2004/11/07 | Friedmann方程[Friedmann's Equation]
类别(Ω〖物理〗) | 评论(0) | 阅读(97) | 发表于 13:19
Let the pressure term go to P=0 in the second of the cosmological equations
(1)

where R is the size scale of the universe, is the curvature of the universe, c is the speed of light, is the cosmological constant,and G is the gravitational constant. Integrating gives
(2)

where C is a constant of integration. Now note that first of the cosmological equations
(3)

where is the density of the universe gives the constant C as
(4)

Now, plugging (4) into (2) gives
(5)

For a flat universe,the curvature ,so
(6)

If , making the substitution
(7)

(8)

gives
(9)

If making the substitution
(10)

(11)

gives
(12)

If (i.e, the Einstein-de Sitter cosmological model), then
(13)

Summarizing, for
(14)

For a universe with and
(15)

For a universe with and
(16)

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