Olbers's Paradox		What's the first thing you notice when you look outside at night? That the sky is dark! And yet this is a basic cosmological observation. Sometimes a little thinking can go a long way! The fact that the night sky is dark means that the Universe can't be: unchanging, uniform (same everywhere), and infinite. If it were, then there would be a paradox, first pointed out by Kepler, I believe, although in the 19th century Olbers popularized it. If you look at all the stars at some distance R away from us, and then consider another greater distance R', you'll find that each star at R' is dimmer (by the inverse square law) but there are more of them (because the surface area of a sphere increases with the radius). In fact the inverse square law (apparent brightness is luminosity / 4 pi R2 exactly cancels the surface area of a sphere, which is 4 pi R2. So the sphere of stars at radius R is just as bright as the sphere of stars at radius R'! This means that when you add up the brightness of all stars in an infinite eternal Universe, it would come out infinite--the spheres don't get dimmer as you go further out!
The Cosmic Microwave Background		Take a TV and turn it to a channel where nothing is being broadcast--use an antenna TV (not cable). You'll see "snow"--1% of this noise is radiation from the Big Bang! Back in 1965, a couple of scientists working for Bell Labs, the research part of AT&T at the time, were trying to figure out why their radio detector had so much noise in it. They tried everything they could to reduce the noise--they even carefully cleaned out the detector of pidgeon droppings! But still there was this annoying noise! Eventually they figured out it was the echo of the Big Bang! Below you can see images of the microwave radiation over the entire sky--the top image taken with the original pidgeon-droppings-cleaned radio receiver of 1965. Below that is the image of the sky formed by a satellite called COBE (Cosmic Background Explorer) from 1992. COBE measured the microwave radiation across the sky with a resolution of 7 angular degrees (it could make out details 7 degrees across, but no smaller). It showed the radiation from the Big Bang was nearly a perfect blackbody spectrum, corresponding to a temperature of 2.73 K. That's 2.73 degrees above absolute zero! COBE also found slight differences in temperature from the radiation from different corners of the sky. First of all, the wavelengths were slightly shorter in one direction, and longer in the exact opposite direction. That can be explained as a Doppler shift resulting from our total motion relative to the Big Bang. The Milky Way is moving at something like 600 km/s from the gravitational pull of other galaxies. More important than that difference in the radiation--which has been subtracted from the images below--is that there are small fluctuations over the sky. Parts of the sky give off radiation from the Big Bang that are about 10-5 degrees different! (That's 10 millionths of a degree!) The Big Bang couldn't have been perfectly symmetric in all directions because galaxies formed somehow out of lumps that were extra dense. You'll notice that there's a line through the center in these images--that's our own Milky Way galaxy--we can't see the Big Bang through our galaxy. Finally, the bottom panel shows a simulation of what MAP, the Microwave Anisotropy Probe currently taking measurements might see ("anisotropy"=not-equal-ness; this will measure how the radiation is slightly unequal in different directions.) MAP will measure differences in temperature in the Big Bang radiation with an accurancy of about 1/7 of an angular degree in the sky, as opposed to 7 degrees that COBE could see. When we look at this radiation, we're only seeing to something like 500,000 years after the Big Bang. We can't see back any further because too soon after the Big Bang, light couldn't flow freely. It's like we're looking back to the surface of the Sun, and can't see inside. Light given off by the Big Bang bounced around inside, just as it does inside the Sun (remember your Sun lab?) Then about 500,000 years later, the Universe cooled off enough for electrons and nuclei to form atoms--then there were fewer free electrons to scatter the radiation.
Core evidence for the Big Bang		What is the main evidence that our Universe started in a fiery expansion 14 billion years ago (or so)? The Hubble Law The Cosmic Microwave background radiation The fact that even in the oldest stars, even in gas we see from quasars at the edge of the Universe as we look back in time--there is Helium. There are also other elements: a rare isotope of Helium and Lithium. If the Universe started with just hydrogen, only stars could make Helium. But it would take time for that Helium to be made! Our explanation is that these elements were formed in fusion--not inside stars--but in the heat of the Big Bang itself! Actually if we go far back enough in time, the Big Bang was so hot that the energy of the explosion broke apart even light nuclei. Just like the energy of a supernova explosion can fuse together heavy elements, at the cost of energy--neither goes on naturally in a star but can happen in an explosion. So the Big Bang didn't create much Carbon, etc., not because it wasn't hot enough, but because Helium had to be created first in fusion of Hydrogen. By then it was getting colder in the Universe--not hot enough to drive the fusion of Helium into Carbon. Here's a plot, from Scientific American, of how the abundances of elements in the early Universe, uncontaminated by fusion in stars, depends on how much matter there was in the Big Bang: The gray area shows what's compatible with the observed amounts of these elements. The x-axis shows the density of normal matter in the Universe divided by the "critical density". The critical density is 10-29 grams per cubic centimeter. If the Universe has more than this much matter in it on average, then the matter has enough gravity to eventually slow down the expansion from the Big Bang and cause a Big Crunch (or gnaB giB). The lessons here are that (1) the Big Bang theory can make sense of how much of these elements there are and (2) the amount of normal matter in the Universe is only 1-10% of the amount needed to stop the Big Bang through gravity. There could be more matter though, in the form of WIMPs--particles that weakly interact with normal matter--if they were present during the Big Bang, they wouldn't have changed fusion rates.
Our Density is Our Destiny		The graph above summarizes our current knowledge of the fate of the Universe! There are two basic numbers that go into this graph. OmegaM and Omegalambda define the two axes. OmegaM is the density of matter in our Universe divided by the "critical density." The vertical axis plots how much energy there is in our Universe in the form of a "cosmological constant" (this is also called "dark energy" nowadays.) Recent studies of white dwarf supernovas as standard candles have measured the expansion of the Universe and found that the expansion is accelerating. The cosmological constant, a factor that Einstein put into his equations to keep the Universe from expanding, before Hubble showed that it was in fact expanding, could be responsible for the acceleration of the Universe. Essentially, if this constant were not zero, the law of gravity would say that empty space creates a kind of "anti-gravity" that accelerates the expansion of the Universe. Our best measurements of OmegaM and Omegalambda place it within the plaid region in the plot above. This region is the intersection of what we know from white dwarf supernova measurements of the Universe's expansion (the elliptical curves show the probability that the Universe's numbers are within those curves) and from the cosmic microwave background (the dark blue strip). There are both solid and dashed elliptical curves because there were two independent teams who measured supernovas to learn about cosmology. Both teams found similar results. The end result (the plaid region) suggests that our Universe has 70% of the critical density in the form of the cosmological constant (dark energy, or the energy of empty space). Another 30% of the critical density is in the form of matter, although most of it is probably extraordinary dark matter (WIMPs). All together, the amount of matter and "dark energy" cosmological constant in the Universe add up to the critical density--and yet the Universe shouldn't be pulled back together, because the dark energy force is pushing out. But having the total density of matter and energy add up to the critical density does say something important about the Universe: that it's flat. Einstein showed space could be curved, that we might have to use non-Euclidean geometry (where the angles of a triangle don't add up to 180 degrees--like on the surface of a sphere). Near a massive object, space would be especially curved. But what about the overall curvature of space, on average? That would depend on how much matter with gravity there is to curve it. Space could be negatively curved or open like a saddle, it could be positively curved or closed like a sphere, or it could be just on the boundary, or flat. It's extraordinarily close to that boundary (the equation Omegamatter+Omegalambda=1). In the traditional Big Bang theory, there's no explanation for why our Universe appears so close to flat.
Inflation		The Big Bang is pretty well established. However, there are details that we still are very ignorant about! For example, there's a version of the Big Bang that says that the Universe expanded a huge amount in an incredibly short time soon after time began. This theory, called inflation, will be tested a lot in the next few years. Inflation was designed to solve two problems with the Big Bang. First, the flatness problem described above, and second the horizon problem. The horizon problem is that the different corners of the sky have microwave radiation from 500,000 years after the Big Bang that differ by only 10-5 K. And yet, as shown in the following illustration from your textbook, there's no way that those two regions of the Universe could ever have communicated with each other as long as the communication is limited by the speed of light: If there was an early period of inflation, then those two regions were once in close enough contact so that if one were hotter than the other, it could have cooled off and warmed the other up, equalizing them: