Cosmology is the study of the Universe as whole and its components. Modern cosmology grew from early ideas before recorded history of "What's going on around me?" into "How does the Universe work?". Many of the earliest recorded observations were about cosmology, and pursuit of understanding has continued for over 5000 years. Cosmology has exploded in the last 10 years with radically new information about the structure, origin and evolution of the Universe, bascially the search for the understanding of not only what makes up the Universe (the objects within it) but also its overall architecture.

Very early cosmology, from Neolithic times of 20,000 to 100,000 years ago, was extremely local. The Universe was what you immediately interacted with. Things outside your daily experience appeared supernatural, and so we call this time the age of Magical Cosmology.

Both Plato and Pythagoras influenced the first logically consistent cosmological worldview, developed by the Greeks in the 4th century B.C. This early cosmology was an extrapolation of the Greek theory of matter proposed by Empedocles. This theory states that all matter in the Universe is composed of some combination of four elements: Earth, Water, Fire, Air. These four elements arise from the working of the two properties of hotness (and its contrary coldness) and dryness (and its contrary wetness) upon an original unqualified or primitive matter. The possible combinations of these two properties of primitive matter give rise to the four elements or elemental forms.

In a seemingly unrelated discovery, Euclid, a Greek mathematician, proved that there are only five solid shapes that can be made from simple polygons (the triangle, square and hexagon). Plato, strongly influenced by this pure mathematical discovery, revised the four element theory with the proposition that there were five elements to the Universe (earth, water, air, fire and quintessence) in correspondence with the five regular solids.

The distinction between matter and form became a medieval Christian preoccupation, with the sinfulness of the material world opposed to the holiness of the heavenly realm. The medieval Christian cosmology placed the heavens in a realm of perfection, derived from Plato's Theory of Forms

Can science explain everything in the physical Universe? It is a crucial assumption that the Universe is both rational and intelligible. This is often expressed as the principle of sufficient reason, which states that everything in the Universe is as it is for some reason.

Causes always precede effects, therefore it is natural to explain the current state of the Universe by appealing to eariler cosmic epochs. Does the chain of cause and effect ever end? Did `something' start the physical Universe and is this `something', the origin of the Universe, within the scope of scientific inquiry?

Also note that its easy to imagine a chaotic Universe appearing spontaneously out of nothingness, but how do we understand the present highly complex state of the Universe just popping into existence ready-made? In other words, not only do we need a Universe that is self-creating, it also must be self-organizing. Self-organization may be a more deeply mystery then the actual creation event.

__Creation Event__:

The debate about the origin of the Universe presupposes that there was an origin. Instead of a beginning, the Universe may be experiencing an endless number of cycles. Ancient Chinese believed that all events formed a periodic pattern driven by two basic forces, Yin and Yang.

Judeo-Christian tradition was unique in its belief that God created the Universe at some specfic moment in the past, and that events form an unfolding unidirectional sequence. Key to this philosophy is that the Creator is entirely separate from and independent of His creation. God brings order to a primordal chaos.

A Creation event implies that everything came from nothing (creation ex nihilo) since if there were something before Creation, than an earlier Creation is needed to explain that something. God existed before Creation, and be definition is not limited to work with pre-existing matter or pre-existing physical laws either. In fact, the most obvious distinction between the Creator and the created Universe is that the Creator is eternal and the created Universe had a beginning.

__Olber's Paradox__:

The oldest cosmological paradox concerns the fact that the night sky should not appear dark in a very large (or infinite), ageless Universe. It should glow with the brightness of a stellar surface.

Note that the paradox cannot be resolved by assuming that parts of the Universe are filled with absorbing dust or dark matter, because eventually that material would heat up and emit its own light.

The resolution of Olber's paradox is found in the combined observation that 1) the speed of light is finite (although a very high velocity) and 2) the Universe has a finite age, i.e. we only see the light from parts of the Universe less than 15 billion light years away.

__Galaxies__:

With the development of large telescopes in the 19th century, astronomers were able to discover that their existed other objects in the Universe besides stars and planets. Extended regions of faint light could be found in various locations in the sky and were called nebula.

The discovery of `nebula', fuzzy objects in the sky that were not planets, comets or stars, is attributed to Charles Messier in the late 1700's. His collection of 103 objects is the first galaxy catalog. Herschel (1792-1871) used a large reflecting telescope to produce the first General Catalog of galaxies.

Before photographic plates, galaxies were drawn by hand by the astronomer.

By the 20th century it was found that several of the spiral nebula had variable stars in them, stars that change in brightness acoording to their total luminosity. Their apparent luminosity was such that spiral nebula must be very far away and were comprable in size to our own Galaxy, the Milky Way. Suddenly, the Universe was much larger than previously thought, our own Galaxy simply one amoung many other galaxies.

A galaxy is a collect of stars,
gas and dust bound together by their common gravitational pull. Galaxies
range from 10,000 to 200,000 light-years in size and between
10^{9} and 10^{14} solar luminosities in brightness.

Galaxies have certain features in common. Gravity holds the billions of stars together, and the densest region is in the center, called a core or bulge. Some galaxies have spiral or pinwheel arms. All galaxies have a faint outer region or envelope and a mysterious dark matter halo.

Almost all current systems of galaxy classification are outgrowths of the initial scheme proposed by American astronomer Edwin Hubble in 1926. In Hubble's scheme, which is based on the optical appearance of galaxy images on photographic plates, galaxies are divided into three general classes: ellipticals, spirals, and irregulars.

__ Hubble's law __:

In the 1930's, Edwin Hubble discoveried that all galaxies have a positive redshift. In other words, all galaxies were receding from the Milky Way. By the Copernican principle (we are not at a special place in the Universe), we deduce that all galaxies are receding from each other, or we live in a dynamic, expanding Universe.

The expansion of the Universe is described by a very simple equation called Hubble's law; the velocity of the recession of a galaxy is equal to a constant times its distance (v=Hd). Where the constant is called Hubble's constant and relates distance to velocity in units of light-years.

__ Hot Big Bang __:

The discovery of an expanding Universe implies the obvious, that the Universe must have had an initial starting point, an alpha point or Creation. In other words, there existed a point in the past when the radius of the Universe was zero. Since all the matter in the Universe must have been condensed in a small region, along with all its energy, this moment of Creation is referred to as the Big Bang.

A common question that is asked when considering a Creation point in time is ``What is before the Big Bang?''. This type is question is meaningless or without context since time was created with the Big Bang. It is similar to asking ``What is north of the North Pole?''. The question itself can not be phrased in a meaningful way.

The Big Bang theory has been supported by numerous observations and, regardless of the details in our final theories of the Universe, remains the core element to our understanding of the past. Note that an alpha point automatically implies two things: 1) the Universe has a finite age (about 15 billion years) and 2) the Universe has a finite size (its expanding at a finite speed in a finite time).

__Geometry of the Universe__:

Can the Universe be finite in size? If so, what is ``outside'' the Universe? The answer to both these questions involves a discussion of the intrinsic geometry of the Universe.

There are basically three possible shapes to the Universe; a flat Universe (Euclidean or zero curvature), a spherical or closed Universe (positive curvature) or a hyperbolic or open Universe (negative curvature). Note that this curvature is similar to spacetime curvature due to stellar masses except that the entire mass of the Universe determines the curvature. So a high mass Universe has positive curvature, a low mass Universe has negative curvature.

Note that these pictures are 3D resprentations of a 4D space, much like a hypercube. All three geometries are classes of what is called Riemannian geometry, based on three possible states for parallel lines

or one can think of triangles where for a flat Universe the angles of a triangle sum to 180 degrees, in a closed Universe the sum must be greater than 180, in an open Universe the sum must be less than 180.

Standard cosmological observations do not say anything about how those volumes fit together to give the universe its overall shape--its topology. The three plausible cosmic geometries are consistent with many different topologies. For example, relativity would describe both a torus (a doughnutlike shape) and a plane with the same equations, even though the torus is finite and the plane is infinite. Determining the topology requires some physical understanding beyond relativity.

Like a hall of mirrors, the apparently endless universe might be deluding us. The cosmos could, in fact, be finite. The illusion of infinity would come about as light wrapped all the way around space, perhaps more than once--creating multiple images of each galaxy. A mirror box evokes a finite cosmos that looks endless. The box contains only three balls, yet the mirrors that line its walls produce an infinite number of images. Of course, in the real universe there is no boundary from which light can reflect. Instead a multiplicity of images could arise as light rays wrap around the universe over and over again. From the pattern of repeated images, one could deduce the universe's true size and shape.

Topology shows that a flat piece of spacetime can be folded into a torus when the edges touch. In a similar manner, a flat strip of paper can be twisted to form a Moebius Strip.

The 3D version of a moebius strip is a Klein Bottle, where spacetime is distorted so there is no inside or outside, only one surface.

The usual assumption is that the universe is, like a plane, "simply connected," which means there is only one direct path for light to travel from a source to an observer. A simply connected Euclidean or hyperbolic universe would indeed be infinite. But the universe might instead be "multiply connected," like a torus, in which case there are many different such paths. An observer would see multiple images of each galaxy and could easily misinterpret them as distinct galaxies in an endless space, much as a visitor to a mirrored room has the illusion of seeing a huge crowd.

Its important to remember that the above images are 2D shadows of 4D space, it is impossible to draw the geometry of the Universe on a piece of paper (although we can come close with a hypercube), it can only be described by mathematics. All possible Universes are finite since there is only a finite age and, therefore, a limiting horizon. The geometry may be flat or open, and therefore infinite in possible size (it continues to grow forever), but the amount of mass and time in our Universe is finite.

__ Density of the Universe__:

The description of the various geometries of the Universe (open, closed, flat) also relate to their futures. There are two possible futures for our Universe, continual expansion (open and flat), turn-around and collapse (closed). Note that flat is the specific case of expansion to zero velocity.

The key factor that determines which history is correct is the amount of mass/gravity for the Universe as a whole. If there is sufficient mass, then the expansion of the Universe will be slowed to the point of stopping, then retraction to collapse. If there is not a sufficient amount of mass, then the Universe will expand forever without stopping. The flat Universe is one where there is exactly the balance of mass to slow the expansion to zero, but not for collapse.

The parameter that is used to measure the mass of the Universe is the critical density, Omega. Omega is usually expressed as the ratio of the mean density observed to that of the density in a flat Universe.

Given all the range of values for the mean density of the Universe, it is strangely close to the density of a flat Universe. And our theories of the early Universe (see inflation) strongly suggest the value of Omega should be exactly equal to one. If so our measurements of the density by galaxy counts or dynamics are grossly in error and remains one of the key problems for modern astrophysics.

__ Cosmological Constants__:

The size, age and fate of the Universe are determined by two constants:

The measurement of these constants consumes major amounts of telescope time over all wavelengths. Both constants remain uncertain to about 30%; however, within this decade we can expect to measure highly accurate values for both due to the Hubble Space Telescope and the Keck twins.