The Way of Science


Cosmology and Relativity

VI. Gravity as Bending of Spacetime

What is the fate of everything? Will the Universe end, or reverse its expansion, or what? Although the cause of the initial expansion has not yet been discussed (we will try to return to it, given time), it's time to consider anything which opposes expansion, and might thus slow or even stop it. Such an opposing force is gravity. All mass (and energy, since E = mc2) engages in that weak but very large-scale mutual attraction. The fate of expansion thus hinges on how much mass and energy is present in spacetime. It's now time to give your common sense another bash, this time with gravity as described by General Relativity theory. Read your text carefully, but here it is in a nutshell: gravity is a bending of spacetime. It's difficult enough to try to imagine our three dimensions of space somehow "bent" by mass (see the "rubber sheet" analogy in your text, and we will do it in class), but we must eventually also consider the bending of the time dimension. There is an old saw frequently quoted when discussing Einsteinian gravity: "mass tells spacetime how to bend; spacetime tells mass how to move."

We now have the major question still remaining, but rephrased. Instead of asking "is there enough mass to stop expansion," we could ask "what is the large-scale shape of spacetime?" If there is more than the critical amount of mass/energy present, then we can say that our Universe is closed: somehow spacetime curls back on itself, and the reversal of expansion might lead to the "Big Crunch."

Astronomers have known for some time that about 90% of the Universe's mass is not directly detectable. For example, all rotating galaxies must have enormous quantities of invisible matter to maintain the speed and positions of their stars via gravitational attraction. Is this "missing mass" enough to "close" the universe, and thus lead to collapse and the "Big Crunch"? And --- what is this cold dark matter?

The answer to the first question (is there enough mass?) seems clear. No, the Universe is not closed. The second question (what is this cold dark matter?) has no clear answer yet. Astronomers have postulated the existence of completely new and unknown forms of matter to account for this mass; matter not composed of protons, neutrons, etc ("non-baryonic matter"). Bizarre, and certainly revolutionary if correct.

VII. The Fate of the Universe

If the universe is not closed, it could be open or flat. In both cases, expansion would continue forever. An open Universe may well have the shape of a four-dimensional infinite saddle. (If you thought that a closed, finite, four-dimensional sphere was difficult to imagine, the saddle is infinitely worse.)

To cut to the chase: most astronomers, until 1998, thought that the Universe was flat, with just enough mass to produce slowing of expansion at an ever-decreasing rate. The final condition (the fate of everything)? All galaxies eventually will be too far apart for any interactions. Stars, without any sources of replenishment, will eventually all die. Entropy wins; the Universe becomes a cold and inactive place. This condition is known as the heat death of the Universe. (Remember, entropy means disorder. Heat is a highly disordered state. When astronomers say "heat death," they do not mean that the Universe "burns up," but rather that there is no chance for elaborate chemistry to occur. Randomness wins in that cold and desolate end-state.)

Until recently, the flat universe with unceasing but ever-decreasing expansion was the favored model. Then came some very controversial observations of distant type Ia supernovae. First, be sure that you understand what a supernova is. They are important in many ways, e.g., as the sources of both black holes and neutron stars. These topics are covered in pp. 136-139 of Hazen and Trefil. Be sure that you read these pages. A brief summary of supernova characteristics is included here, but is not a substitute for the reading.

Small stars like ours have a rather dull death. A few billion years in the future, Sol will form a "red giant," toasting the earth and all the inner planets, and then collapse to a "white dwarf." Large stars are more interesting. After the simple atoms are "burned" in these nuclear furnaces, the enormous mass leads to rapid collapse of the core. The intense heat leads to synthesis of all the heavy elements, right up to plutonium, and these are blown into space. (The expelled atoms are now available for forming new stars, new solar systems; our system was formed only about 4.5 billion years ago, and is therefore a second or third generation product. All organisms on earth - including you - are made of "stardust.") The core which remains will collapse to the stage where electrons and protons fuse, forming neutrons. We now have an immensely dense neutron star. If the star was very massive, collapse may continue beyond "neutronium," and a black hole results. Read your text very carefully about black holes; we will discuss these strange objects at length in class. Be sure that you understand why they are called both "black" and "holes." In class, we will add the event horizon.

Turn your thoughts back to type Ia supernovae and their importance for determining the fate of the Universe. Remember, when we talked about Cepheids, we used them as an example of a "standard candle", an object whose intrinsic luminosity is known. Most astronomers think that Type Ia supernovae can be used the same way. If so, we would then have a long yardstick that is independent of red shift, and could be used to check distances. Very recent work (starting in 1998) seems to indicate that the two yardsticks disagree. The supernovae are too dim to be at the distances calculated from red shift. Why? Many astronomers conclude that the expansion of the Universe is not decreasing, as the standard model suggests, but increasing! Why should this be so? Well, maybe it's Einstein's rejected "cosmological constant" at work. Before Hubble's work convinced everyone of the expansion of spacetime, Einstein and most others held to a static Universe. In order to maintain the static condition, Einstein proposed a constant force (the cosmological constant) that acted as anti-gravity over large distances (where matter is spread out, and gravity weak). Wow! Anti-gravity? Revolutionary stuff! When the expansion of the universe was verified, Einstein dropped the constant, and called it "his biggest blunder." Maybe he was right after all. In any case, it looks like the evidence for "heat death" is being reinforced.

If you think that the Universe is weird (anti-gravity, whole new forms of matter, etc.), just wait. It is much more odd than that.

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© copyright 2001, Michael Wirth and Sachiko Howard, New England College