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In affine geometry, uniform scaling (or isotropic scaling[1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically). The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so ...
The vertical exaggeration is given by: = where VS is the vertical scale and HS is the horizontal scale, both given as representative fractions.. For example, if 1 centimetre (0.39 in) vertically represents 200 metres (660 ft) and 1 centimetre (0.39 in) horizontally represents 4,000 metres (13,000 ft), the vertical exaggeration, 20×, is given by:
e. The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components: a cosmological constant, denoted by lambda (Λ), associated with dark energy. the postulated cold dark matter, denoted by CDM. ordinary matter. It is referred to as the standard model of Big Bang cosmology [1 ...
A positive, zero or negative value of corresponds to a respectively closed, flat or open universe. The constants and are Newton's gravitational constant and the speed of light, respectively. Cosmologists often simplify this equation by defining a critical density, . For a given value of , this is defined as the density required for a flat ...
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 parameter k discussed below takes the value 0, 1, −1, or the Gaussian curvature, in these three cases respectively. It is this fact that allows us to sensibly speak of a "scale factor" a(t). Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe.
The evolution of the universe and its horizons in proper distances. The x-axis is distance, in billions of light years; the left-hand y-axis is time, in billions of years since the Big Bang; the right-hand y-axis is the scale factor. This is the same model as in the earlier figure, with dark energy and an event horizon.
t. e. The deceleration parameter in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann–Lemaître–Robertson–Walker universe. It is defined by: where is the scale factor of the universe and the dots indicate derivatives by proper time. The expansion of the universe is said to be ...