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The example above illustrates how certain scale factors can cause unnecessary precision loss or rounding error, highlighting the importance of choosing the right scale factor. Using the scale factor of 1 ⁄ 11 and converting to binary representations, the following values are obtained:
A scale factor is usually a decimal 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 ...
The measure problem in cosmology concerns how to compute the ratios of universes of different types within a multiverse. It typically arises in the context of eternal inflation . The problem arises because different approaches to calculating these ratios yield different results, and it is not clear which approach (if any) is correct.
then v is an eigenvector of the linear transformation A and the scale factor λ is the eigenvalue corresponding to that eigenvector. Equation ( 1 ) is the eigenvalue equation for the matrix A . Equation ( 1 ) can be stated equivalently as
The scale factor is dimensionless, with counted from the birth of the universe and set to the present age of the universe: [4] giving the current value of as () or . The evolution of the scale factor is a dynamical question, determined by the equations of general relativity , which are presented in the case of a locally isotropic, locally ...
The radius of a sphere lives in the third dimension: it is not part of the 2 dimensional surface. However, the value of this radius affects distances measure on the two dimensional surface. Similarly the cosmological scale factor is not a distance in our 3 dimensional space, but its value affects the measurement of distances. [7]: 147
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From the generic solution one easily sees that in a matter-dominated universe the scale factor goes as / matter-dominated Another important example is the case of a radiation-dominated universe, namely when w = 1 / 3 . This leads to / radiation-dominated