2004/11/03 | 膨胀系数[Expansion Parameter]
类别(Ω〖物理〗) | 评论(0) | 阅读(302) | 发表于 16:07
The scale factor R at time t for the size of the universe is related to the scale factor at time by
(1)

where a is called the expansion parameter. Then the speed of expansion is
(2)

Rearranging gives
(3)

which is just the Hubble law with Hubble constant[u/].
(4)

The ratio is related to the [u]redshift z by th equation.
(5)

A series expansion of a(t) gives


(6)

where q is known as the deceleration parameter. The nonrelativistic time evolution follows the law
[center]
(7)

so
[center]
(8)

The relativistic time evolution follows
[center]
(9)

so
[center]
(10)

The dynamical equation for the scale factor R is one of the cosmological equations. If the cosmological constant satisfies , then
[center]
(11)

where G is the gravitational constant, is the mass density, P is the pressure, and c is the speed of light. Integrating gives
[center]
(12)

[center]
(13)

But for critical density
[center]
(14)

i.e.,
[center]
(15)

so
[center]
(16)

and
[center]
(17)

Rewriting is terms of the parameter gives
[center]
(18)

so
[center]
(19)

Solving for q gives
[center]
(20)

Now, if P = 0, then
[center]
(21)
0

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