What is "scale factor"

n. a number used as a multiplier in scaling

A scale factor is a number which scales, or multiplies, some quantity. In the equation y = Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x. For example, doubling distances corresponds to a scale factor of two for distance, while cutting a cake in half results in pieces with a scale factor of one half. The basic equation for it is image over primeage. In the field of measurements, the scale factor of an instrument is sometimes referred to as sensitivity. The ratio of any two corresponding lengths in two similar geometric figures is also called a scale factor.

The relative expansion of the universe is parametrized by a dimensionless scale factor a. Also known as the cosmic scale factor or sometimes the Robertson-Walker scale factor, this is a key parameter of the Friedmann equations.

In the early stages of the big bang, most of the energy was in the form of radiation - and that radiation was the dominant influence on the expansion of the universe. Later, with cooling from the expansion the roles of mass and radiation changed and the universe entered a mass-dominated era. Recently results suggest that we have already entered an era dominated by dark energy, but examination of the roles of mass and radiation are most important for understanding the early universe.

Using the dimensionless scale factor to characterize the expansion of the universe, the effective energy densities of radiation and mass scale differently. This leads to a radiation-dominated era in the very early universe but a transition to a matter-dominated era at a later time - and then, since about 5 billion years ago a dark energy-dominated era.

A scale factor is used in computer science when a real world set of numbers needs to be represented on a different scale in order to fit a specific number format. For instance, a 16 bit unsigned integer (uint16) can only hold a value as large as 65,535. If uint16's are to be used to represent values from 0 to 131,070, then a scale factor of 1/2 would be introduced. Notice that while the scale factor extends the range, it also decreases the precision. In this example, for instance, the number 3 could not be represented because a stored 1 represents a real world 2, and a stored 2 represents a real world 4.