in normal three-dimensional space? Why or why not?
  8. Why is an analogy like flat houses on an expanding balloon used to try to picture the expansion?
  9. Is the space between stars inside a galaxy expanding? Why or why not? Is the space between the molecules in your body expanding with the universe? Why or why not?
  10. How is looking at faraway objects equivalent to looking back in time?
  11. What is the cosmological principle? What is the perfect cosmological principle? Which one can an evolving universe fit in? Why?

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last update: 05 April 1999


Nick Strobel -- Email: strobel@lightspeed.net

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Bakersfield College
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