Background Cosmological Information
The Universe began with an event called the Big Bang. Based on the Big Bang theory the Universe began in an unimaginably hot, inconceivably dense fireball that began as a single point. This single point comprised the entire Universe. Then the space expanded and the Universe got larger. As the Universe got larger the temperature cooled. Over the next 13.7 billion years the Universe has continued to expand. In the last two billion years, surprisingly, the expansion of the Universe has begun to accelerate from the repulsive affect of Dark Energy. It appears that the Universe will continue to expand forever, getting ever colder and colder.
The Big Bang
In scientific explanations of the Big Bang we can only go so far back in time. In essence we are rolling back the film of the Universe. We are able to do this because we have formulas that enable us to determine the trajectory of the Universe and the laws of physics are valid in reverse. However, because the Universe appears to go back to a single point, our projection back into time can only go so far before the math reaches a singularity, or breaks down. Currently, our understanding of the Universe reaches its limit and we cannot explore any earlier that that time, which is known as the Planck time. Remarkably, though, we are able to go back to 10 - 4 3 second, or about one billionth of a billionth of a billionth of a billionth of a billionth of a second! That is nearly the beginning of time, but earlier than that we can not say what occurred. It is difficult to imagine, but at that time the entire Universe was shrunk down to a size smaller than a single atom and we can determine that the temperature was around 10 3 2 degrees Kelvin or an unimaginably hot, one hundred billion, billion, billion degrees (Weinberg, 146). The Universe which had been concentrated at one point underwent an "explosion" that continues to this day, 13.7 billion years later. This explosion is different than what we normally think of though, because space itself is actually what is expanding! Thus, the Universe did not "explode" out into space, but instead the space itself continues to expand so that the Universe does not have any edge or boundary.
Primordial Nucleosynthesis
Nucleosynthesis is any process that builds up heavy elements. Nuclear synthesis requires millions of degrees and only occurs in the extreme heat of the early universe, known as primordial nucleosynthesis, and in the center of stars, which is known as stellar nucleosynthesis. The early Universe was a fireball that "expanded with space" and as it did the energy also was spread out. The energy density is directly related to the temperature so as the Universe expanded the temperature dropped proportionally. As the energy dropped, matter gradually formed. Eventually, about three minutes after the Big Bang, when the Universe had cooled sufficiently to about nine hundred million degrees, protons and neutrons were able to undergo primordial nucleosynthesis (Freedman and Kaufmann, 668), which is the formation of the helium and traces of lithium and beryllium from the fusion of hydrogen and neutrons. Before this time, there was sufficient energy from collisions of particles to combine together but there was so much energy that the particles were torn apart again. This is known as the deuterium bottleneck.
Deuterium is a proton and a neutron combined together and is an essential building block for the creation of elements. When two deuterium elements combine they form Helium, which is a stable nucleus that can be used to form heavier nuclei. At the energies present before this time deuterium did not survive long enough to be fused into helium. Before this point there were 13% neutrons, which decay quickly when free, and 87% protons. Primordial nucleosynthesis fused virtually all of the neutrons into helium resulting in a composition of 26% helium and the rest was hydrogen, with just traces of lithium with three protons and beryllium with four protons (Weinberg, 110). It turns out that all of the heavier elements in our periodic table are created from the processes of supernovae, but primordial nucleosynthesis is the only way to account for the cosmic abundance of helium. Nucleosynthesis also occurs in stars. Although stellar nucleosynthesis, the nuclear process in stars, produces helium, this helium is "locked up" inside white dwarf stars. The majority of stars end up as low mass white dwarfs, so unlike supernovae which explode, the helium within these stars is permanently contained within the star.
The Last Scattering Surface
For the next 380,000 years the Universe continued to cool until it reached about three thousand degrees. At a point, known as recombination, the decreased energy of the particles allowed the Coulomb attraction of the protons to capture the electrons, forming atoms for the first time. This is simply the result of positive and negative charges attracting one another. Up until this point, the tremendous amount of radiation that was traveling through the Universe at the speed of light had been scattered by the ionic charged "soup" of the Universe. The formation of atoms virtually eliminated the free charged particles, bonding all protons and electrons into small atoms. The photons interact easily with free electrons, but very little with neutral atoms. Consequently, the photons which are scattered when they collide with charged particles, very rarely encountered these bound charged particles and the Universe is said to have become transparent to radiation.
Radiation is said to have decoupled from matter so from this point on radiation was free to move through the Universe without being scattered by electrons. This radiation from what is known as the last scattering surface has continued to radiate unimpeded for the last 13.7 billion years and remarkably can be detected today. This radiation is known as the cosmic background radiation (CMB) and permeates the Universe in every direction that we look with a constant temperature of 2.7 degrees Kelvin (which is 2.7 degrees above absolute zero). This radiation has remained the same except for the effect of cooling, resulting from the stretching of space, which has resulted in the drop in temperature. The CMB is a perfect black-body spectrum, which means that it achieved thermal equilibrium. The CMB was first detected in the early 1960's and is definitive proof of the Big Bang!
Redshift of the Cosmic Background Radiation
Once decoupled the CMB radiation was only affected by the expansion of space itself. The expansion of space affects radiation (any form of light) by stretching out the wavelength just as a rubber band is stretched by pulling it out in space. This stretching results in a longer wavelength, which is the same thing as a lower frequency. In light, blue is a shorter wavelength and red is a longer wavelength, so the radiation is said to be redshifted. This redshift which is the result of the expansion of space is an equivalent effect to the Doppler shift which is caused by the motion of a source. An example of the Doppler Effect is the change in pitch that we experience when a car is moving past us. As the car approaches the pitch increases and after it passes us the pitch drops. This is caused by the compression of the waves as the source moves toward you and the dilution of the waves as the source moves away. The effect is increased with the speed of the source and can be used to accurately calculate the velocity of the source. Astronomers have determined that the light from virtually all of the galaxies in the Universe are redshifted. This means that all of the galaxies in the Universe are moving away from us. So the Universe is expanding! And we can calculate that the rate of expansion, known as the Hubble constant, is 22 km per second per million light years. From this redshift we can determine how fast galaxies are moving away from us and how far away they are.
The Formation of Galaxies Due to Gravity
As the Universe expanded and cooled, gravity acted on matter to increase the slight variations of density that had existed in the early Universe. Over time, gravity caused matter to coalesce into more dense regions. This attraction of matter into higher density regions eventually resulted in the formation of superclusters, clusters, galaxies and stars. Stars, like the sun are the result of matter achieving high enough densities and temperature sufficient to initiate nuclear fusion (5 million degrees) and the emission of light and other radiation. One of the critical ideas in studying the Universe is known as the cosmological principle. This principle states that the Universe is both isotropic and homogenous over large distances. Isotropic means that the Universe looks the same in every direction, and homogenous means that every region is the same as every other region. So although there are variations in density on small scales, the Universe on the scale of one hundred million light years appears to be the same!
Now, how do we know anything about the Universe, such as where things are in the Universe and how big it is when we are stuck on this little rock floating through space? The key is the light and other radiation that reaches us from luminous objects. Astronomers, or sky watchers, have been analyzing the light from stars nearly since the beginning of human history. The light that reaches us from the stars is, in fact, a sort of time machine that records history. Since light travels at a constant speed (of 300,000 km/s) it takes time for light to reach us. Consequently, the light that reaches us gives us information about what the star was like when the light left the star! The light from the closest star to us, the Sun, is eight minutes old. The light from the next closest star, which is Proxima Centauri, takes three and a half years to get to us. The oldest light that we are able to see comes from galaxies, which contain about a hundred billion stars, and has been traveling for billions of years. The oldest radiation that can be detected is the CMB which has been traveling for over 13 billion years and has been stretched by the expansion of space so that its energy has gone from billions of degrees to a mere three degrees above absolute zero. We can only see back to the last scattering surface, so we can only see as far as light has been able to travel since this time, which is known as our cosmic light horizon.
Determining Distances Using Parallax and Standard Candles
So how do we determine how far away luminous sources are? This is a very challenging problem. The most straight forward way is to use geometry to calculate distance. The method used is called parallax and is the same process that we use with our two eyes for depth perception. The idea is that each eye has a different line of sight. We look at an object with each eye and our brains compare how much the object changes relative to the background to estimate how far away the object is. If the object moves a lot relative to the background, then we know that the object is very close, whereas if the object moves little relative to the background then we know that the object is far away. This observation can be done mathematically using geometry to determine distances with great precision. This is done astronomically by viewing objects from two different locations.
You may ask, how can we do this since we are stuck on this Earth, and the distance from one side of the Earth to the other is not significant enough to determine the parallax? We must make two observations from as far away from each other as possible. So, we make measurements six months apart. Thus we are half way around our orbit of the sun and therefore, we are at a distance equal to the diameter of our orbit! Another method is to measure how much of the light is getting to us from luminous objects whose light production we know. This is based on the knowledge that the apparent brightness of a star diminishes as the reciprocal of the square of the distance from that star. So if we know how bright a star actually is and we measure how bright it appears to us on Earth, we can calculate the distance to that star. So the million dollar question is How do we know what the intrinsic brightness of any luminous object is? This is a very challenging endeavor, but there are luminous objects that emit a calculable amount of light and are, therefore, known as standard candles.
The two main types of standard candles that are particularly useful because they are incredibly bright objects and can be seen from great distances are Cepheid variable stars and type1A supernovae. Cepheids are pulsating stars that produce periodic light curves, whose intrinsic luminosity is directly related to its period, and can be calculated (Freedman and Kaufmann, 480). The second type of standard candle, which is magnitudes brighter than cepheids, is the type 1A supernova. A supernova is an exploding star that can rival the luminosity of an entire galaxy of a hundred billion stars for a short period of time. Type 1A supernovae are singularly useful because in addition to their incredibly high luminosity, the luminosity is also standard because this type of supernova produces the same amount of light. A Type IA supernova can be identified by its light curve. The reason for this is that type 1A supernovae are binary stars in which a white dwarf draws matter from its companion star until it exceeds an exact mass, known as the Chandrasekhar limit, which is 1.4 Solar masses. At this point the white dwarf star can no longer produce enough pressure to resist its gravitational attraction and the star goes "supernova" and explodes. The mass is the critical value associated with the brightness of the star, so the luminosity of these type 1A supernovae also are constant. The distance to these stars can then be calibrated using the information from cepheids and nearby type 1A supernova and the use of redshift to determine the distance to supernovae billions of light years away!
Two major challenges in using standard candles is to calculate their luminosity by differentiating them from other types and also increasing the reliability of distances to nearby objects (Kirshner, 35). The light, or radiation, reaching us can be analyzed using spectroscopy, which allows us to decipher information about the source. Spectral emission and absorption lines, which are a type of celestial light fingerprint of stars, tell us the chemical composition of the source and help us distinguish the properties of individual stars. Analysis of the spectral lines and how much they are displaced, or shifted in frequency, is the method used to measure the cosmic redshift.
Dark Matter
The existence of Dark Matter was postulated to account for the "missing" matter of the Universe and has only been verified in the last decade. The amount of visible matter in the Universe, predominantly in the form of galaxies, is only about one sixth of the amount that we expect from our calculations of the amount of gravitational forces (caused by mass) in the Universe.
There are two main sources of the evidence that there has to be more matter for which we cannot account. The first
source of evidence is based on Kepler's Third Law that the velocities of object revolving around a center of mass
decreases as you move away from the center, by the formula: 
. So, when
you get beyond the galaxy where all of the visible mass is, the velocity should fall off as 
. However,
this does not happen. Instead the velocities continue relatively constant, and this can only be accounted for if
there is mass beyond the galaxy that we do not see! The second source of evidence that there must be Dark Matter
involves the velocity of galaxies within clusters of galaxies. Galaxies in clusters have a velocity dispersion that
can be measured. Based on the mass and distances between the galaxies, it is possible to determine the escape
velocity, which is the velocity at which the galaxy would break its bounds to the cluster and go flying off into
space. You have all experienced this if you have been on a merry-go-round at a playground and go so fast that you
cannot hold on, and go flying off. We have, in fact detected that galaxies are going much too fast, well beyond
their escape velocity for the visible mass, and this can only be accounted for if the mass in the clusters is much
greater than the visible matter in all the galaxies. These two sources of evidence have led to the calculation that
85% of the mass of the Universe is Dark Matter!
So what is Dark Matter? There are currently two proposed candidates for Dark Matter, amusingly named, MACHOS, which are familiar objects, such as dead stars, that produce no radiation, and WIMPS, which are particles that only respond to the forces of gravity and the weak force, and include neutrinos and theoretical particles. MACHOS are able to account for less than twenty percent of the required mass within the Milky Way. Therefore, it has been determined that Dark Matter is non-luminous matter that, unlike all of the matter we are familiar with, is not made of baryons (protons and neutrons) and is detectable by its gravitational effect. Although neutrinos seemed a promising candidate because they have been shown to have a rest mass and are pervasive through the Universe, from current calculations they can account for less than a half of a percent of the cosmic density (Adams, et al, 345-351). There is much that we still do not know about Dark Matter, but the search is on to learn more.
Dark Energy
As much as we do not know about Dark Matter, we know even less about Dark Energy. What we do know is that Dark Energy comprises most of the Universe, about 73%, and it provides a repulsive force that can account for the acceleration of the expansion of the Universe! Dark Energy is a source of negative pressure that overcomes the effect of gravity and results in the acceleration of the expansion of the Universe. It fills the entire Universe like a fluid. Currently, there are three proposed explanations for Dark Energy. For the first two, Dark Energy remains constant as the Universe expands. The first is that Dark Energy is the cosmological constant proposed by Einstein that is a constant, like the gravitational constant, that defies explanation.
The second possibility, based on the Heisenberg uncertainty principle of quantum mechanics, is that there is a vacuum energy. Vacuum energy is negative pressure that is the consequence of the continual creation of virtual particles in "empty space" and is supported by the phenomenon known as the Casimir effect. The third possibility is quintessence which is a very exotic form of matter that is equivalent to an energy density that fills the Universe. Unlike vacuum energy, quintessence is variable (Adams, et al, 352-355). These are the best theories that physicists are currently able to imagine that agree with the limited evidence that we have concerning the nature of Dark Energy. This is the frontier of exploration in physics and presents an unlimited opportunity for discovery. Understanding Dark Energy is the essential key to determining the fate of our Universe!
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