cosmological models

cosmological models

(world models) Possible representations of the Universe in simple terms. Models are an essential link between observation and theory and act as the basis for prediction. Complications are added only when necessary (Occam's razor). A simple model for a two-dimensional Universe is the surface of an expanding balloon, on which Hubble's law and the isotropy of the microwave background radiation may be demonstrated.

Most standard cosmological models of the Universe are mathematical and are based on the Friedmann Universe, derived by Aleksandr Friedmann in 1922 and independently by Georges Lemaître in 1927. They assume the homogeneity and isotropy of an expanding (or contracting) Universe in which the only force that need be considered is gravitation. The Big Bang theory is such a model. These models result from considerations of Einstein's field equations of general relativity. When the pressure is negligible the equations reduce to

(dR /dt )2/R 2 + kc 2/R 2 = (8π/3)G ρ

for energy conservation – this is known as the Friedmann equation – and

ρR 3 = constant

for mass conservation. R is the cosmic scale factor, ρ the mean density of matter, G the gravitational constant, and c the speed of light; k is the curvature index of space of value +1 (closed Universe), –1 (open Universe), or 0 (flat or Einstein–de Sitter Universe). See illustration.

Other models involving the cosmological constant, λ, have been proposed, such as the de Sitter model, in which no mass is present, the Lemaître model, which exhibits a coasting phase during which R is roughly constant, the steady-state theory, and those in which the gravitational constant, G, varies with time (see Brans–Dicke theory). The cosmological constant is an arbitrary constant. Although it is possible for it to have any value that does not conflict with observation, it is highly probable that it is close to zero. Cosmological models involving λ have recently come back into fashion. See also static Universe.