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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 ...
Solutions for the dependence of the scale factor with respect to time for universes dominated by each component can be found. In each we also have assumed that Ω 0,k ≈ 0, which is the same as assuming that the dominating source of energy density is approximately 1.
With the scale-factor cutoff shown by the gray dotted lines, only observers who exist before the region has expanded by the scale factor are counted, giving normal observers (blue) time to dominate the measure, while the left-hand universe hits the scale cutoff even before it exits inflation in this example. [3]
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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 ...
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables.Up to rescaling, it coincides with the chi distribution with two degrees of freedom.
In an orthogonal coordinate system the lengths of the basis vectors are known as scale factors. The scale factors for the elliptic coordinates ( μ , ν ) {\displaystyle (\mu ,\nu )} are equal to h μ = h ν = a sinh 2 μ + sin 2 ν = a cosh 2 μ − cos 2 ν . {\displaystyle h_{\mu }=h_{\nu }=a{\sqrt {\sinh ^{2}\mu +\sin ^{2 ...
This scale factor is defined as the theoretical value of the value obtained by dividing the required scale parameter by the asymptotic value of the statistic. Note that the scale factor depends on the distribution in question. For instance, in order to use the median absolute deviation (MAD) to estimate the standard deviation of the normal ...