Cosmology

The COSMOLOGICAL PRINCIPLE - The first pillar of Big Bang Cosmology

Three Basic Assumptions in Cosmology:

Homogeneity - the assumption that matter is uniformly spread throughout space - not on a small scale, but on the largest of scales.

Isotropy - the assumption that the universe looks the same in every direction - not on a small scale, but on the largest of scales.

Universality - the assumption that the physical laws we know on Earth apply everywhere.

Two Fundamental Observations of Cosmology

The first is the COSMOLOGICAL PRINCIPLE - any observer in any galaxy sees the same general features of the universe - not on a small scale, but on the largest of scales. Copernicus stated that the Earth is not a special place; it is just one of a number of planets orbiting the sun. So too, the cosmological principle states that there is no special place in the universe. Looking beyond any local irregularities, the universe will look the same to any observer from any location within it. To learn about what the Universe is made of and to understand what the picture you see below means, go to Large Scale Structure of the Universe.

The result of this thinking leads to two important conclusions:
1) The universe has no edge - if you were to get to the place where the Universe is expanding, you would find yourself at the beginning of the Universe.
2) The universe has no center - if a center exists, we could not find it because everything looks the same from anywhere you are.

From Michael Seeds "Foundations of Astronomy" Edition 7, pages 383 & 386
Why do we say that the universe can't have an edge or center?
The quick answer is than an edge or a center would violate the cosmological principle, which says that every place in the universe is similar in its general properties to every other place. Then a place at the edge of center would be different, so there can be no edge and no center. Of course, this isn't critical thinking; it is only an appeal to the arbitrary authority of the cosmological principle. What is the real reason we conclude that there can be no edge and no center?
Imagine that the universe has an edge and you went there. What would you see? Of course, you might imagine an edge to the distribution of matter with empty space beyond, but that would not be a real edge. Imagine an edge beyond which there is no space. Could you stick your head beyond the edge and look around? Thinking about an edge to the universe leads us to logical problems we cannot resolve. From thisw, we conclude that an edge is impossible. Of course, if there is no edge, then there is no center because we define the centers of things by reference to their edges.
We believe the universe has no edge and no center for good logical reasons, not because of some arbitrary rule. But then why do we believe the cosmological principle is correct? What evidence or assumptions support it?

The second fundamental observation of cosmology is that THE SPECTRA OF GALAXIES CONTAIN RED SHIFTS THAT ARE PROPORTIONAL TO THEIR DISTANCES. This discovery (announced by Edwin Hubble in 1929) leads to the conclusion that the universe is expanding.
Exapnding you say! How is that possible or measureable?

Four Key Points of Cosmology

Here are four key points to be made regarding the universe. First, we see that the red shifts of the distant galaxies are very large. Second, we notice that the red shifts of these galaxies are NOT Doppler shifts. The galaxies are not moving through space. Space itself is expanding and carrying the galaxies away from each other. The third point is extremely important; the universe cannot have a center or an edge. Finally, we can actually take measurements of the universe in three-dimensions to determine the curvature of a four-dimensonal universe of space-time.

This is all so weird to comprehend, but we will try to do so here. The universe appears to be expanding, but it is not as if the edge were growing outward into previously unoccupied space. The universe already contains all of the volume that exists, but as it expands, there is a change in the very nature of space-time that causes the volume to increase.

According to the evidence gleaned from numerous scientific studies, the universe is expanding. We have looked at the basic assumptions of cosmology, as well as key points in the behavior of the universe. If the universe is expanding, then we should be able to better understand what it was doing in the past and perhaps even at the very beginning.

GENERAL RELATIVITY - The second pillar of Big Bang Cosmology

By assuming that the matter in the universe is distributed uniformly on the largest scales, one can use General Relativity to compute the corresponding gravitational effects of that matter. Since gravity is a property of space-time in General Relativity, this is equivalent to computing the dynamics of space-time itself. The story unfolds as follows:

Given the assumption that the matter in the universe is homogeneous and isotropic (The Cosmological Principle) it can be shown that the corresponding distortion of space-time (due to the gravitational effects of this matter) can only have one of three forms, as shown schematically in the picture below. It can be "positively" curved like the surface of a ball and finite in extent; it can be "negatively" curved like a saddle and infinite in extent; or it can be "flat" and infinite in extent - our "ordinary" conception of space. A key limitation of the picture shown here is that we can only portray the curvature of a 2-dimensional plane of an actual 3-dimensional space! Note that in a closed universe you could start a journey off in one direction and, if allowed enough time, ultimately return to your starting point; in an infinite universe, you would never return.

Before we discuss which of these three pictures describe our universe (if any) we must make a few disclaimers:

Because the universe has a finite age (~13.7 billion years) we can only see a finite distance out into space: ~13.7 billion light years. This is our so-called horizon. The Big Bang Model does not attempt to describe that region of space significantly beyond our horizon - space-time could well be quite different out there.
It is possible that the universe has a more complicated global topology than that which is portrayed here, while still having the same local curvature. For example it could have the shape or a torus (doughnut). There may be some ways to test this idea, but most of the following discussion is unaffected.
Matter plays a central role in cosmology. It turns out that the average density of matter uniquely determines the geometry of the universe (up to the limitations noted above). If the density of matter is less than the so-called critical density, the universe is open and infinite. If the density is greater than the critical density the universe is closed and finite. If the density just equals the critical density, the universe is flat, but still presumably infinite. The value of the critical density is very small: it corresponds to roughly 6 hydrogen atoms per cubic meter, an astonishingly good vacuum by terrestrial standards! One of the key scientific questions in cosmology today is: what is the average density of matter in our universe? While the answer is not yet known for certain, it appears to be tantalizingly close to the critical density.

Given a law of gravity and an assumption about how the matter is distributed, the next step is to work out the dynamics of the universe - how space and the matter in it evolves with time. The details depend on some further information about the matter in the universe, namely its density (mass per unit volume) and its pressure (force it exerts per unit area), but the generic picture that emerges is that the universe started from a very small volume, an event later dubbed the Big Bang, with an initial expansion rate. For the most part this rate of expansion has been slowing down (decelerating) ever since due to the gravitational pull of the matter on itself. A key question for the fate of the universe is whether or not the pull of gravity is strong enough to ultimately reverse the expansion and cause the universe to collapse back on itself. In fact, recent observations have raised the possibility that the expansion of the universe might in fact be speeding up (accelerating), raising the possibility that the evolution of the universe is now dominated by a bizarre form of matter which has a negative pressure.

Expansion of the Universe


Possible scenarios for the expansion (and possibly contraction) of the universe: the bottom orange curve represents a closed, high density universe which expands for several billion years, then ultimately turns around and collapses under its own weight. The green curve represents a flat, critical density universe in which the expansion rate continually slows down (the curves becomes ever more horizontal). The blue curve shows an open, low density universe whose expansion is also slowing down, but not as much as the previous two because the pull of gravity is not as strong. The top (red) curve shows a universe in which a large fraction of the matter is in a form dubbed "dark energy" which is causing the expansion of the universe to speed up (accelerate). There is growing evidence that our universe is following the red curve.

The picture above shows a number of possible scenarios for the relative size of the universe vs. time: the bottom (green) curve represents a flat, critical density universe in which the expansion rate is continually slowing down (the curves becomes ever more horizontal). The middle (blue) curve shows an open, low density universe whose expansion is also slowing down, but not as much as the critical density universe because the pull of gravity is not as strong. The top (red) curve shows a universe in which a large fraction of the matter is in a form dubbed "dark energy" which is causing the expansion of the universe to speed up (accelerate). There is growing evidence that our universe is following the red curve.

Time now to go forward, or deeper into this subject to The Origin and Fate of the Universe or back to the Introduction to Cosmology. Or throw up your hands in total confusion and simply go to the Syllabus .


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