Definition of cosmology: a study of the origin and development of the Universe.
What do we know about cosmology?
It makes sense to start any topic with the history of the topic, i.e. development of thinking on this topic. History of cosmology is sketched in this article of Wikipedia.
So, what does the history of cosmology teach us? First, it is that ideas of cosmology form a part of the social system where they originated. Thus, ideas of cosmology of ancient Babylonians rhyme with their art, and the ideas of ancient Indians are in tune with their art. Hence, it makes no sense to study one area of society, for example its “cosmology”, or “mathematics”, and abstract from other parts of the society. A "cosmology" is always a cosmology of a particular society; a "mathematics" is always a part of that particular society. Any one science, or art, should be studied as an integral part of the society in which it has appeared.
Modern theory of the origin of the Universe is due to the Belgian priest, Georges Lemaitre, 1894-1966. The theory, which he first proposed around 1927, was derisively called “Big Bang” and it says that the Universe originated from a single point, which exploded and this led to formation of galaxies and stellar systems. The theory got its first confirmation in 1929, when Edwin Hubble discovered that galaxies are flying apart. Then, in 1960's, a background cosmic radiation was discovered. For further interest: Carl Sagan discusses the origin of the Universe in episode 10 of "Cosmos", a 13 part series which came out in 1980.
A theory of cosmology which is not mentioned in Wikipedia presentation on “historical cosmologies” is called “fractal cosmology”. The view of Wikipedia authorities is that this is a “fringe theory” (see “template message”). The term “fractal” is due to mathematician Benois Mandelbrodt, in 1970’s. It means a figure in which a part has the same shape as the whole of the figure. In other words, the part repeats, or mimics, the behavior of the whole, which is an important observation in general. The best introduction to fractals is Arthur Clarke's video "The Colors of Infinity". The main idea of fractal cosmology is that the structure of the universe at atomic scale is similar to the structure of the universe at stellar scale. This is well documented on the site of Robert Oldershaw.
We also know that any star has a life cycle typical for that kind of star. In other words, stars are also prone to development, just like any object in the Universe. Their development follows a pattern specific to stars. For example, life cycle of two types of stars is shown in the diagram below. The idea is well presented in episode 9 of Carl Sagan’s “Cosmos”.
Prominent people in cosmology:
Edwin Hubble, 1889-1953, discovered galaxies outside our own galaxy, the Milky Way.
Georges Lemaitre, 1894-1966, proposed the modern theory of the origin of the Universe.
Carl Sagan, 1934-1996, created the miniseries “Cosmos” which popularized our modern knowledge of the Universe.
Robert Oldershaw, b.1946, one of the developers of the theory of fractal cosmology.