The observable universe is a term used in cosmology. Observable universe is used to describe a ball-shaped region of space surrounding the observer. The observable universe is close enough that we might observe objects in it, i.e. there has been sufficient time for light emitted by an object to arrive at the observer. Every position has its own observable universe which may or may not overlap with the one centred around the Earth.
The word observable used in this sense has nothing to do with whether modern technology actually permits us to detect radiation from an object in this region. It simply means that it is possible for light or other radiation from the object to reach an observer on earth.
Both popular and professional research articles in cosmology often use the term "universe" when they really mean "observable universe". The reason for this is that unobservable physical phenomena are scientifically irrelevant; that is, they cannot affect any events that we can perceive. In other words, they are not in causal contact with us. They also cannot be measured, and therefore hypotheses about parts of the universe that are not observable may be ignored.
Size of the observable universe.
In the sense of a comoving distance scaled to the current conditions, the observable universe is 13.7 billion light years in radius because the universe is 13.7 billion years old. However, space itself may expand faster than the speed of light making the physical size associated with this much larger. This occurs when space expands while a photon is in transit, hence the photon must traverse a proper distance which is greater than the Hubble distance, or the traditionally defined edge of the observable universe.
There is some disagreement as to exactly how large the observable universe in proper distance is: a study of the cosmic microwave background radiation by WMAP in May 2004 states the universe is at least 78 billion light years in radius, yet the March 2005 issue of Scientific American cites a figure of 46 billion light years in every direction. The ambiguity in size is dependent on the detailed models of Hubble's law, especially the nonlinear nature of Dark energy component of the universe which is causing the expansion of the universe to accelerate.
In practice, we can only observe objects as far as the surface of last scattering 300,000 years after the Big Bang when the universe had cooled sufficiently to permit electrons to bind to atomic nuclei, which brought a halt to the Compton scattering of ambient photons, meaning that the photons can survive long enough to reach Earth. However, it may be possible to infer information from before this time through the detection of gravitational waves.
Contents of the observable universe.
The observable universe contains about 3 to 5 × 1022 stars, organized in around 80 thousand million galaxies, which themselves form clusters and superclusters.
Two back-of-envelope calculations give the number of atoms in the observable universe to be between 1.7×1077(1) and 4×1079 (2).