Let's now consider the entirety of everything, the universe. If you were God, how would you set up the universe? Would you make it infinite and have it ever lasting? Making an infinite universe isn't as easy as it sounds. Consider what one would see if he/she were to look into space one night. In one region of sky, you might see a nearby galaxy. In another region, you might see a more distant galaxy. But note: although the nearer galaxy would be brighter (as light decreases by 1/r^2), there would be more galaxies in the more-distant region of the sky (by r^2). So the total light from the first region of sky would be equal to that of the second region of sky. Since we are, after all, talking about an infinite universe, the upshot would be that, no matter where you would look, you would eventually see a galaxy, and the total light coming from each line-of-sight in the sky would be the same. There would be no dark regions of the sky. There would be no dark night sky. This is called Olbers' paradox.

So, if you can't make the universe infinite and ever lasting, maybe you place some boundaries around it and call it finite. But, as Newton pointed out, this has a problem, too. If you just scatter galaxies about in a finite universe (or even in a infinite, bounded universe, like the surface of a sphere), gravitational attraction would eventually pull all the matter in the universe together. After a while, you would have one big crunch. So much for an everlasting universe!

This problem vexed astronomers of the early 20th century. In fact, when Einstein proposed his general theory of relativity for the universe, he was so concerned with the fact that gravity would eventually take over and cause a Big Crunch, that he put in a Cosmological Constant in his equations. In effect, he added a pressure or anti-gravity term, which was a new force which would prevent the galaxies from falling in upon each other.

Very shortly after Einstein proposed his Cosmological Constant, Vesto Slipher discovered something extraordinary. When we measure the Doppler shift of stars in the Milky Way galaxy, we find that some stars have some random component of motion towards us, and some have a random amount of motion away from us. Given that the stars have to be moving in some direction, this seems normal. However, Slipher found that virtually all the galaxies in the universe are moving away from us. When Edwin Hubble studied the data, he found an even more interesting trend. Galaxies that were farther away from us were moving away from us faster. In other words, if v is a galaxy's velocity and d is its distance, then v = H d. In this equation, H is the Hubble Constant.

Note what this means. Since the galaxies are moving away, gravity won't necessarily be able to reverse their flow. So a "Big Crunch" is not a necessity. In addition, the further away galaxies are, the faster they are moving away from us. This solves Olbers' paradox, since galaxies at the other end of the universe are redshifted so much that their light is moved out the optical into the infrared and microwave region of the spectrum. Finally, since the galaxies are all moving away from us, then logically, at one time they were all together. Thus, there was a beginning to the universe. (When Einstein learned about the galaxy redshift measurements, he discarded his cosmological constant and called it the greatest mistake he ever made.)

It is important to realize that the observed fact that all the galaxies are moving away from us does not mean that we occupy a special place in the universe. In fact, as history has taught us, it is EXCEEDINGLY unlikely that we occupy a special location. Let us then adopt the cosmological principle, which states that our galaxy does not occupy a special position, and that what we see when we look out into the universe is roughly what someone else would see if they were looking out from a different location in the universe. Let us further suppose that the universe is homogeneous (smooth), and isotropic (which means that there are no preferred directions). Obviously, this is not exactly true, as you do not see the same thing looking south as you do looking north, but for the largest scales of the universe, it appears pretty much true. Then the observation of the Hubble law means that every galaxy must be expanding away from every other galaxy and every observer on every galaxy must see the same thing. The seeming contradiction can be explained by imagining that each galaxy of stars is a raisin in a loaf of expanding raisin bread. Or, as a two-dimensional analogy, think of the 3-dimensional space of the universe as existing on the surface of an expanding balloon, with dots drawn on the balloon to represent galaxies. As the balloon expands, the dots become farther and farther apart, with the expansion rate between dots depending on how close the dots were to each other in the first place. Either analogy results in a Hubble Law.

Note that through the Hubble law, we can estimate an upper limit to the age of the universe. For instance, if a galaxy is 10 Mpc million parsecs (Mpc) away and is expanding away from us at 1 Mpc per billion years, then obviously the expansion started 10 billion years ago. Thus, to measure the age of the universe, all you need to know is the Hubble Constant. You can measure this by measuring the velocity of a galaxy and its distance.

The velocity measurement is easy -- by taking the spectrum of a galaxy, one can measure its Doppler shift, and therefore its velocity. However, distance is more difficult. Moreover, each galaxy has its own peculiar (random) motion, so the Hubble flow motion of a nearby galaxy will impossible to see. For instance, a nearby galaxy may have a Hubble velocity of 100 km/s, but a random velocity of 200 km/s; in this case, the random component will overwhelm the Hubble flow. On the other hand, a distant galaxy may be moving away at 10,000 km/s; this number dwarfs the galaxy's peculiar velocity and makes the random motion irrelevant. Thus, to measure the Hubble Constant, you have to measure the distance to a galaxy that is reasonably far away.

The way astronomers measure the distances to galaxies is through a distance ladder. We've already seen some of the rungs. Consider: we know the distance from the earth to the Sun via radar measurements (and other methods) in the solar system. Using this distance, we can derive distances to nearby stars via parallax. From this, we learned that there is main-sequence exists, on which most stars reside. We can thus spectroscopically observe a distance star, assume it's on the main sequence, and determine its absolute magnitude. A comparison of this absolute magnitude with its apparent magnitude then gives its spectroscopic parallax. Note that spectroscopic parallax measurements depend on our parallax measurements; if the parallax measurements are incorrect, then the main sequence will be wrong, and the spectroscopic parallaxes will be wrong.

Next, we considered several globular clusters with distances determined from spectroscopic parallax. We noted that inside these globular clusters were pulsating stars called RR Lyr stars, and, using our spectroscopic parallaxes, we estimated the absolute magnitudes of these stars. We then concluded that all RR Lyrae stars have the absolute magnitude, and thus used them as a standard candle to estimate the distance to more distance globular clusters. Of course, this assumes that our spectroscopic parallaxes to the nearby globular clusters are accurate.

RR Lyr stars are only 100 times brighter than the Sun; consequently, they can only be seen in the Local Group, that small cluster of galaxies that the Milky Way is a part of. The nearest moderately large Local Group galaxy is the Large Magellanic Cloud, and in the LMC, there is another type of pulsating star, called a Cepheid variable. (There are Cepheids in the Milky Way as well, but because they are Pop I objects, observing them through the dust of our Galaxy is difficult.) In many ways, Cepheids are like RR Lyr stars; the primary differences are 1) they take days or weeks to pulsate (whereas RR Lyrae take hours), 2) they are alot brighter than RR Lyr stars (up to 100,000 times brighter than the Sun), so they can be seen to much greater distances, and 3) not all Cepheid variables are the same brightness. This latter property would be a problem, if not for the work of Henrietta Levitt at the turn of the century. Levitt discovered that the time it takes a Cepheid variable to pulsate is related to its luminosity -- the brighter the (average) luminosity of the Cepheid, the longer the period. There is a period-luminosity relation for Cepheids.

Because we know the distance to the Large Magellanic Cloud (through RR Lyr stars), we know the brightness of the Cepheid variables, and the period-luminosity relation. And, that allows us to obtain the distances to more distant galaxies. Using large groundbased telescopes (or the Hubble Space Telescope), astronomers search for pulsating Cepheid variables --- stars that get brighter and fainter over a timescale of weeks. By measuring the time it takes for the star to pulsate and the period-luminosity, astronomers can know the absolute magnitude of the star. Then, by comparing this absolute magnitude with the star's apparent magnitude, the distance to the star (and galaxy) can be measured.

Even Cepheids don't get us far enough out in the Hubble Flow to measure the Hubble Constant. To go further, astronomers use a host of techniques. One is a relation between the rotation rate of a spiral galaxy and its absolute luminosity, called the Tully-Fisher relation. The relation works this way: according to Newton's laws, the more massive a galaxy is, the more rapid the speed of rotation. So, by measuring the rotation speed of a galaxy via the Doppler shift, one can estimate the absolute mass (and luminosity) of the galaxy. Once the absolute luminosity is known, the object is then a standard candle.

Another notable technique involves the absolute brightness of supernovae. If one can measure the apparent brightness of a supernova in a galaxy with a known distance (say, from a Cepheid measurement), one can measure the supernova's absolute luminosity. Once the absolute luminosity is known, one can then look for a similar supernova at a much larger distance, and use it as a standard candle. In fact, there are about a half-dozen techniques for measuring distances to far-away galaxies. (For example, novae, planetary nebulae, and supernovae are all commonly used to estimate distance.) Most of these techniques are calibrated by Cepheids, i.e., we observe Cepheids in some galaxy, determine the galaxy's distance, and then work out how bright the nova, supernovae, planetary nebulae, or whatever is. Once we figure that out, we can then use that object as a standard candle somewhere else.

Note that our "distance ladder" is susceptible to errors. If the calibration of lower rung of the ladder is wrong, then all subsequent calibrations will also be wrong. As a result, there has been heated arguments over the value of the Hubble Constant. However, in the past few years, a value of about 72 +/- 8 km/s/Mpc has become (more-or-less) accepted. Galaxies that are 100 Mpc away are moving away at approximately 7,200 km/s. After doing the math, this translates into an upper limit to the age of the universe of 13 billion years.

Note that this is an upper limit. The universe could be younger. The calculation above assumes that the galaxies have been moving apart at the same speed since the universe began, but gravity has probably slowed the expansion a bit. How much?

There are 3 possibilities. First, there may not be enough gravity in the universe to stop the universe from expanding. Astronomers call this an open universe. General relativity predicts that space-time in an open-universe is shaped like a saddle, so that the parallel lines would diverge, and that the angles of a triangle add up to less than 180 degrees. If there is enough gravity to stop the universe from expanding (and cause a Big Crunch), then the universe is closed. It's shape would be like a ball, and parallel lines would eventually meet. And, of course, there is the borderline case, where there is just enough mass to stop the the expansion (after an infinite amount of time). This is called a flat universe. The geometry of a flat universe is normal, with 180 degrees in a triangle, and parallel lines always being the same distance from each other.

If there no matter in the universe, then the age of the universe would be 13 billion years. However, if the universe is flat, then gravity must have slowed the expansion. Much earlier in time, the universe was expanding faster. It would only be 2/3 as old as in the no-gravity case. In other words, the universe would be just under 9 billion years old.

An age of 9 billion years (for a critical universe) or even an age of 13 billion years (for an open universe) creates a problem, since the globular cluster stars are at least 13 billion years old. Is something wrong?