Cosmology, the study of the whole universe, has been the endeavor of scholars since the earliest recognition that something existed beyond the limits of Earth. Humanity's concept of the cosmos, however, has changed dramatically over time. The earliest cosmologies dealt only with what is now known as the solar system. The recognition of the existence of distant stars culminated in the Kapteyn Universe concept, which implied that the universe was a flattened sphere of stars, some 17,000 pc (55,000 ly) in diameter and 4,000 pc (13,000 ly) thick, with the Sun near the center. Only in the early twentieth century was the nature of other galaxies established. Modern cosmological investigation presently is attempting to discern the history of the universe back to its very beginning. Astronomers using the Hubble Space Telescope and the new generation of large telescopes seek to discover the most distant galaxies that are observable; because of the finite speed of light, these objects are seen not as they are today, but as they were in the distant past. Earlier times in the history of the universe must be deduced theoretically.
Distances
Fundamental to understanding the universe is the distance scale to galaxies, which relies upon astronomical understanding of the stars that make up the galaxies. If a star of known type (that is, whose properties are identifiable with a specific kind of star in the Milky Way Galaxy) can be observed in another galaxy, then that star's apparent brightness compared to its known absolute luminosity will yield the distance to that galaxy. The most accurate measurements are derived from those stars, standard candles, whose absolute luminosities are well defined. Stars whose properties are calibrated by study of the Milky Way but that may be identified in other galaxies are also termed primary distance indicators and include RR Lyraes, Cepheid variables, novae, and planetary nebulae. The Cepheids are the most important. With the Hubble Space Telescope, astronomers can detect the longest period Cepheids in galaxies out to distances of about 20 Mpc.
At greater distances, even brighter or larger objects in galaxies must be found in order to infer distances. The properties of these secondary distance indicators are calibrated in galaxies whose distances have been obtained by use of the primary indicators. These galaxies include diameters of the largest HII regions, the brightest blue OB stars, the brightest red giant stars, and the brightnesses of supernovae Type I (the explosion of white dwarf stars whose mass has exceeded the Chandrasekhar Limit). Of these, the supernovae appear to produce the most reliable results for cosmological investigation.
With astronomers obtaining distances to a large sample of galaxies by use of the secondary indicators, they can do calibration of the properties of the brightest and largest galaxies. These tertiary distance indicators include the largest of the giant elliptical galaxies in clusters of galaxies (first ranked cluster ellipticals), as well as giant Sc spiral galaxies.
Other techniques used to infer distance depend upon global properties of galaxies. In spiral galaxies, the maximum rotational velocity is correlated with the mass of the galaxy. Similarly, the absolute luminosity is related to mass. The Tully‐Fisher Relationship uses the maximum rotational velocity (which can be obtained by application of the Doppler effect) to deduce the absolute magnitude of the galaxy; comparison of the absolute magnitude with the object's apparent magnitude then yields the distance. In a similar fashion, the Faber‐Jackson Relationship yields the absolute magnitude of an elliptical galaxy based upon a spectroscopic determination of its internal random motions.
The Hubble Relationship
The basis of modern cosmology was established with the recognition in 1929 that absorption features in the spectra of more distant galaxies are shifted progressively toward the red end of the spectrum. That is, the more distant the galaxy, the greater the wavelength displacement. The most apparent explanation of this redshift is a result of a Doppler shift due to a motion away from the observer, with more distant galaxies moving away faster. Distances and line‐of‐sight velocities are simply related as
or expressed algebraically
This relationship is known as the Hubble Law and the constant of proportionality H is the Hubble Constant. (See Figure 1.)
Figure 1
The Hubble Relationship and Law (Hubble 1929).
The value of the Hubble Constant represents not only the present rate of expansion of the universe, but also a distance scale for the universe and a measure of the age of the universe. The distance to a galaxy or any other object at a cosmological distance is given by the Hubble Law expressed in the form
and requires only a spectrum for which a Doppler shift can be measured. With his understanding of the Cepheid Period‐Luminosity Relationship, Hubble in 1929 obtained a value of H = 560 km/s per Mpc. With various refinements and corrections in the data, most recent studies suggest a much smaller value of 50 km/s per Mpc < H < 100 km/s per Mpc with the most likely value about H = 60 km/s per Mpc, that is, the expansion velocities increase by 60 km/s for each increase of 1 Mpc (3,260,000 ly) in distance. In terms of distances, a change in the Hubble Constant represents a change in astronomers' understanding of the distance scale or size of the universe. A galaxy with a recession velocity of 2,000 km/s, for example, is considered to be at a distance of 20 Mpc if H = 100 km/s per Mpc, but at twice this distance, 40 Mpc, if H = 50 km/s per Mpc.
An estimate of the age of the universe may be made by calculating how long a galaxy has taken to achieve its present distance away from the Milky Way. Travel time T is simply distance D traveled divided by the travel velocity V, but as the Hubble Law shows the relationship V = H D
The travel time is independent of present distance! More distant objects are more distant because they have been moving away at a faster pace. Because the self‐gravity of the universe should be slowing its expansion, in standard cosmological theory this “age” for the universe (known as the Hubble Time T H = 1/H) is an upper limit to the time that has elapsed since every position in the universe was superimposed upon every other position, for example, since it had zero extent or infinite density. This is a problem because physicists don't like working with infinities; an infinite quantity is not physical, or real! The initial infinity at which point the cosmological clock is set (the “origin” of the universe) is the result of theorists' limited understanding of physical law. Most theoretical models for the evolution of the universe suggest a more realistic “age” 
; thus, if H = 100 km/s per Mpc, then 
billion years, but if H = 50 km/s per Mpc, 
billion years. The expansion of the universe and its finite time of existence in its present form are the major factors that a theory of cosmology must deal with. It is interesting, however, that these implied ages appear to conflict with the older ages suggested by stellar evolution theory for the oldest stars in the Milky Way Galaxy. Clearly, one or the other (or both!) of the theories is not completely correct. Only additional observation and refinements in theoretical understanding will eliminate this discrepancy.
Olbers' Paradox
If the universe were infinite and filled uniformly with stars, then in every direction we would see a star and hence every point in the sky should be bright. This is Olbers' Paradox, an apparent contradiction between the darkness of the sky and the theoretical expectation that the sky should be bright. Like every other so‐called scientific paradox, Olbers' Paradox reflects not a contradiction in the nature of reality, but an error in interpretation of natural phenomena. That the sky is dark must reflect the fact that the universe is not infinite, or the universe has a finite age (the greatest lookout distance is given by the speed of light times the age of the universe, or 
). Olbers' Paradox is thus consistent with the inferred evolution of the universe as implied by the Hubble Law.
3 K cosmic background radiation
An expansion of the universe implies a high density and temperature in an early era, before a time of about 100,000 years. Earlier than this, at any time the spectrum of black body radiation was characteristic of the high temperature, but this radiation cannot be observed today. As the temperature of the universe cooled, the spectrum of the photons also continually changed, at any instant the maximum in the spectrum of radiation (Wien's Law) simply indicating the current temperature. All spectral record of prior higher temperatures was erased. Only when the universe became transparent (radiation no longer interacting strongly with matter), did the spectrum become permanent with a peak in the gamma‐ray part of the spectrum. Today this radiation is observed as if coming from a large distance and hence subjected (the Hubble Law) to a large redshift. The shape of the spectrum is preserved, but now this cosmic background radiation is observable as black body radiation indicative of a much lower temperature, with its peak radiation in the radio or microwave region of the spectrum (hence the alternate name cosmic microwave radiation).
This cosmic relic radiation was discovered in 1965 when scientists examined interference occurring with the first satellite communication systems. The launch of the COBE ( Cosmic Background Explorer) satellite confirmed the shape of the black body spectrum at a temperature of 2.728 ±± 0.004 K. COBE showed this radiation is too uniform to be coming from myriads of sources, each too faint to be observed individually; thus, it must be coming from the early universe when all material was spread out before gravitational collapse into galaxies. Superimposed on its uniformity, there is a dipole effect in the temperature, a small, smooth change from one direction across the sky to the opposite direction, the result of the motion of the Local Group of galaxies with respect to the cosmic black body radiation. There also are tiny variations, 1 part in 100,000, that show a lack of complete density uniformity in the material that emitted the radiation. The slightly denser regions subsequently collapsed under their self‐gravitation to become galaxies, clusters of galaxies, and so on.